Cornell University Computational Optimization Open Textbook - Optimization Wiki - User contributions [en]

Quadratic programming

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This web page is a duplicate of https://optimization.mccormick.northwestern.edu/index.php/Quadratic_programming

Author: Jack Heider (ChE 345 Spring 2015) 
Steward: Dajun Yue, Fengqi You

=Introduction=
[[File:QPPic.jpg|frame|Optimizating of a quadratic function.12]]

Quadratic programming (QP) is the problem of optimizing a quadratic objective function and is one of the simplests form of non-linear programming.1 The objective function can contain bilinear or up to second order polynomial terms,2 and the constraints are linear and can be both equalities and inequalities. QP is widely used in image and signal processing, to optimize financial portfolios, to perform the least-squares method of regression, to control scheduling in chemical plants, and in [https://optimization.mccormick.northwestern.edu/index.php?title=Sequential_quadratic_programming&action=edit&redlink=1 sequential quadratic programming], a technique for solving more complex non-linear programming problems.3,4 The problem was first explored in the early 1950s, most notably by Princeton University's [http://en.wikipedia.org/wiki/Philip_Wolfe_(mathematician) Wolfe] and [http://en.wikipedia.org/wiki/Marguerite_Frank Frank], who developed its theoretical background,1 and by [http://en.wikipedia.org/wiki/Harry_Markowitz Harry Markowitz], who applied it to portfolio optimization, a subfield of finance.

=Problem formulation=
A general quadratic programming formulation contains a quadratic objective function and linear equality and inequality constraints:2,5,6

<math>\text{min} f(x)=q^{T}x+\frac{1}{2}x^{T}Qx</math> 
<math>s.t. Ax=a</math> 
<math>Bx\le b</math> 
<math>x\ge0</math>

The objective function is arranged such that the vector <math>q</math> contains all of the (singly-differentiated) linear terms and <math>Q</math> contains all of the (twice-differentiated) quadratic terms. Put more simply, <math>Q</math> is the Hessian matrix of the objective function and <math>q</math> is its gradient. By convention, any constants contained in the objective function are left out of the general formulation.6 The one-half in front of the quadratic term is included to remove the coefficient (2) that results from taking the derivative of a second-order polynomial.

As for the constraints, the matrix equation <math>Ax=a</math> contains all of the linear equality constraints, and <math>Bx \le b</math> are the linear inequality constraints.

When there are only inequality constraints (<math>Bx\le b</math>), the Lagrangean is:6 
<math>L(x,\lambda,\mu)=q^{T}x+\frac{1}{2}x^{T}Qx+{\lambda}^T(Ax-a)+{\mu}^T(Bx-b)=0</math> 

==Global solutions==
If the objective function is convex, then any local minimum found is also the sole global minimum. To analyze the function’s convexity, one can compute its Hessian matrix and verify that all eigenvalues are positive, or, equivalently, one can verify that the matrix Q is positive definite.6 This is a sufficient condition, meaning that it is not required to be true in order for a local minimum to be the unique global minimum, but will guarantee this property holds if true.

==KKT conditions==
Solutions can be tested for optimality using Karush-Kuhn-Tucker conditions just as is done for other nonlinear problems:5 

Condition 1: sum of gradients is zero: 
<math>\triangledown L({x}^*,{\lambda}^*,{\mu}^*)=q^{T}+\frac{1}{2}x^{T}Q+{\lambda}^{*T}A+{\mu}^{*T}B</math> 

Condition 2: all constraints satisfied: 
<math>Ax^*-a=0</math> 
<math>Bx^*-b\le0</math>

Condition 3: complementary conditions: 
<math>{\mu}^TBx-b=0</math> 
<math>{x}^{T},{\lambda}^{T},{\mu}^T\ge0</math>

==Solution strategies==
Because quadratic programming problems are a simple form of nonlinear problem, they can be solved in the same manner as other non-linear programming problems.
An unconstrained quadratic programming problem is most straightforward to solve: simply set the derivative (gradient) of the objective function equal to zero and solve.7 More practical (constrained) formulations are more difficult to solve. The typical solution technique when the objective function is strictly convex and there are only equality constraints is the [https://optimization.mccormick.northwestern.edu/index.php?title=Conjugate_gradient_methods&action=edit&redlink=1 conjugate gradient method]. If there are inequality constraints (<math>Bx\le b</math>), then the [https://optimization.mccormick.northwestern.edu/index.php/Interior-point_method_for_NLP interior point] and active set methods are the preferred solution methods. When there is a range on the allowable values of <math>x</math> (in the form <math>x^L\le x\le x^U</math>, which is the case for image and signal processing applications, [https://optimization.mccormick.northwestern.edu/index.php/Trust-region_methods trust-region methods] are most frequently used.4 For all convex cases, an NLP solver in the optimization utility GAMS, such as KNITRO, MINOS, or CONOPT, can find solutions for quadratic programming problems.

=Numerical example=
[[File:ChE345 Wiki Mathematica.png|frame|Plot of the unconstrained objective function. Figure generated using Wolfram Mathematica.]]

This example demonstrates how to determine the KKT point of a specific QP problem:

<math>\text{min}</math>
<math>f(x)=3{x_1}^2+{x_2}^2+2{x_1}{x_2}+x_1+6{x_2}+2</math> 
<math>\text{s.t.}</math>
<math>2{x_1}+3{x_2} \ge 4</math> 
<math>{x_1},{x_2} \ge 0</math>

Rewrite the constraints. 
<math>g_1=-2{x_1}-3{x_2}+4\le 0</math> 
<math>g_2=-{x_1} \le 0</math> 
<math>g_3=-{x_2} \le 0</math> 

Construct the gradients. 
<math>\triangledown f= \begin{bmatrix} 6{x_1}+2{x_2}+1 \\ 2{x_1}+2{x_2}+6 \end{bmatrix}, \triangledown {g_1}= \begin{bmatrix} -2 \\ -3 \end{bmatrix}, \triangledown {g_2}= \begin{bmatrix} -1 \\ 0 \end{bmatrix}, \triangledown {g_3}= \begin{bmatrix} 0 \\ -1 \end{bmatrix} </math>

Assuming all constraints are satisfied, set the gradient equal to zero to attempt to find an optima. 
<math>6{x_1}+2{x_2}+1=0</math> 
<math>2{x_1}+2{x_2}+6=0</math> 

<math>{x_1}=\frac{5}{4}</math>,
<math>{x_2}=-\frac{17}{4}</math> 

Make constraints <math>g_1</math> and <math>g_3</math>, which are violated, active. Set both equal to zero. 
<math>{g_1} = -2{x_1}-3{x_2}+4=0</math> 
<math>{g_3} = -{x_2}=0</math> 

Solve the resulting system of equations. 
<math>\triangledown f+ {\mu_1} \triangledown {g_1}+ {\mu_3} \triangledown {g_3} =0</math> 
<math>{g_1}=0</math> 
<math>{g_3}=0</math> 

<math> \begin{bmatrix} 6{x_1}+2{x_2}+1 \\ 2{x_1}+2{x_2}+6 \end{bmatrix} +{\mu_1} \begin{bmatrix} -2 \\ -3 \end{bmatrix} +{\mu_3} \begin{bmatrix} 0 \\ -1 \end{bmatrix} </math> 
<math>-2{x_1}-3{x_2}+4=0</math> 
<math>-{x_2}=0</math> 

Formulating the system as one matrix and row reducing is one of the simplest ways to solve. Doing so yields: 
<math>{x_1}=2, {x_2}=0, {\mu_1}=6.5, {\mu_3}=-9.5</math> 

Drop constraint <math>g_3</math> because <math>{\mu_3}</math> is negative and resolve the system. Doing so yields: 
<math>{x_1}=0.5, {x_2}=1, {\mu_1}=3</math> 

Which yields an objective function value of <math>f=11.25</math> 

Verify linear dependence of the gradient: 
<math>\triangledown f+ {\mu_1} \triangledown {g_1}</math> 
<math> \begin{bmatrix} 6 \\ 9 \end{bmatrix} +3 \begin{bmatrix} -2 \\ -3 \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \end{bmatrix} \therefore </math> 

Verify the uniqueness of the solution: 
<math>{\triangledown}^2 f(x)= \begin{bmatrix} 6 & 2 \\ 2 & 1 \end{bmatrix} \rightarrow \begin{bmatrix} 6-\lambda & 2 \\ 2 & 1-\lambda \end{bmatrix} =0 \rightarrow \lambda = 0.298, 6.702</math>

Because both eigenvalues are positive, the Hessian matrix is positive determinant, and this local minimum is the global minimum of the objective function given these constraints. 

=Applications=

A few of the many quadratic programming applications are discussed in more detail and accompanied with general models below, and a list of other areas in which QP is important is presented as well.

*Quadratic knapsack problem (QKP)
In the standard knapsack problem, there are a number of items with different weights and values, and the items are selected based on which combination yields the highest overall value without exceeding the overall weight limit of the knapsack.

In the quadratic knapsack problem, the objective function is quadratic or, more specifically, bilinear, and the constraints are the same as in the typical knapsack problem.8 QKP's are used in designing email servers and to optimize the locations of "nodes" in applications such as positioning transportation hubs like airports and train stations.8 Additionally, the problem can model situations in which a limited number of people are assigned to complete specific objectives that require them to interact.9 One formulation is presented below:8 
<math>\text{max or min}</math>
<math>x^{T}Qx</math> 
<math>Ax \le a</math> 
<math>x \in {B}^{n} </math> 

The quadratic knapsack problem, although it looks very simple, is NP-hard and is thus difficult to solve. To make obtaining solutions easier, these problems are often linearized.8

*Model predictive control
Quadratic programming also has important applications in chemical engineering. Model predictive control (MPC) is a group of algorithms that help manage production in chemical plants by dictating production in each batch. While often formulated as linear programs because the resulting models are more stable, robust and easier to solve, MPC models are sometimes made with quadratic programming.11 As an example of its utility, quadratic programming was used by Di Ruscio in an MPC algorithm for a thermomechanical pulping process, which a method for making paper.11

*Least squares
Least squares regression is one of the most common types of regression, and works by minimizing the sum of the squares of the difference between data points and a proposed fit. Quadratic optimization is one method that can be used to perform a least squares regression and is more flexible than most linear methods. One formulation for a quadratic programming regression model is as follows:3

<math>\text{min}</math>
<math>e'Ie</math> 
<math>e = Y-X \beta</math>

In this model, <math>\beta</math> and <math>e</math> are the unknown regression parameters, <math>I</math> is an identity matrix, and <math>X</math> and <math>Y</math> contain data about the independent and dependent variables respectively.3

*Other applications
Quadratic programming is used in a wide range of applications not touched upon in the sample presented above. Other major areas in which QP's are relied upon include signal and image processing12 and a subfield of optimization called partial differential constrained optimization.3 QP's are also extensively used in finance, as variance, which is used to measure risk, is a function containing squares.13,14,15 More specifically, Markowitz won the 1990 Nobel Prize in Economics for his widely-used model that employs quadratic programming to optimizes the amount of risk taken on based on variances.14

Additionally, [https://optimization.mccormick.northwestern.edu/index.php?title=Sequential_quadratic_programming&action=edit&redlink=1 Sequential quadratic programming], an algorithm for solving more complicated NLP's that uses QP subproblems, is one of the most important applications.

=Conclusion=
Quadratic programming, the problem of optimizing a quadratic function, have been widely used since its development in the 1950s because it is a simple type of non-linear programming that can accurately model many real world systems, notably ones dependent on two variables. Problems formulated this way are straightforward to optimize when the objective function is convex. QP has applications in finance, various types of computer systems, statistics, chemical production, and in algorithms to solve more complex NLP's.

=References=
1. Frank, Marguerite, and Philip Wolfe. "An Algorithm for Quadratic Programming." Naval Research Logistics Quarterly 3 (1956): 95-110. Web. 4 June 2015. 
2. Floudas, Christodoulos A., and V. Visweswaran. "Quadratic Optimization." Nonconvex Optimization and Its Applications, 2 (1995): 217-69. Web. 23 May 2015. 
3. McCarl, Bruce A., Moskowitz, Herbert, and Harley Furtan. "Quadratic Programming Applications." The International Journal of Management Science, 5 (1977): 43-55. 
4. Geletu, Abele. "Quadratic programming problems." Ilmenau University of Technology. Web. 23 May 2015. 
5. Bradley, Hax, and Magnanti. Applied Mathematical Programming. Boston: Addison-Wesley, 1997. 421-40. Web. 23 May 2015. 
6. Jensen, Paul A., and Jonathan F. Bard. "Quadratic Programming." Operations Research Models and Methods. The University of Texas at Austin. Web. 23 May 2015. 
7. Binner, David. "Quadratic programming example - no constraints." Miscellaneous mathematical utilities. AKiTi. Web. 23 May 2015. 
8. Pisinger, David. "The Quadratic Knapsack Problem – A Survey." Discrete Applied Mathematics, 155 (2007): 623 – 648. Web. 23 May 2015. 
9. "Quadratic Multiple Knapsack Problem." Optimization of Complex System. Optiscom Project. 2012. Web. 6 June 2015. 
10. Gallo, G., P. L. Hammer, and B. Simeone. "Quadratic Knapsack Problems." Mathematical Programming 12 (1980): 132-149. Web. 24 May 2015. 
11. Di Ruscio, David. "Model Predictive Control and Optimization." Telemark University College. Mar. 2001. Web. 24 May 2015. 
12. Ma, W. K. "Signal Processing Optimization Techniques." The Chinese University of Hong Kong. Web. 24 May 2015. 
13. Tütüncü, Reha H. "Optimization in Finance." Tokyo Institute of Technology. Spring 2003. Web. 23 May 2015. 
14. Van Slyke, R. "Portfolio Optimization." NYU Polytechnic School of Engineering. 16 Nov. 2007. Web. 24 May 2015. 
15. "Portfolio Optimization." SAS/OR(R) 9.2 User's Guide: Mathematical Programming. SAS Institute. Web. 23 May 2015.

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Branch and cut for MINLP

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Asa273: /* History */

Author: Pear Dhiantravan (ChE 345 Spring 2015)

Stewards: Dajun Yue, Fengqi You

Branch and Cut is a method for solving Mixed Integer Non Linear Programming (MINLP) models. There are variations on the exact steps of the algorithm, but the original method developed by Ioannis Akrotirianakis, Istvan Maros, and Berc Rustem in 2000 utilizes the general organization of the Branch and Bound method with the iterative nature of the Outer Approximation.1 The addition of Gomory mixed integer cuts as an alternative to branching improves the efficiency of the overall branch and bound algorithm by reducing the number of nodes and Non-Linear Programming (NLP) problems required to solve the MINLP.

=Introduction=
The organization of general design problems into programming models allows for the defining and finding of their (global) optimal solution. MINLP models represent problems as a sets of continuous variables with binary integer variables. The continuous variables are restricted to defined constraints, and the binary variables represent whether or not a design choice is made.

===History===
[[File:B&C_minlp.JPG|500px|thumb|Branch and Bound with Gomory Cuts and the iterative nature of Outer Approximations 2]]

Mixed integer programming problems were explored most generally in the later half of the 1900s. Ignacio Grossmann published many papers on mixed integer linear programing problems and their solutions and applications in the late 1980s through the 1990s. In those decades, research was focused largely on improving the [https://optimization.mccormick.northwestern.edu/index.php/Branch_and_bound_%28BB%29 Branch and Bound] method to achieve greater time efficiency. The branch and bound method was developed by A.H. Land and A.G. Doig in 1960 to solve linear integer problems,3,1 and expanded in 1965 by R.J. Dakin to incorporate nonlinear integer problem solutions. 4,1 Branch and bound seemed to be a robust method, however the time required to solve increases exponentially as the number of variables increases.5 In the 1950s and 60s, Ralph Gomory developed a different method using cutting planes to solve integer problems. Gomory Cuts were quicker to solve but gave less reliable solutions. The exploration of incorporating Gomory cuts into the branch and bound method gained popularity when solutions showed greater efficacy upon combination of these methods. The joint algorithm is called Branch and Cut.

In the early 2000s, Akrotirianakis, Maros, and Rustem built on the findings of their predecessors to expand the application of the branch and cut method to non linear programs. More research surfaced on broader applications of this method, and with this grew the development of computational programs such as CPLEX and XPRESS-MP to run and solve these problems using given iterative solution methods.6

===Applications===
Mixed integer non linear programming models can cover a wide variety of engineering and design problems with discrete variable values.

The Branch and Cut method is well-known for its long-time use in solving the [https://optimization.mccormick.northwestern.edu/index.php/Traveling_salesman_problems Traveling Salesman Problem].6 In 1991, Padberg and Rinaldi developed a solution to large-scale symmetric traveling salesman problems using the branch and cut method.7 MINLP problems involving scheduling, network design (including facility locating), and a variety of simplified biological models can be solved using the branch and cut algorithm given integer-valued variables.6

=Formulation=
Given that <math>f(x)</math>, <math>g(x)</math>, and <math>h(x)</math> are convex and continuously differentiable, a general MINLP problem solvable by the Branch and Cut method can be formulated as follows:

<math>min Z(x,y)</math> <math>=</math> <math>C^T y</math> <math>+ f(x)</math>

<math>s.t.</math> <math>g(x) + By \leqslant 0</math>

<math> h(x) = 0</math>

<math> x \in X, y \in {0,1}</math>

=Algorithm=
The Branch and Cut algorithm closely follows that of the Outer Approximation for MINLP, but incorporates Gomory cuts in order to decrease the search space of the problem.

The algorithm presented here is the method developed by Akrotirianakis, Maros, and Rustem [1a]. Variations on this method are described below.

===Initialization: Value of the Search Tree Root===
0. Upper bound = inf, Lower bound = -inf

1. Initialize <math>y^0</math>
The Branch and Cut method begins with an initialization of the binary variables <math>(y)</math> by defining each with a finite starting value 0 or 1.
Otherwise, the initialization may be achieved by solving a relaxed NLP setting <math>0\leqslant y \leqslant 1</math>

2. Solve NLP using <math>y^0</math>
'''if''' NLP is feasible
→ solve <math>Z(x^0, y^0)</math>. This yields a new '''upper bound''' to the original problem. Move to step 3
'''else''' NLP is not feasible
→ if an initial set of values for <math>y^0</math> was chosen, choose a new <math>(y^0)</math>.
Repeat 1 and 2 until a feasible solution is obtained. Move to step 3.

The NLP should result in an initial feasible solution <math>x^0</math> and <math>y^0</math> in which <math>Z(x^0, y^0)</math> <math>\leq \infty</math>.

Otherwise, if the relaxed NLP is infeasible, then the MINLP problem is infeasible.

3. Solve MILP

Using <math>x^0</math> and <math>y^0</math> obtained from the NLP, solve the linearized objective and constraints according to the following equations:

<math>min</math> <math>a</math>

<math>s.t.</math> <math>a \leqslant UB^0 </math>

<math>f(x^0,y^0) +</math> <math>\nabla\ f(x^0,y^0)^T</math> <math>\binom{x-x^0}{y-y^0} </math> <math>\leqslant</math> <math>a</math>

<math>g(x^0,y^0) +</math> <math>\nabla\ g(x^0,y^0)^T</math> <math>\binom{x-x^0}{y-y^0} </math> <math>\leqslant</math> <math>0</math>

<math>y \in</math> {0,1}

The solution to the MILP will yield a new set of <math>(x)</math> and <math>(y)</math>. Call these the new <math>(x^0)</math> and <math>(y^0)</math>; this is the '''root''' of the branch and bound search tree.

===Solve Nodes===
4. Select an unsolved node
'''If''' no nodes are left,
'''then''' the problem is solved and <math>Z(x^j, y^j)</math> is the optimal solution.

5. Solve MILP (formulation below)
'''If''' all <math>y^k</math> = {0,1}
This node is the new incumbent
'''and''' Z obtained from this set of <math>x^k</math> and <math>y^k</math> is the current optimal solution.
'''and''' add linearizations of the objective and constraints
using <math>x^k</math> and <math>y^k</math> to each unsolved node according to the equation below.
Go to step 6.
'''Else''' a <math>y^k</math> ∉ {0,1}
Go to step 7.

Solve the corresponding MILP of the problem using the previous feasible solution <math>(x^j, y^j)</math> in the following form:

For the first node (excluding the root), <math>(x^j, y^j)</math> will be <math>(x^0, y^0)</math>, etc.

<math>min</math> <math>a</math>

<math>s.t.</math> <math>a \leqslant UB^j </math>

<math>f(x^j,y^j) +</math> <math>\nabla\ f(x^j,y^j)^T</math> <math>\binom{x-x^j}{y-y^j} </math> <math>\leqslant</math> <math>a</math>

<math>g(x^j,y^j) +</math> <math>\nabla\ g(x^j,y^j)^T</math> <math>\binom{x-x^j}{y-y^j} </math> <math>\leqslant</math> <math>0</math> <math>\forall j \in T</math>

where <math>T</math> is the set containing all indices of the solution tree in which the NLP for <math>y^j</math> is feasible.

<math>g(x^i,y^i) +</math> <math>\nabla\ g(x^i,y^i)^T</math> <math>\binom{x-x^i}{y-y^i} </math> <math>\leqslant</math> <math>0</math> <math>\forall i \in S</math>

where <math>S</math> is the set containing all indices of the solution tree in which the NLP for <math>y^i</math> is infeasible.

<math>\Gamma x + \Gamma y \leqslant \epsilon</math>

This constraint represents the Gomory cuts generated as the algorithm runs. This line decreases the feasible region of the original problem.

<math>y \in</math> {0,1}

The solution to this MILP will yield a new set <math>(x^k)</math> and <math>(y^k)</math>.

6. Solve relaxed NLP
Using the MILP solution <math>y^k</math>
This should result in a new solution <math>x^j</math> and <math>y^j = y^k</math>.
'''If''' NLP<math>(y^j)</math> is feasible
→ solve <math>Z(x^j, y^j)</math>.
'''If''' <math>Z(x^j, y^j)</math> is less than the previous upper bound
'''then''' this yields a new '''upper bound''' <math>UB^j</math> to the original problem.
Fathom all unsolved nodes that do not satisfy this bound.
Return to step 4
'''Else''' retain the old upper bound.
Return to step 4
'''Else''' NLP<math>(y^j)</math> is not feasible
→ Fathom node.
Return to step 4

===Cutting vs Branching===
When the solution to the linear relaxation in Step 5 contains fractional values on binary variables <math>y</math>, either a cutting plane should be generated to exclude that solution or branching can be done at that node to constrain the fractional variable to its binary values 0 or 1.

7. Calculate "skip factor"
'''If''' a cut is to be performed, go to step 8.
'''Else''' the cut is to be skipped, go to step 9.

The decision whether or not to perform a Gomory cut is based on a "skip factor" <math>S</math> which is calculated throughout the enumeration of the tree.

<math>S =</math> <math>min[S_{max}</math>, <math>\dfrac{t + wcd \log_{10} p}{t f}]</math>

where t = number of integer nodes solved

S_{max}, c, w = positive constant parameter

p = number of binary variables y

f = number of violated binary variables in <math>y^k</math>

===Gomory Cuts===
8. Generate an inequality to exclude the fractional variable solution

<<Equation 3. for gomory mixed integer cuts>>

Add these cuts to the constraints of the original problem.

Return to step 5

===Branching===
9. Constrain the/a variable in <math>y^k</math> to branch off of.

One branch will set <math>y^k = 0</math> and the other <math>y^k = 1</math>, creating two new nodes. Return to step 5, following one of these nodes.

=Variations=
A variation on the Branch and Cut method presented by Sven Leyffer in 2013 utilizes cuts for every fractional solution and branches only when solutions are still fractional after multiple cuts. 8 Thus, the algorithm is the same until step 7, where cuts are always chosen to eliminate solutions where <math>y^k</math> ∉ {0,1}. The inequality generated to produce this cut is added to the constraints of the original problem.

=Conclusion=
The general Branch and Cut algorithm follows a scheme which grows exponentially as variables are added to the original design problem. The addition of Gomory Cuts allows bounds to be tightened, reducing the number of feasible nodes to be tested and allowing the solver to converge on the optimal solution with less iterations. However, the formation of inequalities to generate these cuts take time and may slow down the actual resolution of the MINLP problem. The larger the problem, the more useful the cuts can be.

=References=

# I. Akrotirianakis, I. Maros, and B. Rustem. An Outer Approximation Based Branch and Cut Algorithm for convex 0-1 MINLP Problems. ''Optimization Methods and Software.'' 21:47, 2001 https://www.doc.ic.ac.uk/research/technicalreports/2000/DTR00-6.pdf
# S. Leyffer and J. Linderoth. Introduction to Integer Nonlinear Optimization, Nonlinear Branch-and-Cut, Theoretical and Computational Challenges. ''Argonne National Laboratory.'' 2007. http://science.energy.gov/~/media/ascr/pdf/workshops-conferences/mathtalks/Leyffer.pdf
# A. H. Land and A. G. Doig. An Automatic method of solving discrete programming problems. ''Econometrica,'' 28:497 520, 1960.
# R. J. Dakin. A tree search algorithm for mixed integer probramming problems. ''Computer Journal,'' 8:250 255, 1965.
# S. Albert. Solving Mixed Integer Linear Programs Using Branch and Cut Algorithm. ''Masters of Mathematics, North Carolina State University.'' 2006. http://www4.ncsu.edu/~kksivara/masters-thesis/shon-thesis.pdf (good for milp)
# J. E. Mitchell. Branch-and-Cut Algorithms for Combinatorial Optimization Problems. ''Mathematical Sciences,'' 1999. http://homepages.rpi.edu/~mitchj/papers/bc_hao.pdf
# M. Padberg and G. Rinaldi. A Branch-and-Cut Algorithm for the Resolution of Large-Scale Symmetric Traveling Salesman Problems. ''SIAM Rev,'' 33(1), 60-100, 1991. http://epubs.siam.org/doi/abs/10.1137/1033004?journalCode=siread
# S. Leyffer. Mixed-Integer Nonlinear Optimization: Applications, Algorithms, and Computation III. ''Graduate School, Universite catholique de Louvain.'' 2013. https://wiki.mcs.anl.gov/leyffer/images/4/42/Socn-3.pdf

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Extended cutting plane (ECP)

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Asa273: Created page with "Authors: Kyung Je Lee (ChE 345 Spring 2015) Stewards: Dajun Yue, Fengqi You ==Introduction== ===Background=== '''Extended Cutting Plane''' is an optimization method suggested..."

Authors: Kyung Je Lee (ChE 345 Spring 2015)
Stewards: Dajun Yue, Fengqi You

==Introduction==
===Background===
'''Extended Cutting Plane''' is an optimization method suggested by Westerlund and Petersson in 1996 to solve Mixed-Integer NonLinear Programming (MINLP) problems[1]. ECP can be thought as an extension of Kelley's cutting plane method, which uses iterative Newton's method to refine feasible area and ultimately solve a problem within tolerable error. Therefore, ECP method does not require solving Non-Linear Programming(NLP) while Branch and Bound(BB) and Outer Approximation(OA) do require NLP solution for an upper bound. However, ECP generally requires more iterations. Although cutting plane method is criticized for its slow convergence, ECP is more efficient in cases where evaluation of non linear functions are time costly. For example, in optimization of a dynamic separation process done by Stefan Emet and Tapio Westerlund, ECP was 100 times faster than BB and 10 times faster than OA in solving the MINLP[2].

===Comparison with outer approximation===
ECP is closely related to OA in that it uses first differential approximation to cut the plane. The difference is that OA solves a NLP problem for its upper bound while ECP only uses solution of MILP in each iteration. This means that OA is more efficient in main iteration loops. This advantage of OA is more prominent in strongly non-linear MINLP problems that are mainly consisted of continuous variables. However, in pure integer non-linear programming problems, OA method does not have any advantage over ECP. Although it takes less iterations for OA to converge, solving NLP problem in each iteration incur more computation work than solving MILP because MILP has only one additional linear constraints in each iteration.

===Formulation of MINLP problem===

A general MINLP can be formulated as the following:

<math> \min_{x,y} Z=C_x^T x + C_y^T y </math>

<math>s.t. \quad g(x,y) \leq 0</math>

where, cx and cy are vectors with constants, x is a vector of continuous variables, y is a vector with discrete variables
and g(x, y) is a vector with continuous convex functions, all defined on a set.

==ECP algorithm==
Since g(x,y) is a convex function set and continuously differentiable it follows that

<math> g_i(x^k,y^k) + \left( \frac{\partial g_i}{\partial x}\right)_{x^k,y^k} (x-x^k) + \left( \frac{\partial g_i}{\partial y}\right)_{x^k,y^k} (y-y^k) \leq g_i(x,y)</math>

Also, if,

<math> max(g_i(x^k,y^k)) \leq 0 </math>

then for all i

<math> g_i(x^k,y^k) \leq 0</math>

Using these properties, ECP algorithm is as follows:

'''Step 0.''' Set k=1. Leave out all nonlinear constraints and set up an MILP problem.

'''Step 1.''' Solve the MILP problem.

'''Step 2.''' Check if the solution satisfies nonlinear constraints. If all constraints are satisfied, in other words, if <math> g_i(x^k,y^k) \leq 0</math> is true for all i, <math>(x^k, y^k)</math> is a global optimum.

'''Step 3''' If any of the constraints are not satisfied, add a constraint for most violated constraint, g
::<math> g_i(x^k,y^k) + \left( \frac{\partial g_i}{\partial x}\right)_{x^k,y^k} (x-x^k) + \left( \frac{\partial g_i}{\partial y}\right)_{x^k,y^k} (y-y^k)\leq 0 </math>
::set k= k+1 and go to Step 1.

== Example ==
<math> \min z = -x_1-x_2 </math>

<math> s.t. \quad g1(x_1,x_2) = 0.15(x_1-8)^2 + 0.1 (x_2-6)^2+0.025e^{x_1}x_2^{-2}-5 \leq 0 </math>
::<math> g2(x_1,x_2) = 1/x_1 + 1/x_2- x_1^{0.5}x_2^{0.5}+4 \leq 0 </math>
::<math> 2x_1-3x_2-2 \leq 0 </math>
::<math> 1\leq x_1 \leq 20,\quad 1\leq x_2\leq 20, \quad x_1\in \R \quad x_2 \in \N</math>

First MILP can be set-up by leaving out non-linear constraint <math> g_1</math> and <math> g_2</math>
[[File:ECP.PNG|350px|thumb|right|Visualization of how ECP is used to solve MINLP4]]
<math> \min z = -x_1-x_2 </math>

<math> s.t. \quad2x_1-3x_2-2 \leq 0 </math>
::<math> 1\leq x_1 \leq 20,\quad 1\leq x_2\leq 20 </math>
::<math> x_1\in \R \quad x_2 \in \N </math>

The first iteration gives <math>x_1^1 = 20, x_2^1=20 </math>.
This leads to <math>g_1(x_1^1,x_2^1)=30359, \quad g_2(x_1^1,x_2^1)= -15.9 </math>

A new constraint is introduced for the second iteration with the most violated nonlinear constraint <math>g_1</math>

<math> \min z = -x_1-x_2 </math>

<math> s.t. \quad g_1(x_1^1,x_2^1)+\triangledown g_1(x_1^1,x_2^1)^T(x-x_1^1,x-x_2^1) \leq 0 </math>
::<math> 2x_1-3x_2-2 \leq 0 </math>
::<math> 1\leq x_1 \leq 20,\quad 1\leq x_2\leq 20 </math>
::<math> x_1\in \R \quad x_2 \in \N </math>

Same procedure can be taken for consequent iterations, and with 17 iterations, ECP gives answer of <math>x_1^1 = 8.9, x_2^1=12 </math>.

==Non-smooth Functions==
In non-smooth functions, ECP algorithm can be generalized by relaxing continuous differentiability. Therefore, the only change in the algorithm is that subgradients are used instead of gradients. Subgradient of convex function <math>h</math> at point<math>z_0</math> is any vector <math>\xi</math> that satifies
<math>h(z_0) + \xi(z-z_0) \leq h(z)</math> 3 

==Conclusion==
ECP is an extension of cutting plane(CP) method that is used to solve NLP problems. The application of cutting plane to MINLP is rather straight forward and the strength of ECP lies in that it is simple and robust. Therefore, it is suitable for solving large MINLP problems with moderate degree of non-linearity and complex system that require extensive computational work. ECP only requires one additional constraint to improve one solution for MILP problem at each iteration whereas both NLP and MILP problems are solved in other MINLP methods. However, since there is only one adjustment made at a time, it has slow convergence to solution.

==Reference==
1. Tapio Westerlund, Frank Pettersson, An extended cutting plane method for solving convex MINLP problems, Computers & Chemical Engineering, Volume 19, Supplement 1, 11–14 June 1995, Pages 131-136, ISSN 0098-1354, http://dx.doi.org/10.1016/0098-1354(95)87027-X.

2. Stefan Emet and Tapio Westerlund. 2008. Solving a dynamic separation problem using MINLP techniques. Appl. Numer. Math. 58, 4 (April 2008), 395-406. DOI=10.1016/j.apnum.2007.01.023 http://dx.doi.org/10.1016/j.apnum.2007.01.023

3.Tapio Westerlund, Hans Skrifvars, Iiro Harjunkoski, Ray Pörn, An extended cutting plane method for a class of non-convex MINLP problems, Computers & Chemical Engineering, Volume 22, Issue 3, 28 February 1998, Pages 357-365, ISSN 0098-1354, http://dx.doi.org/10.1016/S0098-1354(97)00000-8.
(http://www.sciencedirect.com/science/article/pii/S0098135497000008)

4. An extended supporting hyperplane algorithm for convex MINLP problems http://blogs.abo.fi/ose/files/2014/10/ose2014_kronqvist.pdf

Generalized Benders decomposition (GBD)

2022-04-01T15:27:41Z

Asa273: Created page with "Authors: Yuanxi Zhao (ChE 345 Spring 2015) Steward: Dajun Yue, Fengqi You Date Presented: May 22, 2015 Generalized Benders Decomposition is a procedure to solve..."

Authors: Yuanxi Zhao (ChE 345 Spring 2015) 
Steward: Dajun Yue, Fengqi You 
Date Presented: May 22, 2015 

Generalized Benders Decomposition is a procedure to solve certain types of NLP and MINLP problems. The use of this procedure has been recently suggested as a tool for solving process design problems. While analyzing the solution of nonconvex problems through different implementations of the GBD, it is demonstrated that in certain cases only local minima may be found, whereas in other cases not even convergence to local optima can be achieved. 

=Introduction=
J.F. Benders devised an approach for exploiting the structure of mathematical programming problems with complicating variables (variables which, when temporarily fixed, render the remaining optimization problem considerably more tractable).The algorithm he proposed for finding the optimal value of this vector employs a cutting-plane approach for building up adequate representations of (i) the extremal value of the linear program as a function of the parameterizing vector and (ii) the set of values of the parameterizing vector for which the linear program is feasible. Linear programming duality theory was employed to derive the natural families of cuts characterizing these representations, and the parameterized linear program itself is used to generate what are usually deepest cuts for building up the representations. 

Geoffrion (1972) generalized the approach proposed by Benders (1962) to a broader class of optimization problems in which the parametrized subproblem need no longer be a linear program. Nonlinear convex duality theory is employed to derive the natural families of cuts corresponding to those in Bender's case.

=Model Formulation=
===Target problem===

<math>min_{x,y}</math><math>f(x,y)</math> 
<math>s.t.</math> <math>g(x) \leq 0 </math> <math>(1)</math> 
<math>x\in X</math>,<math>y\in Y</math> 

under the following assumptions: 
# <math> X \subset R</math> and <math>Y \subset R</math> are compact. 
# For all <math> y\in Y</math>,<math>f</math> and <math>g</math> are convex on <math>X</math>. 
# For <math>y</math> fixed to any feasible <math> y\in Y</math>, the problem satisfies Slater's condition. 

The following problem is equivalent to above and is called its projection on <math>Y</math> 

<math>min_y</math><math> v(y)</math> 
<math>s.t. </math> <math>v(y)=</math><math>min_{x \in X}f(x,y)</math> <math>s.t.</math><math> g(x,y) \leq 0</math> <math> (2)</math> 
<math>y\in Y\cap V</math> 

where <math>V</math><math> =</math>{<math>y: g(x,y)\leq 0 </math> for some <math>x</math><math>\in</math><math>X</math>}. 
For problems where <math>X</math> is a convex set, and the functions <math>f(x,y)</math>,<math>g(x,y)</math> are convex with respect to the variable <math>x</math>, Geooffrion (1972) proposed a decomposition of (2) based on the following two problems: 

===Primal problem===
<math>min_x</math><math>f(x,\bar{y})</math> 
<math>s.t. </math> <math>g(x,\bar{y})\leq 0</math> <math>(3)</math> 
<math>x\in X</math> 

where <math>\bar{y}</math> is an arbitrary but fixed point in <math>Y</math>.

===Master problem===
<math>min_{y\in Y}</math><math>[</math><math>max</math><math>_{u\geq 0}</math><math>[min_{x\in X}</math>{<math>f(x,y)</math><math>+u^T</math><math>g(x,y)</math>}<math>]]</math> 
<math>s.t.</math> <math>min_{\lambda}</math>{<math>{\lambda}^T</math><math>g(x,y)</math>}<math>\leq 0</math>, <math>\forall</math><math>{\lambda}</math><math>\in</math><math>{\Lambda}</math> <math> (4)</math>

where <math>{\Lambda}=</math>{<math>{\lambda}\geq 0;</math><math>\sum_i</math><math>{\lambda}</math><math>_i=1</math>} <math>and</math> <math>y>\in Y</math>, <math>x\in X</math>, <math>u\geq 0</math>

===Some Remark===

Before any further analysis, it is appropriate to point out that the master problem is equivalent to the projection (2), only when <math>X</math> is a convex set, and the functions <math>f(x,y),g(x,y)</math>are convex with respect to <math>x</math>. This is so because the dual of <math>v(y)</math>, as defined in (2), was invoked in arriving at the Master problem. Therefore, when <math>X</math> is not a convex set and/or convexity of the functions <math>f(x,y)</math> and <math>g(x,y)</math> in the variable <math>x</math>does not hold, a dual gap may exist between <math>v(y)</math> and its dual. In these cases, since by the weak duality theorem, the solution of <math>v(y)</math> is always greater than or equal to the solution of its dual, the master problem can only provide a lower bound on the optimum, i.e. 

<math>v(y)=</math><math>min_{x\in X}</math><math> f(x,y)</math><math> s.t.</math><math>g(x,y)\leq 0</math> 
<math>v(y)</math><math>\geq</math><math> max</math><math>_{u\geq 0}</math><math>[min_{x\in X}</math>{<math>f(x,y)</math><math>+ u^T g(x,y)</math>}<math>]</math> 
<math>\Rightarrow</math> 
<math>min_{y\in Y\cap V}</math><math>v(y)\geq</math><math>min_{y\in Y\cap V}</math><math>[max</math><math>_{u\geq 0}</math><math>[min_{x\in X}</math><math>f(x,y)</math><math>+u^T g(x,y)</math>}<math>]]</math> 
<math>min_{y\in Y\cap V}</math><math>v(y)</math><math>=min_{y\in Y}</math><math>[max</math><math>_{u\geq 0}</math><math>[min_{x\in X}</math><math>f(x,y)</math><math>+u^T g(x,y)</math>}<math>]]</math> 
<math>s.t.</math> <math>min_{x\in X}</math>{<math>{\lambda}^T g(x,y)</math>}<math>\leq 0</math>, <math>\forall</math><math>{\lambda}</math><math>\in</math><math>{\Lambda}</math> 

=Solution approaches=
===Algorithm flowchart===
[[File:Algorithm.png|800px|Algorithm flowchart]]
===Computational implementation===
The master problem can be rewritten as 

<math>min_{y_0=y} y_0</math> 
<math>s.t.</math> <math>L^*(y,u)</math><math>=min_{x\in X}</math>{<math>f(x,y)</math> <math>+u^Tg(x,y)</math>}<math>\leq y_0</math>, <math>all</math><math>u\geq 0</math>
<math>L_*(y,{\lambda})</math><math>=min_{x\in X}</math>{<math>{\lambda}^Tg(x,y)</math>}<math>\leq 0</math>, <math>all</math><math>{\lambda}\in {\Lambda}</math> 

Geoffrion (1972) suggests to solve a relaxed version of this problem in which all but a few constraints are ignored. Since constraints are continuously added to the master, the optimal values of this problem form a monotone nonedecreasing sequence. When <math>f(x,y)</math> and <math>g(x,y)</math> are convex in <math>x</math> and certain conditions hold, the lowest solution of the primal and the global solution of the master [as defined from above] will approach one another and will thus provide the global optimum of the overall problem within a prespecified tolerance. As analyzed earlier, when convexity in <math>x</math> does not hold, dual gaps may prevent these two values from approaching each other. Nevertheless the global solution of the relaxed master will still provide a valid lower bound on the global optimum of the overall problem. The resulting computational procedure is the following: 

'''Step 1.''' Let a point <math>\bar y</math> in <math>Y\cap V</math> be known. Solve the primal problem and obtain the optimal solution <math>x^*</math>, and the optimal multiplier vector <math>u^*</math>. Put the counters <math>K^f=1</math>,<math>K^i=0</math>. Set <math>U=f(x^*,\bar y)</math>, select a tolerance <math>\varepsilon > 0</math> and put <math>u^{(1)}=u^*</math>. Finally, determine the function <math>L^*(y,u^{(1)})</math>. 

'''Step 2.''' Solve globally the current relaxed master problem: 

<math>min_{y_0=y}</math><math>y_0</math> 
<math>s.t.</math> <math>L^*</math><math>(y,</math><math>u^{(k_1)})</math><math>\leq y_0</math>, <math>k_1=1,\dots</math><math>K^f</math> 
<math>L_*</math><math>(y,</math><math>{\lambda}^{(k_2)})</math><math>\leq 0</math>, <math>k_2=1,\dots</math><math>K^i</math> 

'''Step 3.''' Solve globally the primal problem using <math>\bar {y}=\hat {y}</math>. 
'''Step 3a.''' ''Primal is feasible''. If <math>v(\bar{y})</math><math>\leq \hat{y_0}</math><math>+\epsilon</math> terminate. Otherwise, determine the optimal multiplier vector<math> u^*</math>,increase <math>K^f</math> by one, set <math>u^{(k^f)}</math><math>=u^*</math>.Additionally, if <math>u(\bar{y})</math><math><U</math>,put <math>U=v(\bar{y})</math>. Finally, determine the function <math>L^*(y</math><math>,u^{(k^f)})</math> and return to Step 2. 
'''Step 3b.''' ''Primal is infeasible''. Determine a set of values of <math>{\lambda}^*</math><math>\in {\Lambda}</math> which satisfy

<math>min_{x \in X}</math>{<math>{\lambda}</math><math>^{*T}g(x,y)</math>}<math>>0</math> 

Increase <math>K^i</math>by one, put <math>{\lambda}</math><math>^{(K^i)}</math><math>={\lambda}^*</math> and determine the function <math>L*(y,</math><math>{\lambda}</math><math>^{(K^i)}</math><math>)</math>. Return to Step 2. 

When referring to "solutions" of nonconvex optimization problems it is sometimes understood that these may be locally, rather than globally, optimal points. In the above computational procedure it is necessary that the master be solved globally. When problems are jointly convex in <math>x</math> and <math>y</math>, the master is convex and globality is then achieved. Global solutions of the primal are also needed if convexity of X and/or convexity of <math>f(x,y)</math> and/or <math>g(x,y)</math> in <math>x</math>does not hold. 

===Determination of lambda*===
The determination of <math>{\lambda}^*</math> in Step 3b can be done by any Phase I algorithm. In particular Floudas et al (1989) proposed to solve the following problem: 

<math>min_{\alpha,x}</math><math>{\alpha}</math> 
<math>s.t.</math> <math>g(x,\bar{y})</math><math>-{\alpha}\underline{1}</math><math>\leq 0</math> 
<math>x\in X</math><math>,{\alpha}\in R</math> 

where <math>\underline{1}</math><math>=(1,1,</math><math>\dots</math><math>,1)^T</math>. 
Since the primal problem is infeasible, it is already known that the solution of this problem is positive. Once this problem is solved and a stationary point <math>x^*</math> is obtained, the following necessary Kuhn-Tucker conditions are satisfied: 
<math>1-\sum_i</math><math>\lambda_i^*</math><math>=0</math> 
<math>\lambda^{*T}\triangledown_x</math><math>g(x^*,\bar{y})=0</math> 
<math>\lambda_i^*</math><math>[g_i(x^*,\bar y)</math><math>-\alpha]=0</math><math>,\forall_i</math> 
<math>\lambda_i</math><math>\leq 0</math><math>,\forall_i</math> 

From them it is concluded that by solving the problem the condition <math>\lambda^*</math><math>\in\Lambda</math> is satisfied. Note that in this step it is not imperative to achieve globality.

===Explicit determination of L===
In most cases, the function <math>L^*</math> and <math>L_*</math> are implicitly defined. One case in which these functions can be obtained in explicit form is when the global minimum over <math>x</math> can be obtained independently of <math>y</math>. i.e. when Property (P) is satisfied. Two examples in which this property is satisfied arise when the functions <math>f(x,y)</math> and <math>g(x,y)</math> are separable in <math>x</math> and <math>y</math>, and in the variable factor programming case. 
Once Property (P) holds, evalution of <math>L^*(y,u^*)</math><math>,L_*(y,u^*)</math> simply requires that the minima in the master problem be global. This is the so called L-Dual-Adequacy property, which upon satisfaction of Property (P) can be achieved only if a global search of the solution of both 

<math>min_{x\in X}</math>{<math>f(x,y)</math><math>+u^{*T}g(x,y)</math>} <math>and</math> <math>min_{x\in X}</math>{<math>\lambda^{*T}</math><math>g(x,y)</math>} 

is conducted. 
Another case in which these functions can be obtained in explicit form is when Property (P') is satisfied, i.e. when the globally optimal solution of the primal, <math>x^*</math>, is also the solution of the minimization of the problems defined in the master problem. This is guaranteed when <math>f(x,y)</math> and <math>g(x,y)</math> are convex and separable in x. 

If Property (P') is simply assumed, then this implementation of Generalized Benders Decomposition may only be used, without guarantees, to identify candidates for local, but not global minima. 

The above discussion does not mean that Properties (P) and/or (P') must always hold. Other procedures may exist in which the Master problem can be solved without using these requirements.

===Advantages and Disadvantages of the algorithm===
The GBD method is similar in nature to the Outer-Approximation method. The difference arises in the definition of the MILP master problem (M-MIP). In the GBD method only active inequalities are considered and the set is <math>x\in X</math> is disregarded. In particular, assume an outer approximation given at a given point <math>(x^k,y^k)</math> , where for a fixed <math>y^k</math> the point <math>x^k</math> corresponds to the optimal solution to the problem. Making use of the Karush-Kuhn-Tucker conditions and eliminating the continuous variables x, the inequalities can be reduced to Lagrangrian cut projected in the y-space. This can be interpreted as a surrogate constraint because it is obtained as a linear combination of these. 

For the case where there is no feasible solution to the problem, if the point <math>x^k</math> is obtained from the feasibility subproblem (NLPF), the feasibility cut projected in y can be obtained using a similar procedure. In this way, the problem (M-MIP) reduces to a problem projected in the y-space. Since the master problem can be derived from the master problem of the Outer-Approximation algorithm in the context of problem. GBD can be regarded as a particular case of the Outer Approximation algorithm. In fact the following property, holds between the two methods: 

'''Property 1.''' ''Given the same set of K subproblems, the lower bound predicated by the relaxed master problem (RM-OA) is greater or equal to the one predicted by the relaxed master problem (RM-GBD).'' 

The above proof follows from the fact that the Lagrangian and feasibility cuts, <math>(LC^k)</math> and <math>(FC^k)</math>, are surrogates of the outer approximations <math>(OA^k)</math>. Given the fact that the lower bounds of GBD are generally weaker, this method commonly requires a large number of cycles or major iterations. As the number of 0-1 variables increases this differences become more pronounced. This is to be expected since only one new cut is generated per iteration. Therefore, user-supplied constraints must often be added to the master problem to strengthen the bounds. As for the OA algorithm, the trade-off is that while is generally predicts stronger lower bounds than GBD, the computational cost for solving the master problem (M-OA) is greater since the number of constraints added per iteration is equal to the number of nonlinear constraints plus the nonlinear objective. 

The following convergence property applies to the GBD method: 

'''Property 2.''' ''If problem (PI) has zero integrality gap, the GBD algorithm converges in one iteration once the optimal is found.'' 

The above property implies that the only case one can expect the GBD method to terminate in one iteration, is when the initial discrete vector is the optimum, and when the objective value of the NLP relaxation of problem (P1) is the same as the objective of the optimal mixed-integer solution. Given the relationship of GBD with the OA algorithm, Property 2 is also inherited by the OA method. 

One further property that relates the OA and GBD algorithms is the following: 

'''Property 3.''' ''The cut obtained from performing one Benders iteration on the MILP master (RM-OA) is equivalent to the cut obtained from the GBD algorithm.'' 

By making use of this property, instead of solving the MILP (RM-OA) to optimality, for instance by LP-based brand and bound, one can generate a GBD cut by simply performing one Benders iteration on the MILP. This property will prove to be useful when deriving a logic-based version of the GBD algorithm. With the above in mind, the advantages and disadvantages of GBD can thus be summarized as below: 

'''Advantages:''' Geoffrion (1972) generalized Benders approach to a broader class of programs in which the parameterized subproblem need no longer be a linear program. Nonlinear convex duality theory was employed to derive the quivalent masster problem. In GBD, the algorithm alternates between the solution of relaxed master problems and convex nonlinear subproblems. It is a helpful tool for solving process design problems. 

'''Disadvantages:''' Some restrictions regarding the convexity and other properties of the function involved were identified. Also, it is found that in certain cases only local minima may be found, whereas in other cases not even convergence to local optima can be achieved. These suggests that the procedure should be used with caution, especially when global optimality is being sought. More specifically, it is demonstrated that the implementation of the procedure guarantees globality when certain properties are satisfied (primal convexity, global solution of the master, Property (P) and L-Dual-Ade-quacy).

=Application=
Generalized Benders decomposition has been applied to a variety of problems that were modeled as mixed integer linear programming (MDLP) or mixed integer nonlinear programming (MINLP) problems. Geoffrion and Graves (1974) were among the first to use the algorithm to solve an MILP model for the design industrial distribution systems. Noonan and Giglio (1977) used Benders decomposition coupled with a successive linearization procedure to solve a nonlinear multiperiod mix integer model for planning the expansion of electric power generation networks. Rouhani et aL (1985) used GBD to solve an MINLP model for reactive source planning in power systems. Floudas and Ciric (1989) applied GBD to their MINLP formulation for heat exchanger network synthesis. EL-Halwagi and Manouthiosakis (1989) developed an MINLP model for the design and analysis of mass exchange networks and suggested the use of GBD for its solution. Sahinidis and Grossman (1990) applied the algorithm to the problem of scheduling multiproduct parallel production lines by solving the corresponding large scale MINLP model. The technique has also been used for solving nonconvex nonlinear programming (NLP) and MINLP problems: Geoffrion (1971) applied it to the variable factor programming problem and Floudas et aL (1989) suggested a Benders-based procedure for searching for the global optimum of nonconvex problems. 

Unfortunately, Benders decomposition has not been uniformly successful in all its application Florial et aL (1976) have noticed that the algorithm often converged very slowly when applied to their MILP model for scheduling the movement of railway engines. Bazaraa and Sherali (1980) observed that a large number of iterations were needed to solve their MILP model for quadratic assignment problems of realistic size. Sahinidis et aL (1989) have found brand and bound to be significantly faster than Benders decomposition for the solution of their multiperiod MILP for long range planning in the chemicla industries. Finally, with respect to the application of GBD to nonconvex problems, in contrast to Geoffrion (1972) and Floudas et aL (1989), Sahinidis and Grossmann (1989) have encountered cases where the application of this technique to their MINLP model for the planning of chemical processes fail to produce the global optima of these problems.

=Sources=
#Geoffrion, A. M., Elements of Large-Scale Mathematical Programming, Management Science, Vol. 16, No. 11, 1970.
#BENDERS, J. F., Partitioning Procedures for Solving ~lixed-Variables Programming Problems, Numerische Mathematik, Vol. 4, 1962.
#WILSON, R. Programming Variable Factors, Management Science, VoI. 13, No. 1, 1966.
#Balas, E., Duality in Discrete Programming: IV. Applications, CarnegieMellon University, Graduate School of Industrial Administration, Report No. 145, 1968.
#Meyer, R., The Validity of a Family of Optimization Methods, SIAM Journal on Control, Vol. 8, No. I, 1970.
#Dantzic, G. B., Linear Programming and Extensions, Princeton University Press, Princeton, New Jersey, 1963.
#Geoffriosi, A. M., Primal Resource-Directive Approaches for Optimizing Nonlinear Decomposable Systems, Operations Research, Vol. 18, No. 3, 1970.
#Hogan, W., Application of a General Convergence Theory for Outer Approximation Algorithms, University of California at Los Angeles, Western Management Science Institute, Working Paper No. 174, 1971.
#Eaves, B. C., and Zangwill, W. I., Generalized Cutting Plane Algorithms, SIAM Journal on Control, Vol. 9, No. 4, 1971.
#Geoffrion, A. M., A New Global Optimization Technique for Gaseous Diffusion Plant Operation and Capital Investment, University of California at Los Angeles, Graduate School of Business Administration, Discussion Paper, 1970.
#Geoffrion A. M., Duality in Nonlinear Programming: £1 Simplified Application-Oriented Development, SIAM Review, Vol. 13, No. 1, 1971.

Branch and cut for MINLP

2022-04-01T15:27:08Z

Asa273: Created page with "Author: Pear Dhiantravan (ChE 345 Spring 2015) Stewards: Dajun Yue, Fengqi You Branch and Cut is a method for solving Mixed Integer Non Linear Programming (MINLP) models...."

Author: Pear Dhiantravan (ChE 345 Spring 2015)

Stewards: Dajun Yue, Fengqi You

Branch and Cut is a method for solving Mixed Integer Non Linear Programming (MINLP) models. There are variations on the exact steps of the algorithm, but the original method developed by Ioannis Akrotirianakis, Istvan Maros, and Berc Rustem in 2000 utilizes the general organization of the Branch and Bound method with the iterative nature of the Outer Approximation.1 The addition of Gomory mixed integer cuts as an alternative to branching improves the efficiency of the overall branch and bound algorithm by reducing the number of nodes and Non-Linear Programming (NLP) problems required to solve the MINLP.

=Introduction=
The organization of general design problems into programming models allows for the defining and finding of their (global) optimal solution. MINLP models represent problems as a sets of continuous variables with binary integer variables. The continuous variables are restricted to defined constraints, and the binary variables represent whether or not a design choice is made.

===History===
[[File:B&C minlp.JPG|500px|thumb|Branch and Bound with Gomory Cuts and the iterative nature of Outer Approximations 2]]

Mixed integer programming problems were explored most generally in the later half of the 1900s. Ignacio Grossmann published many papers on mixed integer linear programing problems and their solutions and applications in the late 1980s through the 1990s. In those decades, research was focused largely on improving the [https://optimization.mccormick.northwestern.edu/index.php/Branch_and_bound_%28BB%29 Branch and Bound] method to achieve greater time efficiency. The branch and bound method was developed by A.H. Land and A.G. Doig in 1960 to solve linear integer problems,3,1 and expanded in 1965 by R.J. Dakin to incorporate nonlinear integer problem solutions. 4,1 Branch and bound seemed to be a robust method, however the time required to solve increases exponentially as the number of variables increases.5 In the 1950s and 60s, Ralph Gomory developed a different method using cutting planes to solve integer problems. Gomory Cuts were quicker to solve but gave less reliable solutions. The exploration of incorporating Gomory cuts into the branch and bound method gained popularity when solutions showed greater efficacy upon combination of these methods. The joint algorithm is called Branch and Cut.

In the early 2000s, Akrotirianakis, Maros, and Rustem built on the findings of their predecessors to expand the application of the branch and cut method to non linear programs. More research surfaced on broader applications of this method, and with this grew the development of computational programs such as CPLEX and XPRESS-MP to run and solve these problems using given iterative solution methods.6

===Applications===
Mixed integer non linear programming models can cover a wide variety of engineering and design problems with discrete variable values.

The Branch and Cut method is well-known for its long-time use in solving the [https://optimization.mccormick.northwestern.edu/index.php/Traveling_salesman_problems Traveling Salesman Problem].6 In 1991, Padberg and Rinaldi developed a solution to large-scale symmetric traveling salesman problems using the branch and cut method.7 MINLP problems involving scheduling, network design (including facility locating), and a variety of simplified biological models can be solved using the branch and cut algorithm given integer-valued variables.6

=Formulation=
Given that <math>f(x)</math>, <math>g(x)</math>, and <math>h(x)</math> are convex and continuously differentiable, a general MINLP problem solvable by the Branch and Cut method can be formulated as follows:

<math>min Z(x,y)</math> <math>=</math> <math>C^T y</math> <math>+ f(x)</math>

<math>s.t.</math> <math>g(x) + By \leqslant 0</math>

<math> h(x) = 0</math>

<math> x \in X, y \in {0,1}</math>

=Algorithm=
The Branch and Cut algorithm closely follows that of the Outer Approximation for MINLP, but incorporates Gomory cuts in order to decrease the search space of the problem.

The algorithm presented here is the method developed by Akrotirianakis, Maros, and Rustem [1a]. Variations on this method are described below.

===Initialization: Value of the Search Tree Root===
0. Upper bound = inf, Lower bound = -inf

1. Initialize <math>y^0</math>
The Branch and Cut method begins with an initialization of the binary variables <math>(y)</math> by defining each with a finite starting value 0 or 1.
Otherwise, the initialization may be achieved by solving a relaxed NLP setting <math>0\leqslant y \leqslant 1</math>

2. Solve NLP using <math>y^0</math>
'''if''' NLP is feasible
→ solve <math>Z(x^0, y^0)</math>. This yields a new '''upper bound''' to the original problem. Move to step 3
'''else''' NLP is not feasible
→ if an initial set of values for <math>y^0</math> was chosen, choose a new <math>(y^0)</math>.
Repeat 1 and 2 until a feasible solution is obtained. Move to step 3.

The NLP should result in an initial feasible solution <math>x^0</math> and <math>y^0</math> in which <math>Z(x^0, y^0)</math> <math>\leq \infty</math>.

Otherwise, if the relaxed NLP is infeasible, then the MINLP problem is infeasible.

3. Solve MILP

Using <math>x^0</math> and <math>y^0</math> obtained from the NLP, solve the linearized objective and constraints according to the following equations:

<math>min</math> <math>a</math>

<math>s.t.</math> <math>a \leqslant UB^0 </math>

<math>f(x^0,y^0) +</math> <math>\nabla\ f(x^0,y^0)^T</math> <math>\binom{x-x^0}{y-y^0} </math> <math>\leqslant</math> <math>a</math>

<math>g(x^0,y^0) +</math> <math>\nabla\ g(x^0,y^0)^T</math> <math>\binom{x-x^0}{y-y^0} </math> <math>\leqslant</math> <math>0</math>

<math>y \in</math> {0,1}

The solution to the MILP will yield a new set of <math>(x)</math> and <math>(y)</math>. Call these the new <math>(x^0)</math> and <math>(y^0)</math>; this is the '''root''' of the branch and bound search tree.

===Solve Nodes===
4. Select an unsolved node
'''If''' no nodes are left,
'''then''' the problem is solved and <math>Z(x^j, y^j)</math> is the optimal solution.

5. Solve MILP (formulation below)
'''If''' all <math>y^k</math> = {0,1}
This node is the new incumbent
'''and''' Z obtained from this set of <math>x^k</math> and <math>y^k</math> is the current optimal solution.
'''and''' add linearizations of the objective and constraints
using <math>x^k</math> and <math>y^k</math> to each unsolved node according to the equation below.
Go to step 6.
'''Else''' a <math>y^k</math> ∉ {0,1}
Go to step 7.

Solve the corresponding MILP of the problem using the previous feasible solution <math>(x^j, y^j)</math> in the following form:

For the first node (excluding the root), <math>(x^j, y^j)</math> will be <math>(x^0, y^0)</math>, etc.

<math>min</math> <math>a</math>

<math>s.t.</math> <math>a \leqslant UB^j </math>

<math>f(x^j,y^j) +</math> <math>\nabla\ f(x^j,y^j)^T</math> <math>\binom{x-x^j}{y-y^j} </math> <math>\leqslant</math> <math>a</math>

<math>g(x^j,y^j) +</math> <math>\nabla\ g(x^j,y^j)^T</math> <math>\binom{x-x^j}{y-y^j} </math> <math>\leqslant</math> <math>0</math> <math>\forall j \in T</math>

where <math>T</math> is the set containing all indices of the solution tree in which the NLP for <math>y^j</math> is feasible.

<math>g(x^i,y^i) +</math> <math>\nabla\ g(x^i,y^i)^T</math> <math>\binom{x-x^i}{y-y^i} </math> <math>\leqslant</math> <math>0</math> <math>\forall i \in S</math>

where <math>S</math> is the set containing all indices of the solution tree in which the NLP for <math>y^i</math> is infeasible.

<math>\Gamma x + \Gamma y \leqslant \epsilon</math>

This constraint represents the Gomory cuts generated as the algorithm runs. This line decreases the feasible region of the original problem.

<math>y \in</math> {0,1}

The solution to this MILP will yield a new set <math>(x^k)</math> and <math>(y^k)</math>.

6. Solve relaxed NLP
Using the MILP solution <math>y^k</math>
This should result in a new solution <math>x^j</math> and <math>y^j = y^k</math>.
'''If''' NLP<math>(y^j)</math> is feasible
→ solve <math>Z(x^j, y^j)</math>.
'''If''' <math>Z(x^j, y^j)</math> is less than the previous upper bound
'''then''' this yields a new '''upper bound''' <math>UB^j</math> to the original problem.
Fathom all unsolved nodes that do not satisfy this bound.
Return to step 4
'''Else''' retain the old upper bound.
Return to step 4
'''Else''' NLP<math>(y^j)</math> is not feasible
→ Fathom node.
Return to step 4

===Cutting vs Branching===
When the solution to the linear relaxation in Step 5 contains fractional values on binary variables <math>y</math>, either a cutting plane should be generated to exclude that solution or branching can be done at that node to constrain the fractional variable to its binary values 0 or 1.

7. Calculate "skip factor"
'''If''' a cut is to be performed, go to step 8.
'''Else''' the cut is to be skipped, go to step 9.

The decision whether or not to perform a Gomory cut is based on a "skip factor" <math>S</math> which is calculated throughout the enumeration of the tree.

<math>S =</math> <math>min[S_{max}</math>, <math>\dfrac{t + wcd \log_{10} p}{t f}]</math>

where t = number of integer nodes solved

S_{max}, c, w = positive constant parameter

p = number of binary variables y

f = number of violated binary variables in <math>y^k</math>

===Gomory Cuts===
8. Generate an inequality to exclude the fractional variable solution

<<Equation 3. for gomory mixed integer cuts>>

Add these cuts to the constraints of the original problem.

Return to step 5

===Branching===
9. Constrain the/a variable in <math>y^k</math> to branch off of.

One branch will set <math>y^k = 0</math> and the other <math>y^k = 1</math>, creating two new nodes. Return to step 5, following one of these nodes.

=Variations=
A variation on the Branch and Cut method presented by Sven Leyffer in 2013 utilizes cuts for every fractional solution and branches only when solutions are still fractional after multiple cuts. 8 Thus, the algorithm is the same until step 7, where cuts are always chosen to eliminate solutions where <math>y^k</math> ∉ {0,1}. The inequality generated to produce this cut is added to the constraints of the original problem.

=Conclusion=
The general Branch and Cut algorithm follows a scheme which grows exponentially as variables are added to the original design problem. The addition of Gomory Cuts allows bounds to be tightened, reducing the number of feasible nodes to be tested and allowing the solver to converge on the optimal solution with less iterations. However, the formation of inequalities to generate these cuts take time and may slow down the actual resolution of the MINLP problem. The larger the problem, the more useful the cuts can be.

=References=

# I. Akrotirianakis, I. Maros, and B. Rustem. An Outer Approximation Based Branch and Cut Algorithm for convex 0-1 MINLP Problems. ''Optimization Methods and Software.'' 21:47, 2001 https://www.doc.ic.ac.uk/research/technicalreports/2000/DTR00-6.pdf
# S. Leyffer and J. Linderoth. Introduction to Integer Nonlinear Optimization, Nonlinear Branch-and-Cut, Theoretical and Computational Challenges. ''Argonne National Laboratory.'' 2007. http://science.energy.gov/~/media/ascr/pdf/workshops-conferences/mathtalks/Leyffer.pdf
# A. H. Land and A. G. Doig. An Automatic method of solving discrete programming problems. ''Econometrica,'' 28:497 520, 1960.
# R. J. Dakin. A tree search algorithm for mixed integer probramming problems. ''Computer Journal,'' 8:250 255, 1965.
# S. Albert. Solving Mixed Integer Linear Programs Using Branch and Cut Algorithm. ''Masters of Mathematics, North Carolina State University.'' 2006. http://www4.ncsu.edu/~kksivara/masters-thesis/shon-thesis.pdf (good for milp)
# J. E. Mitchell. Branch-and-Cut Algorithms for Combinatorial Optimization Problems. ''Mathematical Sciences,'' 1999. http://homepages.rpi.edu/~mitchj/papers/bc_hao.pdf
# M. Padberg and G. Rinaldi. A Branch-and-Cut Algorithm for the Resolution of Large-Scale Symmetric Traveling Salesman Problems. ''SIAM Rev,'' 33(1), 60-100, 1991. http://epubs.siam.org/doi/abs/10.1137/1033004?journalCode=siread
# S. Leyffer. Mixed-Integer Nonlinear Optimization: Applications, Algorithms, and Computation III. ''Graduate School, Universite catholique de Louvain.'' 2013. https://wiki.mcs.anl.gov/leyffer/images/4/42/Socn-3.pdf

Nonconvex generalized disjunctive programming (GDP)

2022-04-01T15:25:53Z

Asa273: Created page with "Author: Kaiwen Li (ChE345 Spring 2015) Steward: Prof.Fengqi You, Dajun Yue =Introduction= General disjunctive programming, GDP, is an alternative approach to repre..."

Author: Kaiwen Li (ChE345 Spring 2015) 
Steward: Prof.Fengqi You, Dajun Yue
 
=Introduction=
General disjunctive programming, GDP, is an alternative approach to represent the formulation of traditional Mixed-Integer Nonlinear Programming, solving discrete/continuous optimization problems. By using algebraic constraints, disjunctions and logic propositions, Boolean and continuous variables are involved in the GDP formulation. The formulation process of GDP problem are more intuitive, and the underlying logic structure of the problem can be kept, so that solution can be found more efficiently. GDP has been successfully applied to Process Design and Planning and Scheduling areas. 
 
However, funtions in GDP problem sometimes could be nonconvex. Due to nonconvexites, conventional MINLP algorithms are often trapped in suboptimal solutions. Thus, solutions to nonconvex GDP has been receiving increasing attention. 

=Algorithm=
In the GDP formulation, some functions might be nonconvex, which will lead to a nonconvex GDP problem. Traditional algorithms for MINLP such as Generalized Benders Decomposition (GBD), or Outer Approximation (OA) will fail to provide a global optimum because the solution of the NLP subproblem can be only a local optimum, while the cuts in master problem may not be valid either. Therefore, in order to get a global optimum, we need to introduce special algorithm for nonconvex GBD problems. 
Most of the methods rely on spatial branch and bound method.

==Motivation==
In order to find the best design and operation of a system in many problems in engineering, a set of algebraic expressions are used to reduce the problem with continuous and discrete variables. Normally theses problems lead to Mixed-Integer Nonlinear Programming (MINLP). However, in order to represent the behavior of physical, chemical, biological, financial or social systems accurately, nonlinear expressions are often used and leads to a MINLP with a nonconvex solution space. Instead of reaching a global optimal, this may give rise to local solutions that are suboptimal. Meanwhile, most algorithms for nonconvex problems are just particular implementation of the spatial branch and bound framework. Therefore, in order to find the global optimum of a large-scaled nonconvex MINLP models in reasonable computational time, Grossmann and others proposed nonconvex generalized disjunctive programming method.

==General Formulation for GDP==
Consider the following Generalized Disjunctive Programming problem, which includes Boolean variables, disjunctions and logic propositions: 
<math>min Z</math> <math>=</math> <math>\sum_{k\in K} c_k</math> <math>+ f(x)</math> 
 
s.t. <math>r(x)\le 0</math> 
 
<math>\bigvee_{j\in J_k}</math> <math>\begin{bmatrix} Y_{jk} \\ g_{jk}(x) \le 0 \\ c_k = \gamma_{jk} \end{bmatrix}</math>, <math> k\in K</math> 
 
<math>\Omega(Y) = True </math> 
 
<math>0 \le x \le U</math> 
 
<math>x \in R^n</math>, <math> c_k \in R^1</math>, <math> Y_{jk} \in {true, false}</math> 
 

where, <math>f:R^n \rightarrow R^1</math> is a function of the continuous variables x in the objective function, <math>g:R^n \rightarrow R^1</math> bolongs to the set of global constraints, the disjuctions <math> k\in K</math> are composed of a number of terms <math> j\in J_k</math>, which is connected by the OR operator. <math>Y_{jk}</math> is a Boolean varibale, <math>g_{jk}(x) \le 0</math> is a set of inequalities, and <math>c_k</math> is a cost variable. When <math>Y_{jk}</math> is true, <math>g_{jk}(x) \le 0</math> and <math>c_k</math> are enforced.Also, <math>x</math>represents continuous variables, with lower and upper bounds.Each term in the disjunctions gives rise to a nonempty feasible region which is generally nonconvex. Also, <math>\Omega(Y) = True </math> are logic propositions for the Boolean variables. 

==Overall Procedure==
The following flowchart(Fig.1) shows the overall procedure of the proposed two-level branch and bound algorithm.
[[File:Flowchart01_KL.png|600px]] 
First, introduce convex underestimators in the non-convex GDP problem (P), and construct the underestimating problem (R). This convex GDP problem is then reformulated as the convex NLP problem (CRP) by using the convex hull relaxation of each disjunction, which generates valid lower bound. Initial upper bound is obtained in step 0, by sloving P-MIP problem. It is a MINLP reformulation of the nonconvex GDP by a standard MINLP method. Then, use upper bound for bound contraction to reduce the feasible region, which is solved as a Bound Contraction Problem (BCP) in step 1. Next in step 2, discrete branch and bound method is applied at the first level to slove problem (CRP). After fixing all Boolean variables, solve the corresponding nonconvex NLP problems for a upper bound by using spatial branch and bound at the second level. Then, problem (CRP) is solved with fixed discrete choice in step 3.

==Detailed Formulation and Models==
===Convex Relaxation of GDP===
The following reformulation shows the introduction of valid convex underestimating functions to change Problem (P) into a convex GDP problem. 
 
<math>min Z^R</math> <math>=</math> <math>\sum_{k\in K} c_k</math> <math>+ \bar{f}(x)</math> 
 
s.t. <math>\bar{r}(x)\le 0</math> 
 
<math>\bigvee_{j\in J_k}</math> <math>\begin{bmatrix} Y_{jk} \\ \bar{g}_{jk}(x) \le 0 \\ c_k = \gamma_{jk} \end{bmatrix}</math>, <math> k\in K</math> 
 
<math>\Omega(Y) = True </math> 
 
<math>0 \le x \le U</math> ,<math>c_k \ge 0</math>
 
<math>x \in R^n</math>, <math>c_k \in R^1</math>, <math> Y_{jk} \in \{ true, false\} </math> 
 
where <math>\bar{f}</math>,<math>\bar{r}</math>,<math>\bar{g}</math> are valid convex underestimators so that <math>\bar{f}(x) \le f(x)</math>, <math>\bar{r}(x) \le 0</math>,<math>\bar{g}(x) \le 0</math> are satisfied if <math>r(x) \le 0</math>,<math>g(x) \le 0</math> (see fig.2) 
[[File:Fig02_KL.png|450px]] 
Considering problem (R) is a convex GDP, by replacing each disjunction by its convex hull we can relax problem (R), which generates the folloing convex NLP model: 
 
<math>min Z^L</math> <math>=</math> <math>\sum_{k\in K}\sum_{j\in J_k} \gamma_{jk}\lambda_{jk} + \bar{f}(x)</math> 
 
s.t. <math>\bar{r}(x)\le 0</math> 
 
<math> x = \sum_{j \in J_k} \nu_{jk}, \sum_{j \in J_k} \lambda_{jk} = 1, k\in K</math> 
 
<math> 0 \le \nu_{jk} \le \lambda_{jk}U_{jk}, j \in J_k, k\in K</math> 
 
<math> \lambda_{jk}\bar{g}_{jk}(\nu_{jk}/\lambda_{jk}) \le 0, j \in J_k, k\in K</math> 
 
<math> A\lambda \le a </math>
 
<math>0 \le x, \nu_{jk} \le U, 0 \le \lambda_{jk} \le 1, j \in J_k, k\in K, (CRP)</math> 
 
where <math>\nu_{jk}</math> is the disaggregated continuous variable for the <math>j </math>th term in the <math>k </math>th disjunction and <math>\lambda_{jk}</math> is the corresponding multiplier for each term <math>j \in J_k</math> in a given disjunction <math>k\in K</math> 
Given the problem (R) yields a lower bound, the problem (CRP) is a relaxation of problem (R).

===Global Upper Bound Subproblem===
This is step is to obtain a valid upper bound for problem (P) based on MINLP reformulation of (P) using big-M formulation.
 
<math>min Z = \sum_{k\in K}\sum_{j\in J_k} \gamma_{jk}y_{jk} + f(x)</math> 
 
s.t. <math>r(x)\le 0</math> 
 
<math>g_{jk}(x) \le M_jk(1-y_jk), j \in J_k, k\in K</math> 
 
<math> x = \sum_{j \in J_k} y_{jk}= 1, k\in K</math> 
 
<math> Ay \le a </math>
 
<math>0 \le x \le U, y_{jk} \in \{0,1\}, j \in J_k, k\in K, (P-MIP)</math> 
 
where <math>M_jk</math> is the big-M parameter, which provides a valid upper bound to the violation of <math>g_jk \le 0</math> and <math>U</math> is an upper bound to <math>x</math>.

===Bound Contraction Procedure===
The bound contraction scheme is designed to tighten the lower and upper bound of a given continuous variable <math>x_i</math>, which will eliminate the nonoptimal subregions and accelerate the search. This will greatly reduce the difference between lower and upper bounds of the objective function and save computational work. 
The contraction scheme is shown by the following NLP problem: 
 
<math>min/max </math> <math>x_i </math> 
 
s.t. <math>\sum_{k\in K}\sum_{j\in J_k} \gamma_{jk}\lambda_{jk} + \bar{f}(x)r(x)\le GUB</math> 
 
<math>\bar{r}(x) \le 0 </math> 
 
<math> x = \sum_{j \in J_k}\nu_{jk}, \sum_{j \in J_k}\lambda_{jk}= 1, k\in K</math> 
 
<math> 0 \le \nu_{jk} \le \lambda_{jk}U_{jk},j \in J_K, k \in K</math> 
 
<math> \lambda_{jk}\bar{g}_{jk}(\nu_{jk}/\lambda_{jk}) \le 0, j \in J_k, k\in K</math> 
 
<math> Ay \le a </math>
 
<math>0 \le \nu^{jk} \le U, 0 \le \lambda_{jk} \le 1, j \in J_k, k\in K, (BCP)</math> 
 
As is shown in the following Fig.3, if the solution point <math>x_i</math> of problem (CRP) does not lie at its bound, then we solve the NLP problem (CRP) and update the upper and lower bounds based on the relative distance from the solution to each bound of to decide the direction of bound contraction. Bound contraction is applied to only the continuous variables. Not much reduction will be made if the contraction is not successful, and then move to next variable. 
[[File:Fig03_KL.png|300px]] 
===Branch and Bound on Boolean Variables===
This step is where branch and bound method is applied in the space of the terms of the disjunctions by solving the relaxed convex NLP problem (CRP) at each node. The rule is to select the variable <math>\lambda_{jk}</math> with the largest fractional value in the solution. By creating two child nodes with <math>\lambda_{jk}=1</math> and <math>\lambda_{jk}=0</math>, <math>Y_{jk}</math> is fixed in problem (R) respectively. The nodes number should be finite due to finite Boolean variables and the global lower bound increases monotonically. 
Upper bound needs to be updated when there is a gap between the solution of this problem and the original nonconvex GDP problem (P). When the feasible solution to problem (R) is obtained and the gap between nonconvex term and convex underestimator in problem (P) and problem (R) is nonzero, all Boolean variables should be fixed and Spatial Branch and Bound Method should be introduced. 

===Spatial Branch and Bound Method===
Since there is a specific wiki page introducing this method, there is no need to discuss the detailed algorithm here. In this case, by solving problem (CRP), the nonconvex term with the max gap is chosen. Then, choose the middle point of the variable bound as the branching point. Lastly, select the node with lowest objective value. The current node will be fathomed if the lowest objective value of the node is greater than GUB.
==Advantages and Disadvantages==
===Advantages===
Many application shows that tighter lower bounds can be obtained in bilinear and concave problems by applying basic Nonconvex GDP steps, which often leads to a significant reduction of the numbers of nodes in Spatial Branch and Bound method. This is a direct indication of achieving tightening bounds. 
Meanwhile, GDPs are often reformulated as an MINLP, which enables us to take advantages of the existing MINLP solvers.

===Disadvantages===
The main problem about this method is that the question how to efficiently implement the strong relaxations within a spatial branch and bound framework in a large scale system still cannot be answered.

=Applications and Examples=
==Application: Solution Algorithm for nonconvex GDP problems==
===Step 0 Heuristic Search (Nonconvex MINLP)===
Use MINLP solvers (such as DICOPT++) to solve the nonconvex problem (P-MIP), and set GUB as the best upper bound and let <math>(Y^*,x*)</math> be the solution. 
===Step 1 Bound Contraction (Convex NLP)===
# Initialize the Relative Distance from <math>x^*_i</math> to each bound 
<math>RDL_i = \frac{x^*_i - x^L_i}{x^U_i - x^L_i}, RDU_i = \frac{x^U_i - x^*_i}{x^U_i - x^L_i}</math> 
# Increase iteration, solve problem (BCP) 
Update bound and continue with <math>x^*_i</math> when contraction is greater than <math>SP_M</math>. Otherwise select next x. 
# Return to 2 and repeat until max iteration. 
===Step 2 Branch and Bound on Discrete Variables (Convex NLP)===
# set tolerance <math>\alpha</math> for difference in <math>Z^L</math> and GUB. Set <math>\varepsilon</math> for max gap.
# Solve problem (CRP) to obtain lower bound <math>Z^L</math>. Update lowest lower bound as GLB.
# Fathom, go to step 3 or Branch on the node.
===Step 3 Spatial Branch and Bound (Convex NLP)===
# Fix all <math>\lambda_{jk}</math> according to solution from step 2
# Solve problem (CRP) until no open node with <math>Z^L \le GUB - \alpha</math>
# Go to step 2

==Example==
===Optimal structure for process system===
The system net work is shown in the following Fig4. 

[[File:Fig04_KL.png|thumb|left|450px|Fig4. Superstructure of the process]]
 

The formulation for this problem is shown as follows: 
<math> min Z =-35P1A - 30P2B +10F1 + 8F2 + F4A + F4B + 4F5A + 4F5B + 2CF + 50CD</math> 
 
<math>s.t. F3A = 0.55F1 + 0.5F2</math> 
 
<math>F3B = 0.45F1 + 0.5F2</math> 
 
<math>P1A = F8A + F10A + F6A </math> 
 
<math>P1B = F8B + F10B + F6B </math> 
 
<math>P2A = F9A + F11A + F7A</math> 
 
<math>P2B = F9B +F11B+F7B</math> 
 
<math>F6A=E6F3A,F6B=F6F3B</math> 
 
<math>F7A=E7F3A,F7B=E7F3B</math> 
 
<math>E4+D5+D6+D7 = 1</math> 
 
<math>P1A \ge 4.0P1B, P2B \ge 3.0P2A</math> 
 
<math>P1A+P1B \le 15, P2A +P2B \le 18</math> 
 

<math>\begin{bmatrix}
YF\\
F4A=E4F3A,F4B=E4F3B\\
2.5 \le F4A+F4B \le 25\\
F8A=0.85F4A, F8B=0.20F4B\\
F9A=0.15F4A,F9B=0.8F4B\\
CF=2
\end{bmatrix}</math>
<math>\or</math>
<math>\begin{bmatrix}
\lnot YF\\
F4A=F4B=0\\
F8A=F8B=0\\
F9A=F9B=0\\
E4=0\\
CF=0
\end{bmatrix}</math> 
 

<math>\begin{bmatrix}
YD\\
F5A=E5F3A,F5B=E5F3B\\
2.5 \le F5A+F5B \le 25\\
F10A=0.975F5A, F10B=0.050F5B\\
F11A=0.025F5A,F11B=0.950F5B\\
CD=25
\end{bmatrix}</math>
<math>\or</math>
<math>\begin{bmatrix}
\lnot YD\\
F5A=F5B=0\\
F10A=F10B=0\\
F11A=F11B=0\\
E5=0\\
CD=0
\end{bmatrix}</math>
 
<math>0 \le CF,CD; F1,F2 \le 25; 0 \le E4,E5,E6,E7 \le 1;</math> 
 
<math>Y\in \{true,false\}</math> 
 
The optimal solution is -510.08, and <math> F1^* = 8, F2^* = 25, P1^* = 15, P2^* = 18, E^* = (0.108,0.758,0,0.134)</math>, and <math>Y^*=(true,true)</math>, shown as the following Fig5. 
[[File:Fig05_KL.png|thumb|left|450px|Fig5. Optimal Solution]]
 

Here is the detailed explanation of the method applied in this example. Bilinear terms are replaced by continuous variables and linear underestimators and overestimators are introduced to construct the relaxed convex GDP problem (R). In step 0, which is mentioned above, DICOPT++ finds the trivial solution of <math>0.0</math> ath first NLP. By solving 14 LP subproblems in step 1, the bound is reduced <math>54.17%</math> for continuous variables. In step 2, discrete branch and bound on problem (CRP) reaches a feasible solution to the relaxed GDP at the third node, where <math>Y^L=(1,1)</math> and objective function of <math>-661.56</math>. When switches to Spatial Branch and Bound in step 3, <math>Y^F=(1,1)</math> is fixed. Then after 27 nodes and gap being reduced, upper bound is found to be <math>-510.08</math>. Using the upper bound to update GUB value in step 2, a cut to exclude <math>Y = (true,true)</math> is added to the previous node and the problem (CRP) is resolved, which leads to a infeasible solution. Then by closing current node and backtrack, two more nodes are searched and fathomed by the GUB.

=Conclusion=
For nonconvex generalized disjunctive programming, specified algorithm can provide a global optimum more efficiently by tightening the lower bound and reduce nodes in Spatial Branch and Bound step, compared with conventional MINLP and GBD algorithms. This method address the increasing need in applications in engineering and other area, where nonlinearity and nonconvexity are essential due to the problem nature.

=References=
# Lee, Sangbum, and Ignacio E. Grossmann. "New algorithms for nonlinear generalized disjunctive programming." Computers & Chemical Engineering 24.9 (2000): 2125-2141.
# Lee, Sangbum, and Ignacio E. Grossmann. "A global optimization algorithm for nonconvex generalized disjunctive programming and applications to process systems." Computers & Chemical Engineering 25.11 (2001): 1675-1697.
# Lee, Sangbum, and Ignacio E. Grossmann. "Global optimization of nonlinear generalized disjunctive programming with bilinear equality constraints: applications to process networks." Computers & chemical engineering 27.11 (2003): 1557-1575.
# Grossmann, Ignacio E., and Juan P. Ruiz. "Generalized Disjunctive Programming: A framework for formulation and alternative algorithms for MINLP optimization." Mixed Integer Nonlinear Programming. Springer New York, 2012. 93-115.

Classical robust optimization

2022-04-01T15:20:13Z

Asa273: Created page with "Author Names: Andre Ramirez-Cedeno Steward: Fengqi You, Dajun Yue ==Introduction and History== Robust optimization is a subset of optimization theory that deals..."

Author Names: Andre Ramirez-Cedeno 
Steward: Fengqi You, Dajun Yue 

==Introduction and History==
Robust optimization is a subset of optimization theory that deals with a certain measure of robustness vs uncertainty. This balance of robustness and uncertainty is represented as variability in the parameters of the problem at hand and or its solution [1]. In robust optimization, the modeler aims to find decisions that are optimal for the worst-case realization of the uncertainties within a given set [2]. Robust optimization dates back to the beginning of modern decision theory in the 1950’s. It became a discipline of its own in the 1970’s with paralleled development in other technological fields.

===Uncertainty===
Sources of uncertainty could be due to at least three different conditions [3]. 
'''1. Ignorance''' - such as not knowing exactly how much oil is in a reserve 
'''2. Noise''' - such as measurement errors, or incomplete data 
'''3. Events that have not yet occurred''' - such as future product demand 

===What is Robustness?===

Robustness refers to the ability of a system to cope with errors during an execution. It can also be defined as the ability of an algorithm to continue operating despite abnormalities in calculations. Most algorithms try to find a balance between robustness and efficiency/execution time [4].

==Applications==

Robust Optimization has traditionally been applied in statistics, but is now applied in; 

1. Operations research 
2. Control theory 
3. Finance and Portfolio management 
4. Logistics 
5. Manufacturing engineering 
6. Chemical engineering (Oil field developing) 
7. Medicine 
8. Computer science 

In engineering problems, these formulations often take the name of "Robust Design Optimization" or "Reliability Based Design Optimization"

==Simple Mathematical Example==

<math>
\begin{align}
\text{Max} & ~~ 5X + 2Y\\
\text{s.t} & ~~ cX + dY \le 15 \\
& ~~ X \le 0 \\
& ~~ Y \le 0\\
& ~~ \forall c,d \\
\end{align}
</math>

This problem is a simple example of a robust optimization problem. The last clause; “for all (c,d) ϵ P” makes it a robust optimization problem because it implies that for a pair (X,Y) to be acceptable, the constraint cX + dY <= 15 must be satisfied for all values of (c,d) including the worst (c,d) pair that maximized the value of cX + dY for the given values of (x,y). For this example, P is simplified to a finite set meaning that for each (c,d) within the set, there is a constraint cX + dY <= 15.

==Engineering Design Example==
===Rolls-Royce [5]===

Robust design allows variation in the design process and the consideration of the appropriate selection of the nominal design point.

'''Step 1:''' Define – Understand what is important to the client and formulate problem in engineering language. Choose design concepts with variation in mind. 

'''Step 2:''' Characterize – Generate measurable “critical to quality” (CTQ’s) criteria. For each CTQ, understand the possible sources of variation and measure the effects of variation. 

'''Step 3:''' Optimize – For each CTQ, choose a strategy to reduce the effects of variation. 

'''Step 4:''' Verify – Use knowledge of variation from previous steps to determine its effects in construction and design plan.

The Variance Transmission equation is given by: 

'''<math> \sigma_Y^2 </math> = <math> \sigma_{X1}^2 \left ( \frac{dY}{dX1} \right )^2 + \sigma_{X2}^2 \left ( \frac{dY}{dX2} \right )^2 + \cdots + \sigma_{Xn}^2 \left ( \frac{dY}{dXn} \right )^2</math>'''

[[File:Rolls_Royce_robust_design.png]]

==References==

[1] Wikipedia page for Robust Optimization 
[2] http://www.robustopt.com/references/Robust%20Optimization%20Made%20Easy%20with%20ROME.pdf 
[3] J. Rosenhead. Robustness analysis: keeping your options open. In J. Rosenhead, editor, Rational analysis for a problematic world: problem structuring methods for complexity, uncertainty and conflict, pages 193–218, Chichester, UK, 1989. John Wiley & Sons. 
[4] http://www.stanford.edu/~bakerjw/Publications/Baker%20et%20al%20(2008)%20Robustness,%20Structural%20Safety.pdf 
[5] http://web.stanford.edu/group/uq/events/optimization/2011/3-rollsroyce.pdf

Data driven robust optimization

2022-04-01T15:18:39Z

Asa273:

Author: Watson Fu (ChE 345 Spring 2015)

Steward: Dajun Yue, Fengqi You

= Background =

Robust optimization is a distinct approach to optimizations problems that allows for the incorporation of uncertainty. The usefulness of robust optimization lies in the ability to solve for every realization of the uncertain parameters. As a result, the problem can be solved for the worst-case scenarios of the entire set of uncertainty.1 The most vital aspect of robust optimization is the determination of the uncertainty set. As an uncertainty set grows, it will be able to undertake more realizations. The drawback from assuming a large uncertainty set is the concern of the overall optimization problem becoming computationally intractable. At the same time, a small uncertainty set will yield an answer that is conservative and ignorant of aspects of the uncertainty.2 The general concepts and usage of robust optimization are now being shifted because of the availability and shear volume of data for every aspect of life.3
 

From complex supply chains to internet user preferences, these data is forcing change in how robust optimization problems are being approached. The existence of these data can eliminate the need for unproven assumptions and reasoning, which were previously needed in many robust optimization problems in order to make the problems tractable.2

= Description =

Data-driven optimization has already been studied and implemented in various systems, but many of these studies are divergent. The basic principle that ties together varying applications of data-driven optimization is the concept of defining uncertainty through data analysis. For example, take a particular parameter or set, <math>\mathbf{u}</math> with uncertainty. This set, <math>\mathbf{u}</math> will be defined as a random variable with probability distribution <math>P</math>. Data-driven optimization is centered around using pertinent data and analysis of data to help define the probability distribution <math>P</math>.3 If the probability distribution of a certain random variable can be realized, it can lead to a more complex analysis of a given problem.

= Methodology and Formulation =

The crux of data-driven robust optimization is the incorporation of hypothesis testing and statistical methods to help design uncertainty sets. 4. The basic definition of the problem can be seen in this linear constraint:

<math>

\mathbf{u}^Tx\leq b\quad \forall \mathbf{u} \in U

</math>

The constraint <math>\mathbf{u}</math> is a robust constraint because it is uncertain. As mentioned before, the probability distribution of <math>\mathbf{u}</math> will be called <math>P</math> and it is unknown and the focus of any data-driven robust optimization problem. It is also important to define a probability, <math>\delta</math>, for a particular set <math>U</math>:

<math>

P(\mathbf{u}^Tx\leq b\quad \forall \mathbf{u})\geq 1-\delta

</math>

This statement defines the probability <math>\delta</math> as the probabilistic guarantee with respect to the given probability distribution <math>P</math> with level <math>\delta</math>.

These definitions are part of every instance of data-driven robust optimization, but the design of the uncertainty set and the probability distribution is different. These nuanced differences in the specific design of the sets can be changed depending on the data available and the characteristics of the optimization problem.

== Different Constructions of Uncertainty Sets ==

The choice of construction of the uncertainty set is dependent on data available and properties of the probability distribution. Each construction involves some hypothesis testing on the probability distribution <math>P</math>. It is useful to have a basic understanding of [http://en.wikipedia.org/wiki/Statistical_hypothesis_testing statistical hypothesis testing].

=== Uncertainty Sets from Discrete Distributions ===

In this specific definition of the uncertainty set, the main assumption is that the probability distribution <math>P</math> has a finite support that is known. For example, a Bernoulli distribution or a binomial distribution are common probability distributions with finite supports. This means that the set of probability is not zero-valued and can be discretized.

As a result, it is possible to use the Pearson's <math>X^2</math> test to aid in the construction of a viable probability distribution. In the Pearson's <math>X^2</math> test, a null hypothesis of <math>P = P_O</math> is defined.

Next, define a empirical probability distribution over the sample <math>p_i</math>, and a confidence level <math>\epsilon</math> at which the null hypothesis will be rejected.

It follows that the confidence region, by this definition, will be 
[[File:Conint.JPG|Conint.JPG]].

Consequently, the original set of uncertain parameters, <math>U</math> can be redefined as only containing the constraints whose probability distributions fall in the acceptable range <math>\epsilon</math>. This will redefine the uncertainty set and give a more relaxed feasible region, but maximizing the confidence in any optimal solution.

=== Uncertainty Sets from Independent Marginal Distributions ===

This construction of the uncertainty set is used for a probability distribution that has a continuous support. The marginal distribution <math>P^*</math> of any probability distribution <math>P_O</math> is the a certain subset that holds a specific probability that does not reference the other values of the set not accounted for in the particular subset. The reason why it is beneficial to consider independent marginal distributions when analyzing a probability distribution with a continuous support is because multivariate fit testing has not reached the capacity to holistically analyze the problem.5 Another common way to approach this problem is to discretize the continuous function so that the support now becomes a discrete function.

==== Utilization of Kolmogorov-Smirnov Test ====
[[File:robustopt.jpg|thumb|right|Development of a confidence region from an arbitrary function based on a Kolmogorov-Smirnov Test4]]

The Kolmogorov-Smirnov test is a generic fit test that will test two continuous samples for equality. This test will be applied in the same fashion as the Pearson's <math>X^2</math> test was utilized for the discrete variable case. It is important to note that there are some limitations to this model can be seen in its formulation because it is mostly utilized for univariate cases.4 This construction requires finding a confidence region for a certain marginal distribution <math>P^*</math> within the probability distribution <math>P</math>. There also needs to be a defined <math>\epsilon</math> at which the null hypothesis that <math>P^*</math> will be rejected. The use of the Kolmogorov-Smirnov test can grant a defined uncertainty set <math>U</math>, but it has the drawback of becoming ineffective at solving multivariate problems. As a result, sometimes data-driven robust optimization problems where the probability distribution of the uncertainty set has a continuous support are solved by converting it to a discrete support and solving by the aforementioned techniques for discrete distributions.5

= Applications =
== Applications in Chemical Engineering ==

Data-driven robust optimization is useful in chemical engineering because of the complexity of design problems. As a result, it can utilize characteristic properties of systematically collected data to optimize certain features of any given system. For example, data-driven robust optimization can be used in complex supply chain optimization problems. The benefit of data-driven robust optimization for supply chain problems is that behavior of suppliers and consumers can be modeled through historical demand data, and the data associated with past decisions.6

In chemical engineering, various operations and reactor systems can also be optimized through data-driven robust optimization. For these problems, data-driven robust optimization can aid in the isolation of complex relationships between given parameters. More importantly, these concepts can be used in a dynamic fashion in combination with various design of experiment techniques.7

=== Example: Reactor Design Optimization ===

Because of the nature of data-driven robust optimization, it requires large amounts of data, even for simple problems. Therefore, a case study for the robust optimization of a simple reversible reaction in batch reactor is presented.7 This is a given reaction for reactant A to product B. The goal of the case study is to maximize the production of B by modeling the problem and applying data-driven robust optimization techniques based on experimental results to try to reach a maximum.

The problem is modeled with certain set set of differential equations, and is constrained by physical requirements. The most notable aspect of this case study is how they implement data-driven optimization. The define an additional constraint of error based on defined factor to temperture. These factors effect is refined through ANOVA (Analysis of variance) and the error is made into a response surface model, and this is reevaluated in iterations of optimization.

== Applications in Finance ==

This form of robust optimization is also useful in portfolio management. While it is an inherent feature in data-driven robust optimization, variance analysis is also the focal point of portfolio management. The idea for any portfolio management approach is centered around maximizing returns while minimizing a risk function for that target return. Data-driven optimization allows for the combination of this generic approach with relationships between stocks and presents a far more robust solution. As an extension, variance and covariance matrices can also be analyzed through data-driven robust optimization.8

= Conclusion =

An important distinction between data-driven robust optimization and many other optimization problem is that it makes a probabilistic guarantee as opposed to making a claim about a deterministic optimal solution. This property of data-driven optimization yields applications in various fields.

Optimization is frequently shaped by a priori assumptions and reasonable estimates about certain features to simplify a problem.2 With data-driven optimization, these assumptions can be limited by data and statistical analysis that will give a more insightful solution. As more data becomes available, data-driven robust optimization will yield more precise and more illuminating solutions.

= References =

1. Bertsimas, Dimitris, Dessislava Pachamanova, and Melvyn Sim. "Robust linear optimization under general norms." Operations Research Letters 32.6 (2004): 510-516.

2. Bandi, Chaithanya, and Dimitris Bertsimas. "Tractable stochastic analysis in high dimensions via robust optimization." Mathematical programming 134.1 (2012): 23-70.

3. Zikopoulos, Paul, and Chris Eaton. Understanding big data: Analytics for enterprise class hadoop and streaming data. McGraw-Hill Osborne Media, 2011.

4. Bertsimas, Dimitris, Vishal Gupta, and Nathan Kallus. "Data-driven robust optimization." arXiv preprint arXiv:1401.0212 (2013).

5. Bertsimas, Dimitris, David B. Brown, and Constantine Caramanis. "Theory and applications of robust optimization." SIAM review 53.3 (2011): 464-501.

6. Ruo-zhen, Qiu, Ge Ru-gang, and Huang Xiao-yuan. "The Supply Chain Robust Coordination Strategy Based on Data-Driven Approach." E-Product E-Service and E-Entertainment (ICEEE), 2010 International Conference IEEE, 2010.

7. Georgakis, Christos. "Design of Dynamic Experiments: A Data-Driven Methodology for the Optimization of Time-Varying Processes." Industrial & Engineering Chemistry Research 52.35 (2013): 12369-12382.

8. Gilli, Manfred, Evis Këllezi, and Hilda Hysi. "A data-driven optimization heuristic for downside risk minimization." Swiss Finance Institute Research Paper 06-2 (2006).

2021 Cornell Optimization Open Textbook Feedback

2021-12-19T14:01:05Z

Asa273: /* Adagrad */

== [[Lagrangean duality|Lagrangian duality]] ==
* Theory, methodology, and/or algorithmic discussions
# The Lagrangian variables associated with equality constraints h(x) are unbounded but the Lagrangian dual problem states them as non-negative. Please fix the same.

* At least one numerical example
# Please update the dual objective function and domain of dual variables accordingly.
== [[Disjunctive inequalities|Disjunctive Inequalities]] ==
==[[Stochastic programming|Stochastic Programming]]==

* An introduction of the topic
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
* Theory, methodology, and/or algorithmic discussions
# The inline notations (`x1`, `s1`) should also be typed using LaTex.

==[[Exponential transformation|Exponential Transformation]]==
== [[Portfolio optimization|Portfolio Optimization]] ==

* Theory, methodology, and/or algorithmic discussions
# Rephrase “Cut the relevant information and conditions in the portfolio optimization, as well as the final requirements into the relevant variables, constraints and linear functions of the linear programming problem.”
* At least one numerical example
# Fix misspelling “dolling decision variables”.
* A section to discuss and/or illustrate the applications

* A conclusion section
# Need some commas here (second sentence hard to read).
* References
# Remove white space between end of sentences and reference numbers.

== [[Chance-constraint method|Chance constraint method]] ==

* Theory, methodology, and/or algorithmic discussions
# Some normal text was expressed as equation.
== [[Bayesian Optimization]] ==
* Theory, methodology, and/or algorithmic discussions
# Consider italicizing keywords rather than bolding.
# Please add a citation to the first sentence.
# Avoid pronouns such as “we”.
# Acquisition function figure could be made larger and clearer to improve readability.
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* References
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== [[Conjugate gradient methods]] ==
* Theory, methodology, and/or algorithmic discussions
# All equations need to be better formatted.
# Please properly format pseudocode.
* A conclusion section
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== [[Geometric programming|Geometric Programming]] ==

== [[Adam]] ==

* Theory, methodology, and/or algorithmic discussions
# Avoid inserting inline citations after words like “This article..” as it is a bit informal. This could be rephrased or changed to something like “According to author,^[2] …” with author name inserted.
== [[A-star algorithm|a* algorithm]] ==

* An introduction of the topic:
# Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.
# There are no citations in the introduction. Please cite every source.
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# The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.
== [[Job shop scheduling|Job-Shop Scheduling Problem]] ==

* Theory, methodology, and/or algorithmic discussions

# Since this Wiki focuses on jobshop scheduling, at least two methods are expected. Branch and bound is a general MILP technique, so, it is recommended to add a tailored technique that can only solve specific jobshop scheduling problems. Solving the numerical example with this technique is not necessary.
== [[Optimization in game theory]] ==

* Theory, methodology, and/or algorithmic discussions
# Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm.
# Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.
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== [[Trust-region methods]] ==
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# Avoid pronouns such as “we”. This goes for all other sections as well.

* Theory, methodology, and/or algorithmic discussions
# Organization of ideas in this section needs work.
# Please format the algorithm in proper algorithmic pseudocode format.

== [[Momentum]] ==
== [[Stochastic dynamic programming|Stochastic Dynamic programming]] ==
== [[Outer-approximation (OA)|Outer-approximation]] ==

* Theory, methodology, and/or algorithmic discussions
# “Minimize” and “subject to” should be “min” and “s.t.” in MathType (inconsistent formatting)

== [[Unit commitment problem]] ==

* At least one numerical example
# Fix typo “while minimize” to “while minimizing”.
== [[Frank-Wolfe]] ==
== [[Line search methods|Line Search Method]] ==

* Theory, methodology, and/or algorithmic discussions
# Avoid pronouns such as “we” (all sections).
== [[Piecewise linear approximation|Piecewise Linear Approximation]]==
== [[Mathematical programming with equilibrium constraints|Mathematical Programming with Equilibrium constraints]] ==

== [[Wing shape optimization|Wing shape Optimization]] ==

* At least one numerical example
# A numerical example is simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments). There is an Application section where you discuss the applications.
* A section to discuss and/or illustrate the applications

* A conclusion section
# These variables should be defined before the conclusion section, they are out of place here.
* References
# Include hyperlinks to references if possible.

== [[Interior-point method for NLP|Interior point method for NLP]] ==

* Theory, methodology, and/or algorithmic discussions
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== [[Branch and bound (BB) for MINLP|Branch and Bound for MINLP]] ==

* At least one numerical example

# Please show a step-by-step solution in the example. The solution is incomplete. The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).

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2021 Cornell Optimization Open Textbook Feedback

2021-12-19T14:00:49Z

Asa273: /* Outer-approximation */

== [[Lagrangean duality|Lagrangian duality]] ==
* Theory, methodology, and/or algorithmic discussions
# The Lagrangian variables associated with equality constraints h(x) are unbounded but the Lagrangian dual problem states them as non-negative. Please fix the same.

* At least one numerical example
# Please update the dual objective function and domain of dual variables accordingly.
== [[Disjunctive inequalities|Disjunctive Inequalities]] ==
==[[Stochastic programming|Stochastic Programming]]==

* An introduction of the topic
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
* Theory, methodology, and/or algorithmic discussions
# The inline notations (`x1`, `s1`) should also be typed using LaTex.

==[[Exponential transformation|Exponential Transformation]]==
== [[Portfolio optimization|Portfolio Optimization]] ==

* Theory, methodology, and/or algorithmic discussions
# Rephrase “Cut the relevant information and conditions in the portfolio optimization, as well as the final requirements into the relevant variables, constraints and linear functions of the linear programming problem.”
* At least one numerical example
# Fix misspelling “dolling decision variables”.
* A section to discuss and/or illustrate the applications

* A conclusion section
# Need some commas here (second sentence hard to read).
* References
# Remove white space between end of sentences and reference numbers.

== [[Chance-constraint method|Chance constraint method]] ==

* Theory, methodology, and/or algorithmic discussions
# Some normal text was expressed as equation.
== [[Bayesian Optimization]] ==
* Theory, methodology, and/or algorithmic discussions
# Consider italicizing keywords rather than bolding.
# Please add a citation to the first sentence.
# Avoid pronouns such as “we”.
# Acquisition function figure could be made larger and clearer to improve readability.
* At least one numerical example
# Please use the equation editor for min, st., etc.
# Avoid including a figure of the code for this example and explicitly describe the steps to the modeling and solution process instead.
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Conjugate gradient methods]] ==
* Theory, methodology, and/or algorithmic discussions
# All equations need to be better formatted.
# Please properly format pseudocode.
* A conclusion section
# Consider adding future research directions
== [[Geometric programming|Geometric Programming]] ==

== [[Adam]] ==

* Theory, methodology, and/or algorithmic discussions
# Avoid inserting inline citations after words like “This article..” as it is a bit informal. This could be rephrased or changed to something like “According to author,^[2] …” with author name inserted.
== [[A-star algorithm|a* algorithm]] ==

* An introduction of the topic:
# Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.
# There are no citations in the introduction. Please cite every source.
* Theory, methodology, and/or algorithmic discussions
# Please add the mathematical description of the algorithm. (Insufficient)
# Please fix grammatical and spelling errors as (“from current position to the goal”, “There are a lot of discussions”, etc). Also, many hyphens are missing as “non playable”.
* At least one numerical example
# The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.
== [[Job shop scheduling|Job-Shop Scheduling Problem]] ==

* Theory, methodology, and/or algorithmic discussions

# Since this Wiki focuses on jobshop scheduling, at least two methods are expected. Branch and bound is a general MILP technique, so, it is recommended to add a tailored technique that can only solve specific jobshop scheduling problems. Solving the numerical example with this technique is not necessary.
== [[Optimization in game theory]] ==

* Theory, methodology, and/or algorithmic discussions
# Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm.
# Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.
# Formatting (incomplete).
* References
# Incorrect reference style.

== [[Trust-region methods]] ==
* An introduction of the topic
# Avoid pronouns such as “we”. This goes for all other sections as well.

* Theory, methodology, and/or algorithmic discussions
# Organization of ideas in this section needs work.
# Please format the algorithm in proper algorithmic pseudocode format.

== [[Momentum]] ==
== [[Stochastic dynamic programming|Stochastic Dynamic programming]] ==
== [[Outer-approximation (OA)|Outer-approximation]] ==

* Theory, methodology, and/or algorithmic discussions
# “Minimize” and “subject to” should be “min” and “s.t.” in MathType (inconsistent formatting)

== [[Unit commitment problem]] ==

* At least one numerical example
# Fix typo “while minimize” to “while minimizing”.
== [[Frank-Wolfe]] ==
== [[Line search methods|Line Search Method]] ==

* Theory, methodology, and/or algorithmic discussions
# Avoid pronouns such as “we” (all sections).
== [[Piecewise linear approximation|Piecewise Linear Approximation]]==
== [[Mathematical programming with equilibrium constraints|Mathematical Programming with Equilibrium constraints]] ==

== [[Wing shape optimization|Wing shape Optimization]] ==

* At least one numerical example
# A numerical example is simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments). There is an Application section where you discuss the applications.
* A section to discuss and/or illustrate the applications

* A conclusion section
# These variables should be defined before the conclusion section, they are out of place here.
* References
# Include hyperlinks to references if possible.

== [[Interior-point method for NLP|Interior point method for NLP]] ==

* Theory, methodology, and/or algorithmic discussions
# Need discussion about the concept of “central path” and the notion of self concordance
# Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
# Fix typo “optimisation”.

== [[AdaGrad|Adagrad]] ==
* References
*# References not properly formatted
== [[McCormick envelopes|McCormick Envelopes]] ==

* Theory, methodology, and/or algorithmic discussions
# References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# The solution technique should be clearly presented, and solved "step-by-step".
* References
# Please follow the standard reference style - the current format is incorrect.

== [[Branch and bound (BB) for MINLP|Branch and Bound for MINLP]] ==

* At least one numerical example

# Please show a step-by-step solution in the example. The solution is incomplete. The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).

# This example does not follow the MINLP structure discussed in the above section since binary variables are missing. Branch and bound may not be appropriate for such problems. Please provide an appropriate numerical example and solve it according to the above comments.

* References
# Too few references overall, you should aggregate information from multiple sources. A quick Google scholar search could provide relevant references.
# Please follow the standard reference style - the current format is incorrect

2021 Cornell Optimization Open Textbook Feedback

2021-12-19T14:00:38Z

Asa273: /* Interior point method for NLP */

== [[Lagrangean duality|Lagrangian duality]] ==
* Theory, methodology, and/or algorithmic discussions
# The Lagrangian variables associated with equality constraints h(x) are unbounded but the Lagrangian dual problem states them as non-negative. Please fix the same.

* At least one numerical example
# Please update the dual objective function and domain of dual variables accordingly.
== [[Disjunctive inequalities|Disjunctive Inequalities]] ==
==[[Stochastic programming|Stochastic Programming]]==

* An introduction of the topic
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
* Theory, methodology, and/or algorithmic discussions
# The inline notations (`x1`, `s1`) should also be typed using LaTex.

==[[Exponential transformation|Exponential Transformation]]==
== [[Portfolio optimization|Portfolio Optimization]] ==

* Theory, methodology, and/or algorithmic discussions
# Rephrase “Cut the relevant information and conditions in the portfolio optimization, as well as the final requirements into the relevant variables, constraints and linear functions of the linear programming problem.”
* At least one numerical example
# Fix misspelling “dolling decision variables”.
* A section to discuss and/or illustrate the applications

* A conclusion section
# Need some commas here (second sentence hard to read).
* References
# Remove white space between end of sentences and reference numbers.

== [[Chance-constraint method|Chance constraint method]] ==

* Theory, methodology, and/or algorithmic discussions
# Some normal text was expressed as equation.
== [[Bayesian Optimization]] ==
* Theory, methodology, and/or algorithmic discussions
# Consider italicizing keywords rather than bolding.
# Please add a citation to the first sentence.
# Avoid pronouns such as “we”.
# Acquisition function figure could be made larger and clearer to improve readability.
* At least one numerical example
# Please use the equation editor for min, st., etc.
# Avoid including a figure of the code for this example and explicitly describe the steps to the modeling and solution process instead.
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Conjugate gradient methods]] ==
* Theory, methodology, and/or algorithmic discussions
# All equations need to be better formatted.
# Please properly format pseudocode.
* A conclusion section
# Consider adding future research directions
== [[Geometric programming|Geometric Programming]] ==

== [[Adam]] ==

* Theory, methodology, and/or algorithmic discussions
# Avoid inserting inline citations after words like “This article..” as it is a bit informal. This could be rephrased or changed to something like “According to author,^[2] …” with author name inserted.
== [[A-star algorithm|a* algorithm]] ==

* An introduction of the topic:
# Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.
# There are no citations in the introduction. Please cite every source.
* Theory, methodology, and/or algorithmic discussions
# Please add the mathematical description of the algorithm. (Insufficient)
# Please fix grammatical and spelling errors as (“from current position to the goal”, “There are a lot of discussions”, etc). Also, many hyphens are missing as “non playable”.
* At least one numerical example
# The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.
== [[Job shop scheduling|Job-Shop Scheduling Problem]] ==

* Theory, methodology, and/or algorithmic discussions

# Since this Wiki focuses on jobshop scheduling, at least two methods are expected. Branch and bound is a general MILP technique, so, it is recommended to add a tailored technique that can only solve specific jobshop scheduling problems. Solving the numerical example with this technique is not necessary.
== [[Optimization in game theory]] ==

* Theory, methodology, and/or algorithmic discussions
# Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm.
# Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.
# Formatting (incomplete).
* References
# Incorrect reference style.

== [[Trust-region methods]] ==
* An introduction of the topic
# Avoid pronouns such as “we”. This goes for all other sections as well.

* Theory, methodology, and/or algorithmic discussions
# Organization of ideas in this section needs work.
# Please format the algorithm in proper algorithmic pseudocode format.

== [[Momentum]] ==
== [[Stochastic dynamic programming|Stochastic Dynamic programming]] ==
== [[Outer-approximation (OA)|Outer-approximation]] ==

* Theory, methodology, and/or algorithmic discussions
*# “Minimize” and “subject to” should be “min” and “s.t.” in MathType (inconsistent formatting)
== [[Unit commitment problem]] ==

* At least one numerical example
# Fix typo “while minimize” to “while minimizing”.
== [[Frank-Wolfe]] ==
== [[Line search methods|Line Search Method]] ==

* Theory, methodology, and/or algorithmic discussions
# Avoid pronouns such as “we” (all sections).
== [[Piecewise linear approximation|Piecewise Linear Approximation]]==
== [[Mathematical programming with equilibrium constraints|Mathematical Programming with Equilibrium constraints]] ==

== [[Wing shape optimization|Wing shape Optimization]] ==

* At least one numerical example
# A numerical example is simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments). There is an Application section where you discuss the applications.
* A section to discuss and/or illustrate the applications

* A conclusion section
# These variables should be defined before the conclusion section, they are out of place here.
* References
# Include hyperlinks to references if possible.

== [[Interior-point method for NLP|Interior point method for NLP]] ==

* Theory, methodology, and/or algorithmic discussions
# Need discussion about the concept of “central path” and the notion of self concordance
# Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
# Fix typo “optimisation”.

== [[AdaGrad|Adagrad]] ==
* References
*# References not properly formatted
== [[McCormick envelopes|McCormick Envelopes]] ==

* Theory, methodology, and/or algorithmic discussions
# References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# The solution technique should be clearly presented, and solved "step-by-step".
* References
# Please follow the standard reference style - the current format is incorrect.

== [[Branch and bound (BB) for MINLP|Branch and Bound for MINLP]] ==

* At least one numerical example

# Please show a step-by-step solution in the example. The solution is incomplete. The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).

# This example does not follow the MINLP structure discussed in the above section since binary variables are missing. Branch and bound may not be appropriate for such problems. Please provide an appropriate numerical example and solve it according to the above comments.

* References
# Too few references overall, you should aggregate information from multiple sources. A quick Google scholar search could provide relevant references.
# Please follow the standard reference style - the current format is incorrect

2021 Cornell Optimization Open Textbook Feedback

2021-12-19T14:00:26Z

Asa273: /* Trust-region methods */

== [[Lagrangean duality|Lagrangian duality]] ==
* Theory, methodology, and/or algorithmic discussions
# The Lagrangian variables associated with equality constraints h(x) are unbounded but the Lagrangian dual problem states them as non-negative. Please fix the same.

* At least one numerical example
# Please update the dual objective function and domain of dual variables accordingly.
== [[Disjunctive inequalities|Disjunctive Inequalities]] ==
==[[Stochastic programming|Stochastic Programming]]==

* An introduction of the topic
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
* Theory, methodology, and/or algorithmic discussions
# The inline notations (`x1`, `s1`) should also be typed using LaTex.

==[[Exponential transformation|Exponential Transformation]]==
== [[Portfolio optimization|Portfolio Optimization]] ==

* Theory, methodology, and/or algorithmic discussions
# Rephrase “Cut the relevant information and conditions in the portfolio optimization, as well as the final requirements into the relevant variables, constraints and linear functions of the linear programming problem.”
* At least one numerical example
# Fix misspelling “dolling decision variables”.
* A section to discuss and/or illustrate the applications

* A conclusion section
# Need some commas here (second sentence hard to read).
* References
# Remove white space between end of sentences and reference numbers.

== [[Chance-constraint method|Chance constraint method]] ==

* Theory, methodology, and/or algorithmic discussions
# Some normal text was expressed as equation.
== [[Bayesian Optimization]] ==
* Theory, methodology, and/or algorithmic discussions
# Consider italicizing keywords rather than bolding.
# Please add a citation to the first sentence.
# Avoid pronouns such as “we”.
# Acquisition function figure could be made larger and clearer to improve readability.
* At least one numerical example
# Please use the equation editor for min, st., etc.
# Avoid including a figure of the code for this example and explicitly describe the steps to the modeling and solution process instead.
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Conjugate gradient methods]] ==
* Theory, methodology, and/or algorithmic discussions
# All equations need to be better formatted.
# Please properly format pseudocode.
* A conclusion section
# Consider adding future research directions
== [[Geometric programming|Geometric Programming]] ==

== [[Adam]] ==

* Theory, methodology, and/or algorithmic discussions
# Avoid inserting inline citations after words like “This article..” as it is a bit informal. This could be rephrased or changed to something like “According to author,^[2] …” with author name inserted.
== [[A-star algorithm|a* algorithm]] ==

* An introduction of the topic:
# Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.
# There are no citations in the introduction. Please cite every source.
* Theory, methodology, and/or algorithmic discussions
# Please add the mathematical description of the algorithm. (Insufficient)
# Please fix grammatical and spelling errors as (“from current position to the goal”, “There are a lot of discussions”, etc). Also, many hyphens are missing as “non playable”.
* At least one numerical example
# The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.
== [[Job shop scheduling|Job-Shop Scheduling Problem]] ==

* Theory, methodology, and/or algorithmic discussions

# Since this Wiki focuses on jobshop scheduling, at least two methods are expected. Branch and bound is a general MILP technique, so, it is recommended to add a tailored technique that can only solve specific jobshop scheduling problems. Solving the numerical example with this technique is not necessary.
== [[Optimization in game theory]] ==

* Theory, methodology, and/or algorithmic discussions
# Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm.
# Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.
# Formatting (incomplete).
* References
# Incorrect reference style.

== [[Trust-region methods]] ==
* An introduction of the topic
# Avoid pronouns such as “we”. This goes for all other sections as well.

* Theory, methodology, and/or algorithmic discussions
# Organization of ideas in this section needs work.
# Please format the algorithm in proper algorithmic pseudocode format.

== [[Momentum]] ==
== [[Stochastic dynamic programming|Stochastic Dynamic programming]] ==
== [[Outer-approximation (OA)|Outer-approximation]] ==

* Theory, methodology, and/or algorithmic discussions
*# “Minimize” and “subject to” should be “min” and “s.t.” in MathType (inconsistent formatting)
== [[Unit commitment problem]] ==

* At least one numerical example
# Fix typo “while minimize” to “while minimizing”.
== [[Frank-Wolfe]] ==
== [[Line search methods|Line Search Method]] ==

* Theory, methodology, and/or algorithmic discussions
# Avoid pronouns such as “we” (all sections).
== [[Piecewise linear approximation|Piecewise Linear Approximation]]==
== [[Mathematical programming with equilibrium constraints|Mathematical Programming with Equilibrium constraints]] ==

== [[Wing shape optimization|Wing shape Optimization]] ==

* At least one numerical example
# A numerical example is simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments). There is an Application section where you discuss the applications.
* A section to discuss and/or illustrate the applications

* A conclusion section
# These variables should be defined before the conclusion section, they are out of place here.
* References
# Include hyperlinks to references if possible.

== [[Interior-point method for NLP|Interior point method for NLP]] ==

* Theory, methodology, and/or algorithmic discussions
*# Need discussion about the concept of “central path” and the notion of self concordance
*# Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
*# Fix typo “optimisation”.
== [[AdaGrad|Adagrad]] ==
* References
*# References not properly formatted
== [[McCormick envelopes|McCormick Envelopes]] ==

* Theory, methodology, and/or algorithmic discussions
# References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# The solution technique should be clearly presented, and solved "step-by-step".
* References
# Please follow the standard reference style - the current format is incorrect.

== [[Branch and bound (BB) for MINLP|Branch and Bound for MINLP]] ==

* At least one numerical example

# Please show a step-by-step solution in the example. The solution is incomplete. The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).

# This example does not follow the MINLP structure discussed in the above section since binary variables are missing. Branch and bound may not be appropriate for such problems. Please provide an appropriate numerical example and solve it according to the above comments.

* References
# Too few references overall, you should aggregate information from multiple sources. A quick Google scholar search could provide relevant references.
# Please follow the standard reference style - the current format is incorrect

2021 Cornell Optimization Open Textbook Feedback

2021-12-19T13:59:40Z

Asa273: /* Stochastic Programming */

== [[Lagrangean duality|Lagrangian duality]] ==
* Theory, methodology, and/or algorithmic discussions
# The Lagrangian variables associated with equality constraints h(x) are unbounded but the Lagrangian dual problem states them as non-negative. Please fix the same.

* At least one numerical example
# Please update the dual objective function and domain of dual variables accordingly.
== [[Disjunctive inequalities|Disjunctive Inequalities]] ==
==[[Stochastic programming|Stochastic Programming]]==

* An introduction of the topic
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
* Theory, methodology, and/or algorithmic discussions
# The inline notations (`x1`, `s1`) should also be typed using LaTex.

==[[Exponential transformation|Exponential Transformation]]==
== [[Portfolio optimization|Portfolio Optimization]] ==

* Theory, methodology, and/or algorithmic discussions
# Rephrase “Cut the relevant information and conditions in the portfolio optimization, as well as the final requirements into the relevant variables, constraints and linear functions of the linear programming problem.”
* At least one numerical example
# Fix misspelling “dolling decision variables”.
* A section to discuss and/or illustrate the applications

* A conclusion section
# Need some commas here (second sentence hard to read).
* References
# Remove white space between end of sentences and reference numbers.

== [[Chance-constraint method|Chance constraint method]] ==

* Theory, methodology, and/or algorithmic discussions
# Some normal text was expressed as equation.
== [[Bayesian Optimization]] ==
* Theory, methodology, and/or algorithmic discussions
# Consider italicizing keywords rather than bolding.
# Please add a citation to the first sentence.
# Avoid pronouns such as “we”.
# Acquisition function figure could be made larger and clearer to improve readability.
* At least one numerical example
# Please use the equation editor for min, st., etc.
# Avoid including a figure of the code for this example and explicitly describe the steps to the modeling and solution process instead.
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Conjugate gradient methods]] ==
* Theory, methodology, and/or algorithmic discussions
# All equations need to be better formatted.
# Please properly format pseudocode.
* A conclusion section
# Consider adding future research directions
== [[Geometric programming|Geometric Programming]] ==

== [[Adam]] ==

* Theory, methodology, and/or algorithmic discussions
# Avoid inserting inline citations after words like “This article..” as it is a bit informal. This could be rephrased or changed to something like “According to author,^[2] …” with author name inserted.
== [[A-star algorithm|a* algorithm]] ==

* An introduction of the topic:
# Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.
# There are no citations in the introduction. Please cite every source.
* Theory, methodology, and/or algorithmic discussions
# Please add the mathematical description of the algorithm. (Insufficient)
# Please fix grammatical and spelling errors as (“from current position to the goal”, “There are a lot of discussions”, etc). Also, many hyphens are missing as “non playable”.
* At least one numerical example
# The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.
== [[Job shop scheduling|Job-Shop Scheduling Problem]] ==

* Theory, methodology, and/or algorithmic discussions

# Since this Wiki focuses on jobshop scheduling, at least two methods are expected. Branch and bound is a general MILP technique, so, it is recommended to add a tailored technique that can only solve specific jobshop scheduling problems. Solving the numerical example with this technique is not necessary.
== [[Optimization in game theory]] ==

* Theory, methodology, and/or algorithmic discussions
# Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm.
# Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.
# Formatting (incomplete).
* References
# Incorrect reference style.

== [[Trust-region methods]] ==
* An introduction of the topic
*# Avoid pronouns such as “we”. This goes for all other sections as well.

* Theory, methodology, and/or algorithmic discussions
*# Organization of ideas in this section needs work.
*# Please format the algorithm in proper algorithmic pseudocode format.
== [[Momentum]] ==
== [[Stochastic dynamic programming|Stochastic Dynamic programming]] ==
== [[Outer-approximation (OA)|Outer-approximation]] ==

* Theory, methodology, and/or algorithmic discussions
*# “Minimize” and “subject to” should be “min” and “s.t.” in MathType (inconsistent formatting)
== [[Unit commitment problem]] ==

* At least one numerical example
# Fix typo “while minimize” to “while minimizing”.
== [[Frank-Wolfe]] ==
== [[Line search methods|Line Search Method]] ==

* Theory, methodology, and/or algorithmic discussions
# Avoid pronouns such as “we” (all sections).
== [[Piecewise linear approximation|Piecewise Linear Approximation]]==
== [[Mathematical programming with equilibrium constraints|Mathematical Programming with Equilibrium constraints]] ==

== [[Wing shape optimization|Wing shape Optimization]] ==

* At least one numerical example
# A numerical example is simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments). There is an Application section where you discuss the applications.
* A section to discuss and/or illustrate the applications

* A conclusion section
# These variables should be defined before the conclusion section, they are out of place here.
* References
# Include hyperlinks to references if possible.

== [[Interior-point method for NLP|Interior point method for NLP]] ==

* Theory, methodology, and/or algorithmic discussions
*# Need discussion about the concept of “central path” and the notion of self concordance
*# Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
*# Fix typo “optimisation”.
== [[AdaGrad|Adagrad]] ==
* References
*# References not properly formatted
== [[McCormick envelopes|McCormick Envelopes]] ==

* Theory, methodology, and/or algorithmic discussions
# References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# The solution technique should be clearly presented, and solved "step-by-step".
* References
# Please follow the standard reference style - the current format is incorrect.

== [[Branch and bound (BB) for MINLP|Branch and Bound for MINLP]] ==

* At least one numerical example

# Please show a step-by-step solution in the example. The solution is incomplete. The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).

# This example does not follow the MINLP structure discussed in the above section since binary variables are missing. Branch and bound may not be appropriate for such problems. Please provide an appropriate numerical example and solve it according to the above comments.

* References
# Too few references overall, you should aggregate information from multiple sources. A quick Google scholar search could provide relevant references.
# Please follow the standard reference style - the current format is incorrect

2021 Cornell Optimization Open Textbook Feedback

2021-12-19T00:42:45Z

Asa273: /* Branch and Bound for MINLP */

2021 Cornell Optimization Open Textbook Feedback

2021-12-19T00:41:11Z

Asa273: /* Branch and Bound for MINLP */

2021 Cornell Optimization Open Textbook Feedback

2021-12-19T00:27:57Z

Asa273: /* Mathematical Programming with Equilibrium constraints */

2021 Cornell Optimization Open Textbook Feedback

2021-12-18T21:02:11Z

Asa273: /* Momentum */

== [[Lagrangean duality|Lagrangian duality]] ==
* Author list, sections and TOC
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions
# The Lagrangian variables associated with equality constraints h(x) are unbounded but the Lagrangian dual problem states them as non-negative. Please fix the same.

* At least one numerical example
# Please update the dual objective function and domain of dual variables accordingly.
* A section to discuss and/or illustrate the applications

* A conclusion section
* References

== [[Disjunctive inequalities|Disjunctive Inequalities]] ==
* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section

* References
==[[Stochastic programming|Stochastic Programming]]==

* An introduction of the topic
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
* Theory, methodology, and/or algorithmic discussions
** The symbol “xi” in the methodology subsection should be explained.
** The inline notations (`x1`, `s1`) should also be typed using LaTex.

* A section to discuss and/or illustrate the applications;
# I suggest eliminating citing the last name of the first author (i.e. Zhou et al.)
==[[Exponential transformation|Exponential Transformation]]==

* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section

* References
== [[Portfolio optimization|Portfolio Optimization]] ==

* Author list

* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions
# Rephrase “Cut the relevant information and conditions in the portfolio optimization, as well as the final requirements into the relevant variables, constraints and linear functions of the linear programming problem.”
* At least one numerical example
# Fix misspelling “dolling decision variables”.
* A section to discuss and/or illustrate the applications

* A conclusion section
# Need some commas here (second sentence hard to read).
* References
# Remove white space between end of sentences and reference numbers.

== [[Chance-constraint method|Chance constraint method]] ==

* Author list:
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions
# Some normal text was expressed as equation.
* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section

* References
== [[Bayesian Optimization]] ==
* Introduction
# Discussion on applications should be moved to a separate section.
* Theory, methodology, and/or algorithmic discussions
# Captions need reformatting.
# Consider italicizing keywords rather than bolding.
# Please add a citation to the first sentence.
# Avoid pronouns such as “we”.
# Acquisition function figure could be made larger and clearer to improve readability.
* At least one numerical example
# Any references to functions or methods in code ‘e.g. fmin’ should be properly formatted as code-stylized text.
# Please use the equation editor for min, st., etc.
# Avoid including a figure of the code for this example and explicitly describe the steps to the modeling and solution process instead.
# Avoid pronouns such as “our” and “we”.
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Conjugate gradient methods]] ==
* Theory, methodology, and/or algorithmic discussions
# All equations need to be better formatted.
# Please indent equation blocks.
# Please properly format pseudocode.
* A conclusion section
# Consider adding future research directions
== [[Geometric programming|Geometric Programming]] ==

* Author list

* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section:

* References

== [[Adam]] ==

* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions
# Avoid inserting inline citations after words like “This article..” as it is a bit informal. This could be rephrased or changed to something like “According to author,^[2] …” with author name inserted.
* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section
* References
== [[A-star algorithm|a* algorithm]] ==

* Author list
* An introduction of the topic:
# Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.
# There are no citations in the introduction. Please cite every source.
* Theory, methodology, and/or algorithmic discussions
# Please add the mathematical description of the algorithm. (Insufficient)
# Please fix grammatical and spelling errors as (“from current position to the goal”, “There are a lot of discussions”, etc). Also, many hyphens are missing as “non playable”.
* At least one numerical example
# The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.
* A section to discuss and/or illustrate the applications
* A conclusion section
* References

== [[Job shop scheduling|Job-Shop Scheduling Problem]] ==

* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

# Since this Wiki focuses on jobshop scheduling, at least two methods are expected. Branch and bound is a general MILP technique, so, it is recommended to add a tailored technique that can only solve specific jobshop scheduling problems. Solving the numerical example with this technique is not necessary.
* At least one numerical example
* A section to discuss and/or illustrate the applications
* A conclusion section
* References

== [[Optimization in game theory]] ==

* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions
# Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm.
# Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.
# Formatting (incomplete).
* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section
# Please add more summarizing especially from theory sentences and avoid long sentences.
* References
# Incorrect reference style.

== [[Trust-region methods]] ==
* An introduction of the topic
** Avoid pronouns such as “we”. This goes for all other sections as well.

* Theory, methodology, and/or algorithmic discussions
# Organization of ideas in this section needs work.
# You have not defined explicitly why the Cauchy point is important to compute beyond a vague allusion to performance improvements, which is also wrong (it is useful because of its guarantees for convergence, not performance) It is also misspelled.
# Please format the algorithm in proper algorithmic pseudocode format.
* References
# Incorrect reference style.

*There are numerous misspellings, grammatical errors, and incorrect claims. Please fix these.

== [[Momentum]] ==
* An introduction of the topic
* Theory, methodology, and/or algorithmic discussions
* At least one numerical example
* A section to discuss and/or illustrate the applications
* References

== [[Stochastic dynamic programming|Stochastic Dynamic programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Discussion on applications should be moved to a separate section.
* Theory, methodology, and/or algorithmic discussions
# Remove the grey box background of equations.
* At least one numerical example
* A section to discuss and/or illustrate the applications
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Outer-approximation (OA)|Outer-approximation]] ==

* An introduction of the topic
# See formatting guideline below
# Avoid opinionated statements such as “MINLP problems are usually the hardest to solve”.
# Rearrange the text such that the MINLP formulation is in the theory section and keep the introduction in words only.
* Theory, methodology, and/or algorithmic discussions
# Consider left aligning equations and optimization problem formulations by the “=”. See [[Stochastic programming|https://optimization.cbe.cornell.edu/index.php?title=Stochastic_programming]] for an example
# The sentence “The Outer-Approximation (OA) algorithm was first proposed by Duran and and Grossmann in 1986 to solve MINLP problems.” needs a reference.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# “Minimize” and “subject to” should be “min” and “s.t.” in MathType
* A section to discuss and/or illustrate the applications
# Does not explicitly point out why OA is applicable (and/or preferred) in these applications, rather than other MINLP approaches (show that the problem formulations are amenable to a solution approach through OA)
# The sentence “... an active research area and there exists a vast number of applications in fields such as engineering, computational chemistry, and finance.” needs references.
# Posting GAMS code on the page is generally inappropriate and discouraged. Please check with the TAs or me if you have a strong desire to post GAMS codes on the Wiki page. A typical textbook should not be limited to a specific software package. If the GAMS code must be posted, please also post ALL other software implementation versions, such as Pyomo and JuliaOPT, among others.
# Consider reformatting to make steps more readable. Inserting spaces and breaking down steps would help.
* A conclusion section
# Too short. Consider discussion on future research direction and discussion on uncertainty
# Please review abbreviations throughout the page. Why is MINLP redefined here? “Outer-Approximation is a well known efficient approach for solving convex mixed-integer nonlinear programs (MINLP)”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove "Template:Reflist"

== [[Unit commitment problem]] ==

* Author list
* An introduction of the topic
# Please expand the introduction and avoid discussions of examples or specific applications in this section.
# The sentence “Nonlinear, Non-convex programming optimization problem.” doesn’t make sense by itself and Non-convex shouldn’t be capitalized.
* Theory, methodology, and/or algorithmic discussions
# Figure/image format should be revised to better display the content.
# Uppercase characters are used randomly (e.g., “non-convex transmission Constraints”) . Please follow correct language conventions for sentence structure.
# Avoid inserting inline citations after words like “written in matrix form as equation [3]..” or “presented in [3]...” as it is a bit informal when you don’t explicitly name the subject. Also these two sentences are grammatically incorrect and appear to be missing an ending period and comma, respectively.
# Don’t say “written in matrix form as equation..” and just cite the reference, actually write out the equation.
# Properly label the figure in this section with a figure number and improve visibility by making it larger.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Label the figures in this section properly with figure numbers.
# Fix typo “while minimize” to “while minimizing”.
# Avoid pronouns such as “we”.
# Use the equation editor when typing equations.
# A numerical example is simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments). There is an Application section where you discuss the applications.
# The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).
* A section to discuss and/or illustrate the applications:
# I suggest changing the order of the subtitles here. For example, Single-Period Unit Commitment.
* A conclusion section
* References

== [[Frank-Wolfe]] ==

* Author list:
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications:
* A conclusion section

* References
== [[Line search methods|Line Search Method]] ==

* Author list
* An introduction of the topic
# Expand the introduction and avoid discussion on some of the specific steps in the solution process.
# Provide references here.
* Theory, methodology, and/or algorithmic discussions
# The phrase “are as follows” in the steepest descent method discussion needs to be followed by a colon.
# Rephrase “has a nice convergence theory” and cite a reference for this claim.
# Avoid pronouns such as “we”.
# Add citation after “.. proposed by Phillip Wolfe in 1969.”
# Figure 1 is between two sections. Please fix this issue.
* At least one numerical example:
# Add some space between iterations or subsection break
* A section to discuss and/or illustrate the applications:
# Too few references in this section.
# Last paragraph makes some claims without references.
* A conclusion section
* References
# References should be properly formatted. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Piecewise linear approximation|Piecewise Linear Approximation]]==

* Author list
* An introduction of the topic
# The content of this section is good, but there are some issues with sentence clarity and some other grammatical errors. Please revisit this section and make changes accordingly.
* Theory, methodology, and/or algorithmic discussions
# Fix typo “to force the x’ values become associated with”.
* At least one numerical example
* A section to discuss and/or illustrate the applications
# Please aim for a maximum average sentence length of ~25 words. Some of these longer sentences are hard to read.
* A conclusion section
# Expand the conclusion section to be longer than one sentence. The conclusion section to include a brief summary of what was discussed above, an emphasis on it’s significance, and a brief discussion of future extensions and research direction if applicable.
* References
# Include hyperlinks to sources when possible.

== [[Mathematical programming with equilibrium constraints|Mathematical Programming with Equilibrium constraints]] ==

* An introduction of the topic
# This section includes several terms like variational inequalities, constraint qualifications that were not discussed in the class. Please add a sentence to explain them before using them.
* Theory, methodology, and/or algorithmic discussions
# The meaning of parameter vector x is unclear. Please add more information or update if necessary.
# Equations and symbols in the PIPA subsection are not formatted correctly. Please use the same formatting for all equations, so they read as mathematical equations and not text. This goes for all other sections as well.
# Use equations instead of images to represent math programs and equations in the Implicit Descent and SQP subsection.
# Apart from the steps for each solution technique, please also add a few sentences that describe each method.
* At least one numerical example
# Please define the terms like NCP, MP before abbreviating them. Also try not to unnecessarily abbreviate simple terms.
# Equations should be typed by LaTex. Images for equations are unacceptable.
# GAMS code is strongly discouraged. Please solve the problem "step-by-step".
# The selected numerical example is fine but is directly solved with the MPEC solver in GAMS. Try to solve it manually like the homework/in-class problems step by step using the steps described in the previous section by choosing any of the methods.
# Avoid using figures in the equations (subject to etc)
* A section to discuss and/or illustrate the applications
# Add references to “power management, highway pricing, chemical process engineering, and traffic planning.”
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# This Wiki contains very few references. Please check the list below and run a quick Google (Scholar) search to identify relevant literature.

== [[Wing shape optimization|Wing shape Optimization]] ==

* Author list: Remove cornell ID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC. Any formatting issue will incur a penalty in the grading.
* An introduction of the topic
# The introduction is missing several references (e.g., “software packages like computational fluid dynamics..”, sentences containing things that aren’t common knowledge, performance claims, etc.)
# Avoid discussion involving finer details of subject methods in this section.
# In the titles, please change the font from bold to normal to have consistent formatting in the site. Same applies to box of content!
* Theory, methodology, and/or algorithmic discussions
# Properly cite the CFD package, don’t just include a link.
# Properly label the figure with a figure number.
# Consider removing white space between isolated sentences to improve readability.
* At least one numerical example
# If you’ve already defined an abbreviation (CFD), there is no need to define it again. Just use the abbreviation.
# Avoid pronouns such as “we” or “they”.
# Phrases like “under the following” need to be followed by a colon.
# Properly label the figure with a figure number and consider making them larger to improve visibility. Call the reader's attention to the figures in text by referencing the figure number.
# “As seen in the video below” is stated yet there are only images present and it may be initially unclear to the reader which figure is being referenced here.
# Avoid inserting inline citations like “[4] introduces an..” as it is a bit informal when you don’t explicitly name the subject.
# Don’t just cite the reference when discussing the problem formulation, explicitly write the model formulation and solution process using LaTex or equation visual editor.
# Your team should ideally create a numerical example independently. If you take a numerical example directly from a textbook, etc., you will need to get explicit permission from the author in writing and share that written permission with me.
# A numerical example is simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments). There is an Application section where you discuss the applications.
# The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).
* A section to discuss and/or illustrate the applications
# Some characters are randomly capitalized in this section.
* A conclusion section
# These variables should be defined before the conclusion section, they are out of place here. Also, please use normal text when explaining variables except for the variable symbol.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Interior-point method for NLP|Interior point method for NLP]] ==

* Theory, methodology, and/or algorithmic discussions
** Need discussion about the concept of “central path” and the notion of self concordance
** Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
** Fix typo “optimisation”.
== [[AdaGrad|Adagrad]] ==
* At least one numerical example
# In the first sentence, “..take the following numerical example” should be followed by a colon.
* A section to discuss and/or illustrate the applications
# This section is too short; include specific applications in which input features are sparse and Adagrad excels.
*
* References

# References not properly formatted

== [[McCormick envelopes|McCormick Envelopes]] ==

* Author list
* Sections
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions
# References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# The solution technique should be clearly presented, and solved "step-by-step".
* A section to discuss and/or illustrate the applications

* A conclusion section:
* References
# Please follow the standard reference style - the current format is incorrect.

== [[Branch and bound (BB) for MINLP|Branch and Bound for MINLP]] ==

* Author list:
** Remove NetIDS
** Please remove abbreviations from the title (i.e. BB).
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# Please cite sources appropriately: References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Introduction is very short for a well-recognized topic. Please expand significantly. You may refer to the Wiki examples to get an idea on writing the Introduction to a topic.
# An illustration might be useful here.
* Theory, methodology, and/or algorithmic discussions
# The algorithm described here considers only binary integer variables. However, MINLP problems may include non-binary integer variables too. Please update the method or provide a short description of the assumptions that the MINLP problem needs to satisfy in order for the presented technique to be applicable.
# Use linked citations please as the Wiki template above.
# Please provide steps in a more organized way. Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
# Step 2 is missing yet it is referenced in the text multiple times. Please address this in addition to the above comment.
# An illustration might be useful here as well.
# Please explain what a Gomory Cut is. If the topic is available on optimization.cb.cornell.edu, you can link it.
# The current equations seem to be simple text written in Italics. All mathematical symbols and equations should be formatted via LaTex.
# Please format the math programs with equations and notations using formulations in lecture notes as templates.
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# Please show a step-by-step solution in the example. The solution is incomplete. The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).
# Please use the equation editor for equations or mathematical symbols. - All mathematical symbols and equations should be formatted via LaTex - this is a learning objective of the Wiki assignment. You can find some useful links on converting your equations/symbols into LaTex code here: (<nowiki>https://optimization.cbe.cornell.edu/index.php?title=Help:Contents</nowiki>). Again, any formatting issue will incur a "compound" penalty in the grading.
# This example does not follow the MINLP structure discussed in the above section since binary variables are missing. Branch and bound may not be appropriate for such problems. Please provide an appropriate numerical example and solve it according to the above comments.
# Make sure your example is not taken from a book as that is strictly disallowed.
* A section to discuss and/or illustrate the applications
# This section is not well-formatted. Please provide 3 applications and explain each in a few sentences and how BB for MINLP could be used. Also, please eliminate having multiple sections (Application, Mathematical problem, industrial application). All these could be merged together.
# This section should be at least a paragraph to discuss relevant applications. Each application should be explicitly linked to the page topic. A few keywords do not meet the requirement at all.
* A conclusion section:
# The sentence is hard to understand "a scheme that grows exponentially because" please use a simple language. Is it also theoretically correct? It is also not mentioned and explained earlier. Thus, please avoid introducing new concepts or terms at the end.
# Please use summarizing sentences to describe earlier sections instead of introducing new concepts/discussion.
* References
# Too few references overall, you should aggregate information from multiple sources. A quick Google scholar search could provide relevant references.
# References are not expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please follow the standard reference style - the current format is incorrect.

2021 Cornell Optimization Open Textbook Feedback

2021-12-18T20:58:03Z

Asa273: /* Job-Shop Scheduling Problem */

== [[Lagrangean duality|Lagrangian duality]] ==
* Author list, sections and TOC
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions
# The Lagrangian variables associated with equality constraints h(x) are unbounded but the Lagrangian dual problem states them as non-negative. Please fix the same.

* At least one numerical example
# Please update the dual objective function and domain of dual variables accordingly.
* A section to discuss and/or illustrate the applications

* A conclusion section
* References

== [[Disjunctive inequalities|Disjunctive Inequalities]] ==
* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section

* References
==[[Stochastic programming|Stochastic Programming]]==

* An introduction of the topic
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
* Theory, methodology, and/or algorithmic discussions
** The symbol “xi” in the methodology subsection should be explained.
** The inline notations (`x1`, `s1`) should also be typed using LaTex.

* A section to discuss and/or illustrate the applications;
# I suggest eliminating citing the last name of the first author (i.e. Zhou et al.)
==[[Exponential transformation|Exponential Transformation]]==

* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section

* References
== [[Portfolio optimization|Portfolio Optimization]] ==

* Author list

* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions
# Rephrase “Cut the relevant information and conditions in the portfolio optimization, as well as the final requirements into the relevant variables, constraints and linear functions of the linear programming problem.”
* At least one numerical example
# Fix misspelling “dolling decision variables”.
* A section to discuss and/or illustrate the applications

* A conclusion section
# Need some commas here (second sentence hard to read).
* References
# Remove white space between end of sentences and reference numbers.

== [[Chance-constraint method|Chance constraint method]] ==

* Author list:
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions
# Some normal text was expressed as equation.
* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section

* References
== [[Bayesian Optimization]] ==
* Introduction
# Discussion on applications should be moved to a separate section.
* Theory, methodology, and/or algorithmic discussions
# Captions need reformatting.
# Consider italicizing keywords rather than bolding.
# Please add a citation to the first sentence.
# Avoid pronouns such as “we”.
# Acquisition function figure could be made larger and clearer to improve readability.
* At least one numerical example
# Any references to functions or methods in code ‘e.g. fmin’ should be properly formatted as code-stylized text.
# Please use the equation editor for min, st., etc.
# Avoid including a figure of the code for this example and explicitly describe the steps to the modeling and solution process instead.
# Avoid pronouns such as “our” and “we”.
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Conjugate gradient methods]] ==
* Theory, methodology, and/or algorithmic discussions
# All equations need to be better formatted.
# Please indent equation blocks.
# Please properly format pseudocode.
* A conclusion section
# Consider adding future research directions
== [[Geometric programming|Geometric Programming]] ==

* Author list

* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section:

* References

== [[Adam]] ==

* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions
# Avoid inserting inline citations after words like “This article..” as it is a bit informal. This could be rephrased or changed to something like “According to author,^[2] …” with author name inserted.
* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section
* References
== [[A-star algorithm|a* algorithm]] ==

* Author list
* An introduction of the topic:
# Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.
# There are no citations in the introduction. Please cite every source.
* Theory, methodology, and/or algorithmic discussions
# Please add the mathematical description of the algorithm. (Insufficient)
# Please fix grammatical and spelling errors as (“from current position to the goal”, “There are a lot of discussions”, etc). Also, many hyphens are missing as “non playable”.
* At least one numerical example
# The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.
* A section to discuss and/or illustrate the applications
* A conclusion section
* References

== [[Job shop scheduling|Job-Shop Scheduling Problem]] ==

* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

# Since this Wiki focuses on jobshop scheduling, at least two methods are expected. Branch and bound is a general MILP technique, so, it is recommended to add a tailored technique that can only solve specific jobshop scheduling problems. Solving the numerical example with this technique is not necessary.
* At least one numerical example
* A section to discuss and/or illustrate the applications
* A conclusion section
* References

== [[Optimization in game theory]] ==

* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions
# Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm.
# Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.
# Formatting (incomplete).
* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section
# Please add more summarizing especially from theory sentences and avoid long sentences.
* References
# Incorrect reference style.

== [[Trust-region methods]] ==
* An introduction of the topic
** Avoid pronouns such as “we”. This goes for all other sections as well.

* Theory, methodology, and/or algorithmic discussions
# Organization of ideas in this section needs work.
# You have not defined explicitly why the Cauchy point is important to compute beyond a vague allusion to performance improvements, which is also wrong (it is useful because of its guarantees for convergence, not performance) It is also misspelled.
# Please format the algorithm in proper algorithmic pseudocode format.
* References
# Incorrect reference style.

*There are numerous misspellings, grammatical errors, and incorrect claims. Please fix these.

== [[Momentum]] ==
* An introduction of the topic
# Apart from an explanation on momentum, it is necessary to briefly point out the limitations of SGD and why momentum could help with these limitations. Please update it accordingly.
# Remove bold on “Momentum”.
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
* Theory, methodology, and/or algorithmic discussions
#
# The definition of the update rule for SGD with momentum looks incorrect, specifically the first expression. Please fix it and also explain all the parameters used.
# Use LaTex code or equation editor to display all equations and variables (e.g., “W”, “V`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “you”.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step". Since writing all iterations is not feasible, at least present a few iterations for both cases.
# Please try to label the plots that explains what each line color means.
# Starting point for SGD with momentum is different in explanation and the table. Please fix the same.
* A section to discuss and/or illustrate the applications
# Please use correct terminology like “optimizing non-convex functions” and not “training non-convex models”.
* References
# Almost all references used are URLs. Please try to add journal/conference articles or books for references, instead of directly citing the URLs. Please check the list below and run a quick Google (Scholar) search to identify relevant literature.

== [[Stochastic dynamic programming|Stochastic Dynamic programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Discussion on applications should be moved to a separate section.
* Theory, methodology, and/or algorithmic discussions
# Remove the grey box background of equations.
* At least one numerical example
* A section to discuss and/or illustrate the applications
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Outer-approximation (OA)|Outer-approximation]] ==

* An introduction of the topic
# See formatting guideline below
# Avoid opinionated statements such as “MINLP problems are usually the hardest to solve”.
# Rearrange the text such that the MINLP formulation is in the theory section and keep the introduction in words only.
* Theory, methodology, and/or algorithmic discussions
# Consider left aligning equations and optimization problem formulations by the “=”. See [[Stochastic programming|https://optimization.cbe.cornell.edu/index.php?title=Stochastic_programming]] for an example
# The sentence “The Outer-Approximation (OA) algorithm was first proposed by Duran and and Grossmann in 1986 to solve MINLP problems.” needs a reference.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# “Minimize” and “subject to” should be “min” and “s.t.” in MathType
* A section to discuss and/or illustrate the applications
# Does not explicitly point out why OA is applicable (and/or preferred) in these applications, rather than other MINLP approaches (show that the problem formulations are amenable to a solution approach through OA)
# The sentence “... an active research area and there exists a vast number of applications in fields such as engineering, computational chemistry, and finance.” needs references.
# Posting GAMS code on the page is generally inappropriate and discouraged. Please check with the TAs or me if you have a strong desire to post GAMS codes on the Wiki page. A typical textbook should not be limited to a specific software package. If the GAMS code must be posted, please also post ALL other software implementation versions, such as Pyomo and JuliaOPT, among others.
# Consider reformatting to make steps more readable. Inserting spaces and breaking down steps would help.
* A conclusion section
# Too short. Consider discussion on future research direction and discussion on uncertainty
# Please review abbreviations throughout the page. Why is MINLP redefined here? “Outer-Approximation is a well known efficient approach for solving convex mixed-integer nonlinear programs (MINLP)”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove "Template:Reflist"

== [[Unit commitment problem]] ==

* Author list
* An introduction of the topic
# Please expand the introduction and avoid discussions of examples or specific applications in this section.
# The sentence “Nonlinear, Non-convex programming optimization problem.” doesn’t make sense by itself and Non-convex shouldn’t be capitalized.
* Theory, methodology, and/or algorithmic discussions
# Figure/image format should be revised to better display the content.
# Uppercase characters are used randomly (e.g., “non-convex transmission Constraints”) . Please follow correct language conventions for sentence structure.
# Avoid inserting inline citations after words like “written in matrix form as equation [3]..” or “presented in [3]...” as it is a bit informal when you don’t explicitly name the subject. Also these two sentences are grammatically incorrect and appear to be missing an ending period and comma, respectively.
# Don’t say “written in matrix form as equation..” and just cite the reference, actually write out the equation.
# Properly label the figure in this section with a figure number and improve visibility by making it larger.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Label the figures in this section properly with figure numbers.
# Fix typo “while minimize” to “while minimizing”.
# Avoid pronouns such as “we”.
# Use the equation editor when typing equations.
# A numerical example is simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments). There is an Application section where you discuss the applications.
# The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).
* A section to discuss and/or illustrate the applications:
# I suggest changing the order of the subtitles here. For example, Single-Period Unit Commitment.
* A conclusion section
* References

== [[Frank-Wolfe]] ==

* Author list:
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications:
* A conclusion section

* References
== [[Line search methods|Line Search Method]] ==

* Author list
* An introduction of the topic
# Expand the introduction and avoid discussion on some of the specific steps in the solution process.
# Provide references here.
* Theory, methodology, and/or algorithmic discussions
# The phrase “are as follows” in the steepest descent method discussion needs to be followed by a colon.
# Rephrase “has a nice convergence theory” and cite a reference for this claim.
# Avoid pronouns such as “we”.
# Add citation after “.. proposed by Phillip Wolfe in 1969.”
# Figure 1 is between two sections. Please fix this issue.
* At least one numerical example:
# Add some space between iterations or subsection break
* A section to discuss and/or illustrate the applications:
# Too few references in this section.
# Last paragraph makes some claims without references.
* A conclusion section
* References
# References should be properly formatted. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Piecewise linear approximation|Piecewise Linear Approximation]]==

* Author list
* An introduction of the topic
# The content of this section is good, but there are some issues with sentence clarity and some other grammatical errors. Please revisit this section and make changes accordingly.
* Theory, methodology, and/or algorithmic discussions
# Fix typo “to force the x’ values become associated with”.
* At least one numerical example
* A section to discuss and/or illustrate the applications
# Please aim for a maximum average sentence length of ~25 words. Some of these longer sentences are hard to read.
* A conclusion section
# Expand the conclusion section to be longer than one sentence. The conclusion section to include a brief summary of what was discussed above, an emphasis on it’s significance, and a brief discussion of future extensions and research direction if applicable.
* References
# Include hyperlinks to sources when possible.

== [[Mathematical programming with equilibrium constraints|Mathematical Programming with Equilibrium constraints]] ==

* An introduction of the topic
# This section includes several terms like variational inequalities, constraint qualifications that were not discussed in the class. Please add a sentence to explain them before using them.
* Theory, methodology, and/or algorithmic discussions
# The meaning of parameter vector x is unclear. Please add more information or update if necessary.
# Equations and symbols in the PIPA subsection are not formatted correctly. Please use the same formatting for all equations, so they read as mathematical equations and not text. This goes for all other sections as well.
# Use equations instead of images to represent math programs and equations in the Implicit Descent and SQP subsection.
# Apart from the steps for each solution technique, please also add a few sentences that describe each method.
* At least one numerical example
# Please define the terms like NCP, MP before abbreviating them. Also try not to unnecessarily abbreviate simple terms.
# Equations should be typed by LaTex. Images for equations are unacceptable.
# GAMS code is strongly discouraged. Please solve the problem "step-by-step".
# The selected numerical example is fine but is directly solved with the MPEC solver in GAMS. Try to solve it manually like the homework/in-class problems step by step using the steps described in the previous section by choosing any of the methods.
# Avoid using figures in the equations (subject to etc)
* A section to discuss and/or illustrate the applications
# Add references to “power management, highway pricing, chemical process engineering, and traffic planning.”
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# This Wiki contains very few references. Please check the list below and run a quick Google (Scholar) search to identify relevant literature.

== [[Wing shape optimization|Wing shape Optimization]] ==

* Author list: Remove cornell ID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC. Any formatting issue will incur a penalty in the grading.
* An introduction of the topic
# The introduction is missing several references (e.g., “software packages like computational fluid dynamics..”, sentences containing things that aren’t common knowledge, performance claims, etc.)
# Avoid discussion involving finer details of subject methods in this section.
# In the titles, please change the font from bold to normal to have consistent formatting in the site. Same applies to box of content!
* Theory, methodology, and/or algorithmic discussions
# Properly cite the CFD package, don’t just include a link.
# Properly label the figure with a figure number.
# Consider removing white space between isolated sentences to improve readability.
* At least one numerical example
# If you’ve already defined an abbreviation (CFD), there is no need to define it again. Just use the abbreviation.
# Avoid pronouns such as “we” or “they”.
# Phrases like “under the following” need to be followed by a colon.
# Properly label the figure with a figure number and consider making them larger to improve visibility. Call the reader's attention to the figures in text by referencing the figure number.
# “As seen in the video below” is stated yet there are only images present and it may be initially unclear to the reader which figure is being referenced here.
# Avoid inserting inline citations like “[4] introduces an..” as it is a bit informal when you don’t explicitly name the subject.
# Don’t just cite the reference when discussing the problem formulation, explicitly write the model formulation and solution process using LaTex or equation visual editor.
# Your team should ideally create a numerical example independently. If you take a numerical example directly from a textbook, etc., you will need to get explicit permission from the author in writing and share that written permission with me.
# A numerical example is simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments). There is an Application section where you discuss the applications.
# The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).
* A section to discuss and/or illustrate the applications
# Some characters are randomly capitalized in this section.
* A conclusion section
# These variables should be defined before the conclusion section, they are out of place here. Also, please use normal text when explaining variables except for the variable symbol.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Interior-point method for NLP|Interior point method for NLP]] ==

* Theory, methodology, and/or algorithmic discussions
** Need discussion about the concept of “central path” and the notion of self concordance
** Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
** Fix typo “optimisation”.
== [[AdaGrad|Adagrad]] ==
* At least one numerical example
# In the first sentence, “..take the following numerical example” should be followed by a colon.
* A section to discuss and/or illustrate the applications
# This section is too short; include specific applications in which input features are sparse and Adagrad excels.
*
* References

# References not properly formatted

== [[McCormick envelopes|McCormick Envelopes]] ==

* Author list: OK but I suggest removing NetID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# First sentence is hard to read. Please consider keeping sentences below 25-30 words.
# No references provided. Please cite all sources.
# Figure 1 is provided in the middle between two sections. Please include in the introduction section.
* Theory, methodology, and/or algorithmic discussions
# References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# When using mathematical expressions and symbols, please use the equation editor. (e.g., x*y, exy + y, sin (x+y) - x2)
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# The solution technique should be clearly presented, and solved "step-by-step".
# GAMS code is unnecessary. Please provide detailed step-by-step calculation results.
* A section to discuss and/or illustrate the applications
# Having a list is not enough. Please explain at least three applications in a few sentences each.
# This section should be at least a paragraph to discuss relevant applications. Each application should be explicitly linked to the page topic. A few keywords do not meet the requirement at all.
* A conclusion section:
* References
# References are not expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please follow the standard reference style - the current format is incorrect.

== [[Branch and bound (BB) for MINLP|Branch and Bound for MINLP]] ==

* Author list:
** Remove NetIDS
** Please remove abbreviations from the title (i.e. BB).
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# Please cite sources appropriately: References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Introduction is very short for a well-recognized topic. Please expand significantly. You may refer to the Wiki examples to get an idea on writing the Introduction to a topic.
# An illustration might be useful here.
* Theory, methodology, and/or algorithmic discussions
# The algorithm described here considers only binary integer variables. However, MINLP problems may include non-binary integer variables too. Please update the method or provide a short description of the assumptions that the MINLP problem needs to satisfy in order for the presented technique to be applicable.
# Use linked citations please as the Wiki template above.
# Please provide steps in a more organized way. Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
# Step 2 is missing yet it is referenced in the text multiple times. Please address this in addition to the above comment.
# An illustration might be useful here as well.
# Please explain what a Gomory Cut is. If the topic is available on optimization.cb.cornell.edu, you can link it.
# The current equations seem to be simple text written in Italics. All mathematical symbols and equations should be formatted via LaTex.
# Please format the math programs with equations and notations using formulations in lecture notes as templates.
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# Please show a step-by-step solution in the example. The solution is incomplete. The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).
# Please use the equation editor for equations or mathematical symbols. - All mathematical symbols and equations should be formatted via LaTex - this is a learning objective of the Wiki assignment. You can find some useful links on converting your equations/symbols into LaTex code here: (<nowiki>https://optimization.cbe.cornell.edu/index.php?title=Help:Contents</nowiki>). Again, any formatting issue will incur a "compound" penalty in the grading.
# This example does not follow the MINLP structure discussed in the above section since binary variables are missing. Branch and bound may not be appropriate for such problems. Please provide an appropriate numerical example and solve it according to the above comments.
# Make sure your example is not taken from a book as that is strictly disallowed.
* A section to discuss and/or illustrate the applications
# This section is not well-formatted. Please provide 3 applications and explain each in a few sentences and how BB for MINLP could be used. Also, please eliminate having multiple sections (Application, Mathematical problem, industrial application). All these could be merged together.
# This section should be at least a paragraph to discuss relevant applications. Each application should be explicitly linked to the page topic. A few keywords do not meet the requirement at all.
* A conclusion section:
# The sentence is hard to understand "a scheme that grows exponentially because" please use a simple language. Is it also theoretically correct? It is also not mentioned and explained earlier. Thus, please avoid introducing new concepts or terms at the end.
# Please use summarizing sentences to describe earlier sections instead of introducing new concepts/discussion.
* References
# Too few references overall, you should aggregate information from multiple sources. A quick Google scholar search could provide relevant references.
# References are not expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please follow the standard reference style - the current format is incorrect.

2021 Cornell Optimization Open Textbook Feedback

2021-12-18T20:57:46Z

Asa273: /* Job-Shop Scheduling Problem */

== [[Lagrangean duality|Lagrangian duality]] ==
* Author list, sections and TOC
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions
# The Lagrangian variables associated with equality constraints h(x) are unbounded but the Lagrangian dual problem states them as non-negative. Please fix the same.

* At least one numerical example
# Please update the dual objective function and domain of dual variables accordingly.
* A section to discuss and/or illustrate the applications

* A conclusion section
* References

== [[Disjunctive inequalities|Disjunctive Inequalities]] ==
* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section

* References
==[[Stochastic programming|Stochastic Programming]]==

* An introduction of the topic
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
* Theory, methodology, and/or algorithmic discussions
** The symbol “xi” in the methodology subsection should be explained.
** The inline notations (`x1`, `s1`) should also be typed using LaTex.

* A section to discuss and/or illustrate the applications;
# I suggest eliminating citing the last name of the first author (i.e. Zhou et al.)
==[[Exponential transformation|Exponential Transformation]]==

* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section

* References
== [[Portfolio optimization|Portfolio Optimization]] ==

* Author list

* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions
# Rephrase “Cut the relevant information and conditions in the portfolio optimization, as well as the final requirements into the relevant variables, constraints and linear functions of the linear programming problem.”
* At least one numerical example
# Fix misspelling “dolling decision variables”.
* A section to discuss and/or illustrate the applications

* A conclusion section
# Need some commas here (second sentence hard to read).
* References
# Remove white space between end of sentences and reference numbers.

== [[Chance-constraint method|Chance constraint method]] ==

* Author list:
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions
# Some normal text was expressed as equation.
* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section

* References
== [[Bayesian Optimization]] ==
* Introduction
# Discussion on applications should be moved to a separate section.
* Theory, methodology, and/or algorithmic discussions
# Captions need reformatting.
# Consider italicizing keywords rather than bolding.
# Please add a citation to the first sentence.
# Avoid pronouns such as “we”.
# Acquisition function figure could be made larger and clearer to improve readability.
* At least one numerical example
# Any references to functions or methods in code ‘e.g. fmin’ should be properly formatted as code-stylized text.
# Please use the equation editor for min, st., etc.
# Avoid including a figure of the code for this example and explicitly describe the steps to the modeling and solution process instead.
# Avoid pronouns such as “our” and “we”.
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Conjugate gradient methods]] ==
* Theory, methodology, and/or algorithmic discussions
# All equations need to be better formatted.
# Please indent equation blocks.
# Please properly format pseudocode.
* A conclusion section
# Consider adding future research directions
== [[Geometric programming|Geometric Programming]] ==

* Author list

* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section:

* References

== [[Adam]] ==

* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions
# Avoid inserting inline citations after words like “This article..” as it is a bit informal. This could be rephrased or changed to something like “According to author,^[2] …” with author name inserted.
* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section
* References
== [[A-star algorithm|a* algorithm]] ==

* Author list
* An introduction of the topic:
# Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.
# There are no citations in the introduction. Please cite every source.
* Theory, methodology, and/or algorithmic discussions
# Please add the mathematical description of the algorithm. (Insufficient)
# Please fix grammatical and spelling errors as (“from current position to the goal”, “There are a lot of discussions”, etc). Also, many hyphens are missing as “non playable”.
* At least one numerical example
# The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.
* A section to discuss and/or illustrate the applications
* A conclusion section
* References

== [[Job shop scheduling|Job-Shop Scheduling Problem]] ==

* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

# Since this Wiki focuses on jobshop scheduling, at least two methods are expected. Branch and bound is a general MILP technique, so, it is recommended to add a tailored technique that can only solve specific jobshop scheduling problems. Solving the numerical example with this technique is not necessary.

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section

* References

== [[Optimization in game theory]] ==

* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions
# Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm.
# Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.
# Formatting (incomplete).
* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section
# Please add more summarizing especially from theory sentences and avoid long sentences.
* References
# Incorrect reference style.

== [[Trust-region methods]] ==
* An introduction of the topic
** Avoid pronouns such as “we”. This goes for all other sections as well.

* Theory, methodology, and/or algorithmic discussions
# Organization of ideas in this section needs work.
# You have not defined explicitly why the Cauchy point is important to compute beyond a vague allusion to performance improvements, which is also wrong (it is useful because of its guarantees for convergence, not performance) It is also misspelled.
# Please format the algorithm in proper algorithmic pseudocode format.
* References
# Incorrect reference style.

*There are numerous misspellings, grammatical errors, and incorrect claims. Please fix these.

== [[Momentum]] ==
* An introduction of the topic
# Apart from an explanation on momentum, it is necessary to briefly point out the limitations of SGD and why momentum could help with these limitations. Please update it accordingly.
# Remove bold on “Momentum”.
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
* Theory, methodology, and/or algorithmic discussions
#
# The definition of the update rule for SGD with momentum looks incorrect, specifically the first expression. Please fix it and also explain all the parameters used.
# Use LaTex code or equation editor to display all equations and variables (e.g., “W”, “V`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “you”.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step". Since writing all iterations is not feasible, at least present a few iterations for both cases.
# Please try to label the plots that explains what each line color means.
# Starting point for SGD with momentum is different in explanation and the table. Please fix the same.
* A section to discuss and/or illustrate the applications
# Please use correct terminology like “optimizing non-convex functions” and not “training non-convex models”.
* References
# Almost all references used are URLs. Please try to add journal/conference articles or books for references, instead of directly citing the URLs. Please check the list below and run a quick Google (Scholar) search to identify relevant literature.

== [[Stochastic dynamic programming|Stochastic Dynamic programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Discussion on applications should be moved to a separate section.
* Theory, methodology, and/or algorithmic discussions
# Remove the grey box background of equations.
* At least one numerical example
* A section to discuss and/or illustrate the applications
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Outer-approximation (OA)|Outer-approximation]] ==

* An introduction of the topic
# See formatting guideline below
# Avoid opinionated statements such as “MINLP problems are usually the hardest to solve”.
# Rearrange the text such that the MINLP formulation is in the theory section and keep the introduction in words only.
* Theory, methodology, and/or algorithmic discussions
# Consider left aligning equations and optimization problem formulations by the “=”. See [[Stochastic programming|https://optimization.cbe.cornell.edu/index.php?title=Stochastic_programming]] for an example
# The sentence “The Outer-Approximation (OA) algorithm was first proposed by Duran and and Grossmann in 1986 to solve MINLP problems.” needs a reference.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# “Minimize” and “subject to” should be “min” and “s.t.” in MathType
* A section to discuss and/or illustrate the applications
# Does not explicitly point out why OA is applicable (and/or preferred) in these applications, rather than other MINLP approaches (show that the problem formulations are amenable to a solution approach through OA)
# The sentence “... an active research area and there exists a vast number of applications in fields such as engineering, computational chemistry, and finance.” needs references.
# Posting GAMS code on the page is generally inappropriate and discouraged. Please check with the TAs or me if you have a strong desire to post GAMS codes on the Wiki page. A typical textbook should not be limited to a specific software package. If the GAMS code must be posted, please also post ALL other software implementation versions, such as Pyomo and JuliaOPT, among others.
# Consider reformatting to make steps more readable. Inserting spaces and breaking down steps would help.
* A conclusion section
# Too short. Consider discussion on future research direction and discussion on uncertainty
# Please review abbreviations throughout the page. Why is MINLP redefined here? “Outer-Approximation is a well known efficient approach for solving convex mixed-integer nonlinear programs (MINLP)”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove "Template:Reflist"

== [[Unit commitment problem]] ==

* Author list
* An introduction of the topic
# Please expand the introduction and avoid discussions of examples or specific applications in this section.
# The sentence “Nonlinear, Non-convex programming optimization problem.” doesn’t make sense by itself and Non-convex shouldn’t be capitalized.
* Theory, methodology, and/or algorithmic discussions
# Figure/image format should be revised to better display the content.
# Uppercase characters are used randomly (e.g., “non-convex transmission Constraints”) . Please follow correct language conventions for sentence structure.
# Avoid inserting inline citations after words like “written in matrix form as equation [3]..” or “presented in [3]...” as it is a bit informal when you don’t explicitly name the subject. Also these two sentences are grammatically incorrect and appear to be missing an ending period and comma, respectively.
# Don’t say “written in matrix form as equation..” and just cite the reference, actually write out the equation.
# Properly label the figure in this section with a figure number and improve visibility by making it larger.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Label the figures in this section properly with figure numbers.
# Fix typo “while minimize” to “while minimizing”.
# Avoid pronouns such as “we”.
# Use the equation editor when typing equations.
# A numerical example is simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments). There is an Application section where you discuss the applications.
# The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).
* A section to discuss and/or illustrate the applications:
# I suggest changing the order of the subtitles here. For example, Single-Period Unit Commitment.
* A conclusion section
* References

== [[Frank-Wolfe]] ==

* Author list:
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications:
* A conclusion section

* References
== [[Line search methods|Line Search Method]] ==

* Author list
* An introduction of the topic
# Expand the introduction and avoid discussion on some of the specific steps in the solution process.
# Provide references here.
* Theory, methodology, and/or algorithmic discussions
# The phrase “are as follows” in the steepest descent method discussion needs to be followed by a colon.
# Rephrase “has a nice convergence theory” and cite a reference for this claim.
# Avoid pronouns such as “we”.
# Add citation after “.. proposed by Phillip Wolfe in 1969.”
# Figure 1 is between two sections. Please fix this issue.
* At least one numerical example:
# Add some space between iterations or subsection break
* A section to discuss and/or illustrate the applications:
# Too few references in this section.
# Last paragraph makes some claims without references.
* A conclusion section
* References
# References should be properly formatted. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Piecewise linear approximation|Piecewise Linear Approximation]]==

* Author list
* An introduction of the topic
# The content of this section is good, but there are some issues with sentence clarity and some other grammatical errors. Please revisit this section and make changes accordingly.
* Theory, methodology, and/or algorithmic discussions
# Fix typo “to force the x’ values become associated with”.
* At least one numerical example
* A section to discuss and/or illustrate the applications
# Please aim for a maximum average sentence length of ~25 words. Some of these longer sentences are hard to read.
* A conclusion section
# Expand the conclusion section to be longer than one sentence. The conclusion section to include a brief summary of what was discussed above, an emphasis on it’s significance, and a brief discussion of future extensions and research direction if applicable.
* References
# Include hyperlinks to sources when possible.

== [[Mathematical programming with equilibrium constraints|Mathematical Programming with Equilibrium constraints]] ==

* An introduction of the topic
# This section includes several terms like variational inequalities, constraint qualifications that were not discussed in the class. Please add a sentence to explain them before using them.
* Theory, methodology, and/or algorithmic discussions
# The meaning of parameter vector x is unclear. Please add more information or update if necessary.
# Equations and symbols in the PIPA subsection are not formatted correctly. Please use the same formatting for all equations, so they read as mathematical equations and not text. This goes for all other sections as well.
# Use equations instead of images to represent math programs and equations in the Implicit Descent and SQP subsection.
# Apart from the steps for each solution technique, please also add a few sentences that describe each method.
* At least one numerical example
# Please define the terms like NCP, MP before abbreviating them. Also try not to unnecessarily abbreviate simple terms.
# Equations should be typed by LaTex. Images for equations are unacceptable.
# GAMS code is strongly discouraged. Please solve the problem "step-by-step".
# The selected numerical example is fine but is directly solved with the MPEC solver in GAMS. Try to solve it manually like the homework/in-class problems step by step using the steps described in the previous section by choosing any of the methods.
# Avoid using figures in the equations (subject to etc)
* A section to discuss and/or illustrate the applications
# Add references to “power management, highway pricing, chemical process engineering, and traffic planning.”
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# This Wiki contains very few references. Please check the list below and run a quick Google (Scholar) search to identify relevant literature.

== [[Wing shape optimization|Wing shape Optimization]] ==

* Author list: Remove cornell ID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC. Any formatting issue will incur a penalty in the grading.
* An introduction of the topic
# The introduction is missing several references (e.g., “software packages like computational fluid dynamics..”, sentences containing things that aren’t common knowledge, performance claims, etc.)
# Avoid discussion involving finer details of subject methods in this section.
# In the titles, please change the font from bold to normal to have consistent formatting in the site. Same applies to box of content!
* Theory, methodology, and/or algorithmic discussions
# Properly cite the CFD package, don’t just include a link.
# Properly label the figure with a figure number.
# Consider removing white space between isolated sentences to improve readability.
* At least one numerical example
# If you’ve already defined an abbreviation (CFD), there is no need to define it again. Just use the abbreviation.
# Avoid pronouns such as “we” or “they”.
# Phrases like “under the following” need to be followed by a colon.
# Properly label the figure with a figure number and consider making them larger to improve visibility. Call the reader's attention to the figures in text by referencing the figure number.
# “As seen in the video below” is stated yet there are only images present and it may be initially unclear to the reader which figure is being referenced here.
# Avoid inserting inline citations like “[4] introduces an..” as it is a bit informal when you don’t explicitly name the subject.
# Don’t just cite the reference when discussing the problem formulation, explicitly write the model formulation and solution process using LaTex or equation visual editor.
# Your team should ideally create a numerical example independently. If you take a numerical example directly from a textbook, etc., you will need to get explicit permission from the author in writing and share that written permission with me.
# A numerical example is simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments). There is an Application section where you discuss the applications.
# The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).
* A section to discuss and/or illustrate the applications
# Some characters are randomly capitalized in this section.
* A conclusion section
# These variables should be defined before the conclusion section, they are out of place here. Also, please use normal text when explaining variables except for the variable symbol.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Interior-point method for NLP|Interior point method for NLP]] ==

* Theory, methodology, and/or algorithmic discussions
** Need discussion about the concept of “central path” and the notion of self concordance
** Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
** Fix typo “optimisation”.
== [[AdaGrad|Adagrad]] ==
* At least one numerical example
# In the first sentence, “..take the following numerical example” should be followed by a colon.
* A section to discuss and/or illustrate the applications
# This section is too short; include specific applications in which input features are sparse and Adagrad excels.
*
* References

# References not properly formatted

== [[McCormick envelopes|McCormick Envelopes]] ==

* Author list: OK but I suggest removing NetID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# First sentence is hard to read. Please consider keeping sentences below 25-30 words.
# No references provided. Please cite all sources.
# Figure 1 is provided in the middle between two sections. Please include in the introduction section.
* Theory, methodology, and/or algorithmic discussions
# References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# When using mathematical expressions and symbols, please use the equation editor. (e.g., x*y, exy + y, sin (x+y) - x2)
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# The solution technique should be clearly presented, and solved "step-by-step".
# GAMS code is unnecessary. Please provide detailed step-by-step calculation results.
* A section to discuss and/or illustrate the applications
# Having a list is not enough. Please explain at least three applications in a few sentences each.
# This section should be at least a paragraph to discuss relevant applications. Each application should be explicitly linked to the page topic. A few keywords do not meet the requirement at all.
* A conclusion section:
* References
# References are not expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please follow the standard reference style - the current format is incorrect.

== [[Branch and bound (BB) for MINLP|Branch and Bound for MINLP]] ==

* Author list:
** Remove NetIDS
** Please remove abbreviations from the title (i.e. BB).
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# Please cite sources appropriately: References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Introduction is very short for a well-recognized topic. Please expand significantly. You may refer to the Wiki examples to get an idea on writing the Introduction to a topic.
# An illustration might be useful here.
* Theory, methodology, and/or algorithmic discussions
# The algorithm described here considers only binary integer variables. However, MINLP problems may include non-binary integer variables too. Please update the method or provide a short description of the assumptions that the MINLP problem needs to satisfy in order for the presented technique to be applicable.
# Use linked citations please as the Wiki template above.
# Please provide steps in a more organized way. Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
# Step 2 is missing yet it is referenced in the text multiple times. Please address this in addition to the above comment.
# An illustration might be useful here as well.
# Please explain what a Gomory Cut is. If the topic is available on optimization.cb.cornell.edu, you can link it.
# The current equations seem to be simple text written in Italics. All mathematical symbols and equations should be formatted via LaTex.
# Please format the math programs with equations and notations using formulations in lecture notes as templates.
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# Please show a step-by-step solution in the example. The solution is incomplete. The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).
# Please use the equation editor for equations or mathematical symbols. - All mathematical symbols and equations should be formatted via LaTex - this is a learning objective of the Wiki assignment. You can find some useful links on converting your equations/symbols into LaTex code here: (<nowiki>https://optimization.cbe.cornell.edu/index.php?title=Help:Contents</nowiki>). Again, any formatting issue will incur a "compound" penalty in the grading.
# This example does not follow the MINLP structure discussed in the above section since binary variables are missing. Branch and bound may not be appropriate for such problems. Please provide an appropriate numerical example and solve it according to the above comments.
# Make sure your example is not taken from a book as that is strictly disallowed.
* A section to discuss and/or illustrate the applications
# This section is not well-formatted. Please provide 3 applications and explain each in a few sentences and how BB for MINLP could be used. Also, please eliminate having multiple sections (Application, Mathematical problem, industrial application). All these could be merged together.
# This section should be at least a paragraph to discuss relevant applications. Each application should be explicitly linked to the page topic. A few keywords do not meet the requirement at all.
* A conclusion section:
# The sentence is hard to understand "a scheme that grows exponentially because" please use a simple language. Is it also theoretically correct? It is also not mentioned and explained earlier. Thus, please avoid introducing new concepts or terms at the end.
# Please use summarizing sentences to describe earlier sections instead of introducing new concepts/discussion.
* References
# Too few references overall, you should aggregate information from multiple sources. A quick Google scholar search could provide relevant references.
# References are not expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please follow the standard reference style - the current format is incorrect.

2021 Cornell Optimization Open Textbook Feedback

2021-12-18T20:50:47Z

Asa273: /* Geometric Programming */

== [[Lagrangean duality|Lagrangian duality]] ==
* Author list, sections and TOC
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions
# The Lagrangian variables associated with equality constraints h(x) are unbounded but the Lagrangian dual problem states them as non-negative. Please fix the same.

* At least one numerical example
# Please update the dual objective function and domain of dual variables accordingly.
* A section to discuss and/or illustrate the applications

* A conclusion section
* References

== [[Disjunctive inequalities|Disjunctive Inequalities]] ==
* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section

* References
==[[Stochastic programming|Stochastic Programming]]==

* An introduction of the topic
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
* Theory, methodology, and/or algorithmic discussions
** The symbol “xi” in the methodology subsection should be explained.
** The inline notations (`x1`, `s1`) should also be typed using LaTex.

* A section to discuss and/or illustrate the applications;
# I suggest eliminating citing the last name of the first author (i.e. Zhou et al.)
==[[Exponential transformation|Exponential Transformation]]==

* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section

* References
== [[Portfolio optimization|Portfolio Optimization]] ==

* Author list

* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions
# Rephrase “Cut the relevant information and conditions in the portfolio optimization, as well as the final requirements into the relevant variables, constraints and linear functions of the linear programming problem.”
* At least one numerical example
# Fix misspelling “dolling decision variables”.
* A section to discuss and/or illustrate the applications

* A conclusion section
# Need some commas here (second sentence hard to read).
* References
# Remove white space between end of sentences and reference numbers.

== [[Chance-constraint method|Chance constraint method]] ==

* Author list:
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions
# Some normal text was expressed as equation.
* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section

* References
== [[Bayesian Optimization]] ==
* Introduction
# Discussion on applications should be moved to a separate section.
* Theory, methodology, and/or algorithmic discussions
# Captions need reformatting.
# Consider italicizing keywords rather than bolding.
# Please add a citation to the first sentence.
# Avoid pronouns such as “we”.
# Acquisition function figure could be made larger and clearer to improve readability.
* At least one numerical example
# Any references to functions or methods in code ‘e.g. fmin’ should be properly formatted as code-stylized text.
# Please use the equation editor for min, st., etc.
# Avoid including a figure of the code for this example and explicitly describe the steps to the modeling and solution process instead.
# Avoid pronouns such as “our” and “we”.
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Conjugate gradient methods]] ==
* Theory, methodology, and/or algorithmic discussions
# All equations need to be better formatted.
# Please indent equation blocks.
# Please properly format pseudocode.
* A conclusion section
# Consider adding future research directions
== [[Geometric programming|Geometric Programming]] ==

* Author list

* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section:

* References

== [[Adam]] ==

* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions
# Avoid inserting inline citations after words like “This article..” as it is a bit informal. This could be rephrased or changed to something like “According to author,^[2] …” with author name inserted.
* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section
* References
== [[A-star algorithm|a* algorithm]] ==

* Author list
* An introduction of the topic:
# Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.
# There are no citations in the introduction. Please cite every source.
* Theory, methodology, and/or algorithmic discussions
# Please add the mathematical description of the algorithm. (Insufficient)
# Please fix grammatical and spelling errors as (“from current position to the goal”, “There are a lot of discussions”, etc). Also, many hyphens are missing as “non playable”.
* At least one numerical example
# The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.
* A section to discuss and/or illustrate the applications
* A conclusion section
* References

== [[Job shop scheduling|Job-Shop Scheduling Problem]] ==

* An introduction of the topic
# The current introduction to the jobshop scheduling problem has only two sentences in addition to the parameter description. Introduction typically contains information about the problem, its importance in the real-world, and some information about the solution techniques and their types to solve the problem. Please add some information that covers the above.
* Theory, methodology, and/or algorithmic discussions
# It is unclear whether the assumptions stated in this section are required to apply the following solution techniques. Please clarify the same. Also use complete sentences to state them.
# The branch and bounds method described in this section only discusses the solution technique for problems with one machines. However, branch and bound is a general technique that can be applied to any MILP problems with varying scales. Please update the “methods” section to be as general as possible.
# Since this Wiki focuses on jobshop scheduling, at least two methods are expected. Branch and bound is a general MILP technique, so, it is recommended to add a tailored technique that can only solve specific jobshop scheduling problems. Solving the numerical example with this technique is not necessary.
# Reference to the branch and bound technique described in this section is a “youtube” video. Please add references in literature that describe this method in detail. The method used in this video is highly tailored for a single machine application. This is also an incorrect way to cite a reference. Please keep this section as general as possible.
# Use LaTex code or equation editor to display all equations and variables in this section and all other sections as well.
# Check grammar in this section. For example, phrases like “are as follows” need to be followed by a colon and not a period.
# Consider rewriting the assumptions as a list in this section.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# The example used in this section is exactly the same as the one in the youtube video. Please use a modification of this example or choose another example/method to demonstrate the solution technique. Your team should ideally create a numerical example independently. If you take a numerical example directly from a particular source, you will need to get explicit permission from the textbook author in writing and share that written permission with the instructors.
# The figure in this section is not numbered when all others are. Relabel this figure for consistency and its number to refer to it in-text.
# A numerical example should be simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments).
* A section to discuss and/or illustrate the applications
# This section should only focus on real-world applications of the jobshop scheduling problem. But currently, this section includes additional information on solution techniques/complexity that is appropriate for the Introduction section. Please discuss the applications of the problem in this section.
* A conclusion section
# The meaning of “Operations applications” is unclear. Please explain or update if necessary.
# The current conclusion section does not properly summarize the problem. Please refer to other Wiki examples for an idea to update the section accordingly.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please reference media sources like reference 5 appropriately.
# A simple Google Scholar search would give you many "formal" references.

== [[Optimization in game theory]] ==

* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions
# Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm.
# Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.
# Formatting (incomplete).
* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section
# Please add more summarizing especially from theory sentences and avoid long sentences.
* References
# Incorrect reference style.

== [[Trust-region methods]] ==
* An introduction of the topic
** Avoid pronouns such as “we”. This goes for all other sections as well.

* Theory, methodology, and/or algorithmic discussions
# Organization of ideas in this section needs work.
# You have not defined explicitly why the Cauchy point is important to compute beyond a vague allusion to performance improvements, which is also wrong (it is useful because of its guarantees for convergence, not performance) It is also misspelled.
# Please format the algorithm in proper algorithmic pseudocode format.
* References
# Incorrect reference style.

*There are numerous misspellings, grammatical errors, and incorrect claims. Please fix these.

== [[Momentum]] ==
* An introduction of the topic
# Apart from an explanation on momentum, it is necessary to briefly point out the limitations of SGD and why momentum could help with these limitations. Please update it accordingly.
# Remove bold on “Momentum”.
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
* Theory, methodology, and/or algorithmic discussions
#
# The definition of the update rule for SGD with momentum looks incorrect, specifically the first expression. Please fix it and also explain all the parameters used.
# Use LaTex code or equation editor to display all equations and variables (e.g., “W”, “V`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “you”.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step". Since writing all iterations is not feasible, at least present a few iterations for both cases.
# Please try to label the plots that explains what each line color means.
# Starting point for SGD with momentum is different in explanation and the table. Please fix the same.
* A section to discuss and/or illustrate the applications
# Please use correct terminology like “optimizing non-convex functions” and not “training non-convex models”.
* References
# Almost all references used are URLs. Please try to add journal/conference articles or books for references, instead of directly citing the URLs. Please check the list below and run a quick Google (Scholar) search to identify relevant literature.

== [[Stochastic dynamic programming|Stochastic Dynamic programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Discussion on applications should be moved to a separate section.
* Theory, methodology, and/or algorithmic discussions
# Remove the grey box background of equations.
* At least one numerical example
* A section to discuss and/or illustrate the applications
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Outer-approximation (OA)|Outer-approximation]] ==

* An introduction of the topic
# See formatting guideline below
# Avoid opinionated statements such as “MINLP problems are usually the hardest to solve”.
# Rearrange the text such that the MINLP formulation is in the theory section and keep the introduction in words only.
* Theory, methodology, and/or algorithmic discussions
# Consider left aligning equations and optimization problem formulations by the “=”. See [[Stochastic programming|https://optimization.cbe.cornell.edu/index.php?title=Stochastic_programming]] for an example
# The sentence “The Outer-Approximation (OA) algorithm was first proposed by Duran and and Grossmann in 1986 to solve MINLP problems.” needs a reference.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# “Minimize” and “subject to” should be “min” and “s.t.” in MathType
* A section to discuss and/or illustrate the applications
# Does not explicitly point out why OA is applicable (and/or preferred) in these applications, rather than other MINLP approaches (show that the problem formulations are amenable to a solution approach through OA)
# The sentence “... an active research area and there exists a vast number of applications in fields such as engineering, computational chemistry, and finance.” needs references.
# Posting GAMS code on the page is generally inappropriate and discouraged. Please check with the TAs or me if you have a strong desire to post GAMS codes on the Wiki page. A typical textbook should not be limited to a specific software package. If the GAMS code must be posted, please also post ALL other software implementation versions, such as Pyomo and JuliaOPT, among others.
# Consider reformatting to make steps more readable. Inserting spaces and breaking down steps would help.
* A conclusion section
# Too short. Consider discussion on future research direction and discussion on uncertainty
# Please review abbreviations throughout the page. Why is MINLP redefined here? “Outer-Approximation is a well known efficient approach for solving convex mixed-integer nonlinear programs (MINLP)”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove "Template:Reflist"

== [[Unit commitment problem]] ==

* Author list
* An introduction of the topic
# Please expand the introduction and avoid discussions of examples or specific applications in this section.
# The sentence “Nonlinear, Non-convex programming optimization problem.” doesn’t make sense by itself and Non-convex shouldn’t be capitalized.
* Theory, methodology, and/or algorithmic discussions
# Figure/image format should be revised to better display the content.
# Uppercase characters are used randomly (e.g., “non-convex transmission Constraints”) . Please follow correct language conventions for sentence structure.
# Avoid inserting inline citations after words like “written in matrix form as equation [3]..” or “presented in [3]...” as it is a bit informal when you don’t explicitly name the subject. Also these two sentences are grammatically incorrect and appear to be missing an ending period and comma, respectively.
# Don’t say “written in matrix form as equation..” and just cite the reference, actually write out the equation.
# Properly label the figure in this section with a figure number and improve visibility by making it larger.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Label the figures in this section properly with figure numbers.
# Fix typo “while minimize” to “while minimizing”.
# Avoid pronouns such as “we”.
# Use the equation editor when typing equations.
# A numerical example is simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments). There is an Application section where you discuss the applications.
# The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).
* A section to discuss and/or illustrate the applications:
# I suggest changing the order of the subtitles here. For example, Single-Period Unit Commitment.
* A conclusion section
* References

== [[Frank-Wolfe]] ==

* Author list:
* An introduction of the topic
# I suggest highlighting disadvantages along with advantages.
* Theory, methodology, and/or algorithmic discussions
# “[n x 1] matrix” please use the equation editor to express mathematical descriptions and symbols (p,b, etc)
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please show at least a few iterations. Even for smaller examples if needed. Report the final solution.
# Please use the LaTex code or equation editor for min and include s.t., etc.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps. For your example, please explicitly state that the derivative is taken etc.
* A section to discuss and/or illustrate the applications:
* A conclusion section
# Same as the introduction. Pros and cons should be evaluated together!
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Line search methods|Line Search Method]] ==

* Author list
* An introduction of the topic
# Expand the introduction and avoid discussion on some of the specific steps in the solution process.
# Provide references here.
* Theory, methodology, and/or algorithmic discussions
# The phrase “are as follows” in the steepest descent method discussion needs to be followed by a colon.
# Rephrase “has a nice convergence theory” and cite a reference for this claim.
# Avoid pronouns such as “we”.
# Add citation after “.. proposed by Phillip Wolfe in 1969.”
# Figure 1 is between two sections. Please fix this issue.
* At least one numerical example:
# Add some space between iterations or subsection break
* A section to discuss and/or illustrate the applications:
# Too few references in this section.
# Last paragraph makes some claims without references.
* A conclusion section
* References
# References should be properly formatted. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Piecewise linear approximation|Piecewise Linear Approximation]]==

* Author list
* An introduction of the topic
# The content of this section is good, but there are some issues with sentence clarity and some other grammatical errors. Please revisit this section and make changes accordingly.
* Theory, methodology, and/or algorithmic discussions
# Fix typo “to force the x’ values become associated with”.
* At least one numerical example
* A section to discuss and/or illustrate the applications
# Please aim for a maximum average sentence length of ~25 words. Some of these longer sentences are hard to read.
* A conclusion section
# Expand the conclusion section to be longer than one sentence. The conclusion section to include a brief summary of what was discussed above, an emphasis on it’s significance, and a brief discussion of future extensions and research direction if applicable.
* References
# Include hyperlinks to sources when possible.

== [[Mathematical programming with equilibrium constraints|Mathematical Programming with Equilibrium constraints]] ==

* An introduction of the topic
# This section includes several terms like variational inequalities, constraint qualifications that were not discussed in the class. Please add a sentence to explain them before using them.
* Theory, methodology, and/or algorithmic discussions
# The meaning of parameter vector x is unclear. Please add more information or update if necessary.
# Equations and symbols in the PIPA subsection are not formatted correctly. Please use the same formatting for all equations, so they read as mathematical equations and not text. This goes for all other sections as well.
# Use equations instead of images to represent math programs and equations in the Implicit Descent and SQP subsection.
# Apart from the steps for each solution technique, please also add a few sentences that describe each method.
* At least one numerical example
# Please define the terms like NCP, MP before abbreviating them. Also try not to unnecessarily abbreviate simple terms.
# Equations should be typed by LaTex. Images for equations are unacceptable.
# GAMS code is strongly discouraged. Please solve the problem "step-by-step".
# The selected numerical example is fine but is directly solved with the MPEC solver in GAMS. Try to solve it manually like the homework/in-class problems step by step using the steps described in the previous section by choosing any of the methods.
# Avoid using figures in the equations (subject to etc)
* A section to discuss and/or illustrate the applications
# Add references to “power management, highway pricing, chemical process engineering, and traffic planning.”
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# This Wiki contains very few references. Please check the list below and run a quick Google (Scholar) search to identify relevant literature.

== [[Wing shape optimization|Wing shape Optimization]] ==

* Author list: Remove cornell ID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC. Any formatting issue will incur a penalty in the grading.
* An introduction of the topic
# The introduction is missing several references (e.g., “software packages like computational fluid dynamics..”, sentences containing things that aren’t common knowledge, performance claims, etc.)
# Avoid discussion involving finer details of subject methods in this section.
# In the titles, please change the font from bold to normal to have consistent formatting in the site. Same applies to box of content!
* Theory, methodology, and/or algorithmic discussions
# Properly cite the CFD package, don’t just include a link.
# Properly label the figure with a figure number.
# Consider removing white space between isolated sentences to improve readability.
* At least one numerical example
# If you’ve already defined an abbreviation (CFD), there is no need to define it again. Just use the abbreviation.
# Avoid pronouns such as “we” or “they”.
# Phrases like “under the following” need to be followed by a colon.
# Properly label the figure with a figure number and consider making them larger to improve visibility. Call the reader's attention to the figures in text by referencing the figure number.
# “As seen in the video below” is stated yet there are only images present and it may be initially unclear to the reader which figure is being referenced here.
# Avoid inserting inline citations like “[4] introduces an..” as it is a bit informal when you don’t explicitly name the subject.
# Don’t just cite the reference when discussing the problem formulation, explicitly write the model formulation and solution process using LaTex or equation visual editor.
# Your team should ideally create a numerical example independently. If you take a numerical example directly from a textbook, etc., you will need to get explicit permission from the author in writing and share that written permission with me.
# A numerical example is simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments). There is an Application section where you discuss the applications.
# The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).
* A section to discuss and/or illustrate the applications
# Some characters are randomly capitalized in this section.
* A conclusion section
# These variables should be defined before the conclusion section, they are out of place here. Also, please use normal text when explaining variables except for the variable symbol.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Interior-point method for NLP|Interior point method for NLP]] ==

* Theory, methodology, and/or algorithmic discussions
** Need discussion about the concept of “central path” and the notion of self concordance
** Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
** Fix typo “optimisation”.
== [[AdaGrad|Adagrad]] ==
* At least one numerical example
# In the first sentence, “..take the following numerical example” should be followed by a colon.
* A section to discuss and/or illustrate the applications
# This section is too short; include specific applications in which input features are sparse and Adagrad excels.
*
* References

# References not properly formatted

== [[McCormick envelopes|McCormick Envelopes]] ==

* Author list: OK but I suggest removing NetID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# First sentence is hard to read. Please consider keeping sentences below 25-30 words.
# No references provided. Please cite all sources.
# Figure 1 is provided in the middle between two sections. Please include in the introduction section.
* Theory, methodology, and/or algorithmic discussions
# References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# When using mathematical expressions and symbols, please use the equation editor. (e.g., x*y, exy + y, sin (x+y) - x2)
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# The solution technique should be clearly presented, and solved "step-by-step".
# GAMS code is unnecessary. Please provide detailed step-by-step calculation results.
* A section to discuss and/or illustrate the applications
# Having a list is not enough. Please explain at least three applications in a few sentences each.
# This section should be at least a paragraph to discuss relevant applications. Each application should be explicitly linked to the page topic. A few keywords do not meet the requirement at all.
* A conclusion section:
* References
# References are not expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please follow the standard reference style - the current format is incorrect.

== [[Branch and bound (BB) for MINLP|Branch and Bound for MINLP]] ==

* Author list:
** Remove NetIDS
** Please remove abbreviations from the title (i.e. BB).
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# Please cite sources appropriately: References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Introduction is very short for a well-recognized topic. Please expand significantly. You may refer to the Wiki examples to get an idea on writing the Introduction to a topic.
# An illustration might be useful here.
* Theory, methodology, and/or algorithmic discussions
# The algorithm described here considers only binary integer variables. However, MINLP problems may include non-binary integer variables too. Please update the method or provide a short description of the assumptions that the MINLP problem needs to satisfy in order for the presented technique to be applicable.
# Use linked citations please as the Wiki template above.
# Please provide steps in a more organized way. Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
# Step 2 is missing yet it is referenced in the text multiple times. Please address this in addition to the above comment.
# An illustration might be useful here as well.
# Please explain what a Gomory Cut is. If the topic is available on optimization.cb.cornell.edu, you can link it.
# The current equations seem to be simple text written in Italics. All mathematical symbols and equations should be formatted via LaTex.
# Please format the math programs with equations and notations using formulations in lecture notes as templates.
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# Please show a step-by-step solution in the example. The solution is incomplete. The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).
# Please use the equation editor for equations or mathematical symbols. - All mathematical symbols and equations should be formatted via LaTex - this is a learning objective of the Wiki assignment. You can find some useful links on converting your equations/symbols into LaTex code here: (<nowiki>https://optimization.cbe.cornell.edu/index.php?title=Help:Contents</nowiki>). Again, any formatting issue will incur a "compound" penalty in the grading.
# This example does not follow the MINLP structure discussed in the above section since binary variables are missing. Branch and bound may not be appropriate for such problems. Please provide an appropriate numerical example and solve it according to the above comments.
# Make sure your example is not taken from a book as that is strictly disallowed.
* A section to discuss and/or illustrate the applications
# This section is not well-formatted. Please provide 3 applications and explain each in a few sentences and how BB for MINLP could be used. Also, please eliminate having multiple sections (Application, Mathematical problem, industrial application). All these could be merged together.
# This section should be at least a paragraph to discuss relevant applications. Each application should be explicitly linked to the page topic. A few keywords do not meet the requirement at all.
* A conclusion section:
# The sentence is hard to understand "a scheme that grows exponentially because" please use a simple language. Is it also theoretically correct? It is also not mentioned and explained earlier. Thus, please avoid introducing new concepts or terms at the end.
# Please use summarizing sentences to describe earlier sections instead of introducing new concepts/discussion.
* References
# Too few references overall, you should aggregate information from multiple sources. A quick Google scholar search could provide relevant references.
# References are not expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please follow the standard reference style - the current format is incorrect.

2021 Cornell Optimization Open Textbook Feedback

2021-12-18T20:50:34Z

Asa273: /* Geometric Programming */

== [[Lagrangean duality|Lagrangian duality]] ==
* Author list, sections and TOC
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions
# The Lagrangian variables associated with equality constraints h(x) are unbounded but the Lagrangian dual problem states them as non-negative. Please fix the same.

* At least one numerical example
# Please update the dual objective function and domain of dual variables accordingly.
* A section to discuss and/or illustrate the applications

* A conclusion section
* References

== [[Disjunctive inequalities|Disjunctive Inequalities]] ==
* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section

* References
==[[Stochastic programming|Stochastic Programming]]==

* An introduction of the topic
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
* Theory, methodology, and/or algorithmic discussions
** The symbol “xi” in the methodology subsection should be explained.
** The inline notations (`x1`, `s1`) should also be typed using LaTex.

* A section to discuss and/or illustrate the applications;
# I suggest eliminating citing the last name of the first author (i.e. Zhou et al.)
==[[Exponential transformation|Exponential Transformation]]==

* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section

* References
== [[Portfolio optimization|Portfolio Optimization]] ==

* Author list

* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions
# Rephrase “Cut the relevant information and conditions in the portfolio optimization, as well as the final requirements into the relevant variables, constraints and linear functions of the linear programming problem.”
* At least one numerical example
# Fix misspelling “dolling decision variables”.
* A section to discuss and/or illustrate the applications

* A conclusion section
# Need some commas here (second sentence hard to read).
* References
# Remove white space between end of sentences and reference numbers.

== [[Chance-constraint method|Chance constraint method]] ==

* Author list:
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions
# Some normal text was expressed as equation.
* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section

* References
== [[Bayesian Optimization]] ==
* Introduction
# Discussion on applications should be moved to a separate section.
* Theory, methodology, and/or algorithmic discussions
# Captions need reformatting.
# Consider italicizing keywords rather than bolding.
# Please add a citation to the first sentence.
# Avoid pronouns such as “we”.
# Acquisition function figure could be made larger and clearer to improve readability.
* At least one numerical example
# Any references to functions or methods in code ‘e.g. fmin’ should be properly formatted as code-stylized text.
# Please use the equation editor for min, st., etc.
# Avoid including a figure of the code for this example and explicitly describe the steps to the modeling and solution process instead.
# Avoid pronouns such as “our” and “we”.
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Conjugate gradient methods]] ==
* Theory, methodology, and/or algorithmic discussions
# All equations need to be better formatted.
# Please indent equation blocks.
# Please properly format pseudocode.
* A conclusion section
# Consider adding future research directions
== [[Geometric programming|Geometric Programming]] ==

* Author list

* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section:

* References

== [[Adam]] ==

* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions
# Avoid inserting inline citations after words like “This article..” as it is a bit informal. This could be rephrased or changed to something like “According to author,^[2] …” with author name inserted.
* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section
* References
== [[A-star algorithm|a* algorithm]] ==

* Author list
* An introduction of the topic:
# Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.
# There are no citations in the introduction. Please cite every source.
* Theory, methodology, and/or algorithmic discussions
# Please add the mathematical description of the algorithm. (Insufficient)
# Please fix grammatical and spelling errors as (“from current position to the goal”, “There are a lot of discussions”, etc). Also, many hyphens are missing as “non playable”.
* At least one numerical example
# The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.
* A section to discuss and/or illustrate the applications
* A conclusion section
* References

== [[Job shop scheduling|Job-Shop Scheduling Problem]] ==

* An introduction of the topic
# The current introduction to the jobshop scheduling problem has only two sentences in addition to the parameter description. Introduction typically contains information about the problem, its importance in the real-world, and some information about the solution techniques and their types to solve the problem. Please add some information that covers the above.
* Theory, methodology, and/or algorithmic discussions
# It is unclear whether the assumptions stated in this section are required to apply the following solution techniques. Please clarify the same. Also use complete sentences to state them.
# The branch and bounds method described in this section only discusses the solution technique for problems with one machines. However, branch and bound is a general technique that can be applied to any MILP problems with varying scales. Please update the “methods” section to be as general as possible.
# Since this Wiki focuses on jobshop scheduling, at least two methods are expected. Branch and bound is a general MILP technique, so, it is recommended to add a tailored technique that can only solve specific jobshop scheduling problems. Solving the numerical example with this technique is not necessary.
# Reference to the branch and bound technique described in this section is a “youtube” video. Please add references in literature that describe this method in detail. The method used in this video is highly tailored for a single machine application. This is also an incorrect way to cite a reference. Please keep this section as general as possible.
# Use LaTex code or equation editor to display all equations and variables in this section and all other sections as well.
# Check grammar in this section. For example, phrases like “are as follows” need to be followed by a colon and not a period.
# Consider rewriting the assumptions as a list in this section.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# The example used in this section is exactly the same as the one in the youtube video. Please use a modification of this example or choose another example/method to demonstrate the solution technique. Your team should ideally create a numerical example independently. If you take a numerical example directly from a particular source, you will need to get explicit permission from the textbook author in writing and share that written permission with the instructors.
# The figure in this section is not numbered when all others are. Relabel this figure for consistency and its number to refer to it in-text.
# A numerical example should be simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments).
* A section to discuss and/or illustrate the applications
# This section should only focus on real-world applications of the jobshop scheduling problem. But currently, this section includes additional information on solution techniques/complexity that is appropriate for the Introduction section. Please discuss the applications of the problem in this section.
* A conclusion section
# The meaning of “Operations applications” is unclear. Please explain or update if necessary.
# The current conclusion section does not properly summarize the problem. Please refer to other Wiki examples for an idea to update the section accordingly.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please reference media sources like reference 5 appropriately.
# A simple Google Scholar search would give you many "formal" references.

== [[Optimization in game theory]] ==

* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions
# Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm.
# Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.
# Formatting (incomplete).
* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section
# Please add more summarizing especially from theory sentences and avoid long sentences.
* References
# Incorrect reference style.

== [[Trust-region methods]] ==
* An introduction of the topic
** Avoid pronouns such as “we”. This goes for all other sections as well.

* Theory, methodology, and/or algorithmic discussions
# Organization of ideas in this section needs work.
# You have not defined explicitly why the Cauchy point is important to compute beyond a vague allusion to performance improvements, which is also wrong (it is useful because of its guarantees for convergence, not performance) It is also misspelled.
# Please format the algorithm in proper algorithmic pseudocode format.
* References
# Incorrect reference style.

*There are numerous misspellings, grammatical errors, and incorrect claims. Please fix these.

== [[Momentum]] ==
* An introduction of the topic
# Apart from an explanation on momentum, it is necessary to briefly point out the limitations of SGD and why momentum could help with these limitations. Please update it accordingly.
# Remove bold on “Momentum”.
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
* Theory, methodology, and/or algorithmic discussions
#
# The definition of the update rule for SGD with momentum looks incorrect, specifically the first expression. Please fix it and also explain all the parameters used.
# Use LaTex code or equation editor to display all equations and variables (e.g., “W”, “V`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “you”.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step". Since writing all iterations is not feasible, at least present a few iterations for both cases.
# Please try to label the plots that explains what each line color means.
# Starting point for SGD with momentum is different in explanation and the table. Please fix the same.
* A section to discuss and/or illustrate the applications
# Please use correct terminology like “optimizing non-convex functions” and not “training non-convex models”.
* References
# Almost all references used are URLs. Please try to add journal/conference articles or books for references, instead of directly citing the URLs. Please check the list below and run a quick Google (Scholar) search to identify relevant literature.

== [[Stochastic dynamic programming|Stochastic Dynamic programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Discussion on applications should be moved to a separate section.
* Theory, methodology, and/or algorithmic discussions
# Remove the grey box background of equations.
* At least one numerical example
* A section to discuss and/or illustrate the applications
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Outer-approximation (OA)|Outer-approximation]] ==

* An introduction of the topic
# See formatting guideline below
# Avoid opinionated statements such as “MINLP problems are usually the hardest to solve”.
# Rearrange the text such that the MINLP formulation is in the theory section and keep the introduction in words only.
* Theory, methodology, and/or algorithmic discussions
# Consider left aligning equations and optimization problem formulations by the “=”. See [[Stochastic programming|https://optimization.cbe.cornell.edu/index.php?title=Stochastic_programming]] for an example
# The sentence “The Outer-Approximation (OA) algorithm was first proposed by Duran and and Grossmann in 1986 to solve MINLP problems.” needs a reference.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# “Minimize” and “subject to” should be “min” and “s.t.” in MathType
* A section to discuss and/or illustrate the applications
# Does not explicitly point out why OA is applicable (and/or preferred) in these applications, rather than other MINLP approaches (show that the problem formulations are amenable to a solution approach through OA)
# The sentence “... an active research area and there exists a vast number of applications in fields such as engineering, computational chemistry, and finance.” needs references.
# Posting GAMS code on the page is generally inappropriate and discouraged. Please check with the TAs or me if you have a strong desire to post GAMS codes on the Wiki page. A typical textbook should not be limited to a specific software package. If the GAMS code must be posted, please also post ALL other software implementation versions, such as Pyomo and JuliaOPT, among others.
# Consider reformatting to make steps more readable. Inserting spaces and breaking down steps would help.
* A conclusion section
# Too short. Consider discussion on future research direction and discussion on uncertainty
# Please review abbreviations throughout the page. Why is MINLP redefined here? “Outer-Approximation is a well known efficient approach for solving convex mixed-integer nonlinear programs (MINLP)”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove "Template:Reflist"

== [[Unit commitment problem]] ==

* Author list
* An introduction of the topic
# Please expand the introduction and avoid discussions of examples or specific applications in this section.
# The sentence “Nonlinear, Non-convex programming optimization problem.” doesn’t make sense by itself and Non-convex shouldn’t be capitalized.
* Theory, methodology, and/or algorithmic discussions
# Figure/image format should be revised to better display the content.
# Uppercase characters are used randomly (e.g., “non-convex transmission Constraints”) . Please follow correct language conventions for sentence structure.
# Avoid inserting inline citations after words like “written in matrix form as equation [3]..” or “presented in [3]...” as it is a bit informal when you don’t explicitly name the subject. Also these two sentences are grammatically incorrect and appear to be missing an ending period and comma, respectively.
# Don’t say “written in matrix form as equation..” and just cite the reference, actually write out the equation.
# Properly label the figure in this section with a figure number and improve visibility by making it larger.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Label the figures in this section properly with figure numbers.
# Fix typo “while minimize” to “while minimizing”.
# Avoid pronouns such as “we”.
# Use the equation editor when typing equations.
# A numerical example is simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments). There is an Application section where you discuss the applications.
# The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).
* A section to discuss and/or illustrate the applications:
# I suggest changing the order of the subtitles here. For example, Single-Period Unit Commitment.
* A conclusion section
* References

== [[Frank-Wolfe]] ==

* Author list:
* An introduction of the topic
# I suggest highlighting disadvantages along with advantages.
* Theory, methodology, and/or algorithmic discussions
# “[n x 1] matrix” please use the equation editor to express mathematical descriptions and symbols (p,b, etc)
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please show at least a few iterations. Even for smaller examples if needed. Report the final solution.
# Please use the LaTex code or equation editor for min and include s.t., etc.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps. For your example, please explicitly state that the derivative is taken etc.
* A section to discuss and/or illustrate the applications:
* A conclusion section
# Same as the introduction. Pros and cons should be evaluated together!
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Line search methods|Line Search Method]] ==

* Author list
* An introduction of the topic
# Expand the introduction and avoid discussion on some of the specific steps in the solution process.
# Provide references here.
* Theory, methodology, and/or algorithmic discussions
# The phrase “are as follows” in the steepest descent method discussion needs to be followed by a colon.
# Rephrase “has a nice convergence theory” and cite a reference for this claim.
# Avoid pronouns such as “we”.
# Add citation after “.. proposed by Phillip Wolfe in 1969.”
# Figure 1 is between two sections. Please fix this issue.
* At least one numerical example:
# Add some space between iterations or subsection break
* A section to discuss and/or illustrate the applications:
# Too few references in this section.
# Last paragraph makes some claims without references.
* A conclusion section
* References
# References should be properly formatted. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Piecewise linear approximation|Piecewise Linear Approximation]]==

* Author list
* An introduction of the topic
# The content of this section is good, but there are some issues with sentence clarity and some other grammatical errors. Please revisit this section and make changes accordingly.
* Theory, methodology, and/or algorithmic discussions
# Fix typo “to force the x’ values become associated with”.
* At least one numerical example
* A section to discuss and/or illustrate the applications
# Please aim for a maximum average sentence length of ~25 words. Some of these longer sentences are hard to read.
* A conclusion section
# Expand the conclusion section to be longer than one sentence. The conclusion section to include a brief summary of what was discussed above, an emphasis on it’s significance, and a brief discussion of future extensions and research direction if applicable.
* References
# Include hyperlinks to sources when possible.

== [[Mathematical programming with equilibrium constraints|Mathematical Programming with Equilibrium constraints]] ==

* An introduction of the topic
# This section includes several terms like variational inequalities, constraint qualifications that were not discussed in the class. Please add a sentence to explain them before using them.
* Theory, methodology, and/or algorithmic discussions
# The meaning of parameter vector x is unclear. Please add more information or update if necessary.
# Equations and symbols in the PIPA subsection are not formatted correctly. Please use the same formatting for all equations, so they read as mathematical equations and not text. This goes for all other sections as well.
# Use equations instead of images to represent math programs and equations in the Implicit Descent and SQP subsection.
# Apart from the steps for each solution technique, please also add a few sentences that describe each method.
* At least one numerical example
# Please define the terms like NCP, MP before abbreviating them. Also try not to unnecessarily abbreviate simple terms.
# Equations should be typed by LaTex. Images for equations are unacceptable.
# GAMS code is strongly discouraged. Please solve the problem "step-by-step".
# The selected numerical example is fine but is directly solved with the MPEC solver in GAMS. Try to solve it manually like the homework/in-class problems step by step using the steps described in the previous section by choosing any of the methods.
# Avoid using figures in the equations (subject to etc)
* A section to discuss and/or illustrate the applications
# Add references to “power management, highway pricing, chemical process engineering, and traffic planning.”
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# This Wiki contains very few references. Please check the list below and run a quick Google (Scholar) search to identify relevant literature.

== [[Wing shape optimization|Wing shape Optimization]] ==

* Author list: Remove cornell ID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC. Any formatting issue will incur a penalty in the grading.
* An introduction of the topic
# The introduction is missing several references (e.g., “software packages like computational fluid dynamics..”, sentences containing things that aren’t common knowledge, performance claims, etc.)
# Avoid discussion involving finer details of subject methods in this section.
# In the titles, please change the font from bold to normal to have consistent formatting in the site. Same applies to box of content!
* Theory, methodology, and/or algorithmic discussions
# Properly cite the CFD package, don’t just include a link.
# Properly label the figure with a figure number.
# Consider removing white space between isolated sentences to improve readability.
* At least one numerical example
# If you’ve already defined an abbreviation (CFD), there is no need to define it again. Just use the abbreviation.
# Avoid pronouns such as “we” or “they”.
# Phrases like “under the following” need to be followed by a colon.
# Properly label the figure with a figure number and consider making them larger to improve visibility. Call the reader's attention to the figures in text by referencing the figure number.
# “As seen in the video below” is stated yet there are only images present and it may be initially unclear to the reader which figure is being referenced here.
# Avoid inserting inline citations like “[4] introduces an..” as it is a bit informal when you don’t explicitly name the subject.
# Don’t just cite the reference when discussing the problem formulation, explicitly write the model formulation and solution process using LaTex or equation visual editor.
# Your team should ideally create a numerical example independently. If you take a numerical example directly from a textbook, etc., you will need to get explicit permission from the author in writing and share that written permission with me.
# A numerical example is simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments). There is an Application section where you discuss the applications.
# The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).
* A section to discuss and/or illustrate the applications
# Some characters are randomly capitalized in this section.
* A conclusion section
# These variables should be defined before the conclusion section, they are out of place here. Also, please use normal text when explaining variables except for the variable symbol.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Interior-point method for NLP|Interior point method for NLP]] ==

* Theory, methodology, and/or algorithmic discussions
** Need discussion about the concept of “central path” and the notion of self concordance
** Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
** Fix typo “optimisation”.
== [[AdaGrad|Adagrad]] ==
* At least one numerical example
# In the first sentence, “..take the following numerical example” should be followed by a colon.
* A section to discuss and/or illustrate the applications
# This section is too short; include specific applications in which input features are sparse and Adagrad excels.
*
* References

# References not properly formatted

== [[McCormick envelopes|McCormick Envelopes]] ==

* Author list: OK but I suggest removing NetID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# First sentence is hard to read. Please consider keeping sentences below 25-30 words.
# No references provided. Please cite all sources.
# Figure 1 is provided in the middle between two sections. Please include in the introduction section.
* Theory, methodology, and/or algorithmic discussions
# References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# When using mathematical expressions and symbols, please use the equation editor. (e.g., x*y, exy + y, sin (x+y) - x2)
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# The solution technique should be clearly presented, and solved "step-by-step".
# GAMS code is unnecessary. Please provide detailed step-by-step calculation results.
* A section to discuss and/or illustrate the applications
# Having a list is not enough. Please explain at least three applications in a few sentences each.
# This section should be at least a paragraph to discuss relevant applications. Each application should be explicitly linked to the page topic. A few keywords do not meet the requirement at all.
* A conclusion section:
* References
# References are not expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please follow the standard reference style - the current format is incorrect.

== [[Branch and bound (BB) for MINLP|Branch and Bound for MINLP]] ==

* Author list:
** Remove NetIDS
** Please remove abbreviations from the title (i.e. BB).
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# Please cite sources appropriately: References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Introduction is very short for a well-recognized topic. Please expand significantly. You may refer to the Wiki examples to get an idea on writing the Introduction to a topic.
# An illustration might be useful here.
* Theory, methodology, and/or algorithmic discussions
# The algorithm described here considers only binary integer variables. However, MINLP problems may include non-binary integer variables too. Please update the method or provide a short description of the assumptions that the MINLP problem needs to satisfy in order for the presented technique to be applicable.
# Use linked citations please as the Wiki template above.
# Please provide steps in a more organized way. Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
# Step 2 is missing yet it is referenced in the text multiple times. Please address this in addition to the above comment.
# An illustration might be useful here as well.
# Please explain what a Gomory Cut is. If the topic is available on optimization.cb.cornell.edu, you can link it.
# The current equations seem to be simple text written in Italics. All mathematical symbols and equations should be formatted via LaTex.
# Please format the math programs with equations and notations using formulations in lecture notes as templates.
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# Please show a step-by-step solution in the example. The solution is incomplete. The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).
# Please use the equation editor for equations or mathematical symbols. - All mathematical symbols and equations should be formatted via LaTex - this is a learning objective of the Wiki assignment. You can find some useful links on converting your equations/symbols into LaTex code here: (<nowiki>https://optimization.cbe.cornell.edu/index.php?title=Help:Contents</nowiki>). Again, any formatting issue will incur a "compound" penalty in the grading.
# This example does not follow the MINLP structure discussed in the above section since binary variables are missing. Branch and bound may not be appropriate for such problems. Please provide an appropriate numerical example and solve it according to the above comments.
# Make sure your example is not taken from a book as that is strictly disallowed.
* A section to discuss and/or illustrate the applications
# This section is not well-formatted. Please provide 3 applications and explain each in a few sentences and how BB for MINLP could be used. Also, please eliminate having multiple sections (Application, Mathematical problem, industrial application). All these could be merged together.
# This section should be at least a paragraph to discuss relevant applications. Each application should be explicitly linked to the page topic. A few keywords do not meet the requirement at all.
* A conclusion section:
# The sentence is hard to understand "a scheme that grows exponentially because" please use a simple language. Is it also theoretically correct? It is also not mentioned and explained earlier. Thus, please avoid introducing new concepts or terms at the end.
# Please use summarizing sentences to describe earlier sections instead of introducing new concepts/discussion.
* References
# Too few references overall, you should aggregate information from multiple sources. A quick Google scholar search could provide relevant references.
# References are not expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please follow the standard reference style - the current format is incorrect.

2021 Cornell Optimization Open Textbook Feedback

2021-12-18T20:43:46Z

Asa273: /* Lagrangian duality */

== [[Lagrangean duality|Lagrangian duality]] ==
* Author list, sections and TOC
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions
# The Lagrangian variables associated with equality constraints h(x) are unbounded but the Lagrangian dual problem states them as non-negative. Please fix the same.

* At least one numerical example
# Please update the dual objective function and domain of dual variables accordingly.
* A section to discuss and/or illustrate the applications

* A conclusion section
* References

== [[Disjunctive inequalities|Disjunctive Inequalities]] ==
* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section

* References
==[[Stochastic programming|Stochastic Programming]]==

* An introduction of the topic
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
* Theory, methodology, and/or algorithmic discussions
** The symbol “xi” in the methodology subsection should be explained.
** The inline notations (`x1`, `s1`) should also be typed using LaTex.

* A section to discuss and/or illustrate the applications;
# I suggest eliminating citing the last name of the first author (i.e. Zhou et al.)
==[[Exponential transformation|Exponential Transformation]]==

* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section

* References
== [[Portfolio optimization|Portfolio Optimization]] ==

* Author list

* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions
# Rephrase “Cut the relevant information and conditions in the portfolio optimization, as well as the final requirements into the relevant variables, constraints and linear functions of the linear programming problem.”
* At least one numerical example
# Fix misspelling “dolling decision variables”.
* A section to discuss and/or illustrate the applications

* A conclusion section
# Need some commas here (second sentence hard to read).
* References
# Remove white space between end of sentences and reference numbers.

== [[Chance-constraint method|Chance constraint method]] ==

* Author list:
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions
# Some normal text was expressed as equation.
* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section

* References
== [[Bayesian Optimization]] ==
* Introduction
# Discussion on applications should be moved to a separate section.
* Theory, methodology, and/or algorithmic discussions
# Captions need reformatting.
# Consider italicizing keywords rather than bolding.
# Please add a citation to the first sentence.
# Avoid pronouns such as “we”.
# Acquisition function figure could be made larger and clearer to improve readability.
* At least one numerical example
# Any references to functions or methods in code ‘e.g. fmin’ should be properly formatted as code-stylized text.
# Please use the equation editor for min, st., etc.
# Avoid including a figure of the code for this example and explicitly describe the steps to the modeling and solution process instead.
# Avoid pronouns such as “our” and “we”.
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Conjugate gradient methods]] ==
* Theory, methodology, and/or algorithmic discussions
# All equations need to be better formatted.
# Please indent equation blocks.
# Please properly format pseudocode.
* A conclusion section
# Consider adding future research directions
== [[Geometric programming|Geometric Programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Examples of applications in this section use the same reference. Please cite their individual sources.
* Theory, methodology, and/or algorithmic discussions
# The symbol denoting the domain in the definition of a monomial is unclear. Please clarify it or fix this if it is incorrect.
# Definition of posynomial refers to section 2.1 which is missing from the Wiki (sections are not numbered in the main text).
# In the generalized posynomial subsection, bullet points do not tell us why h(x) is posynomial. Either provide reasons or simply state that h(x) is posynomial. Also explain why h3 is a generalized posynomial.
# Additional theory on the feasibility analysis could be provided in this section.
* At least one numerical example
# In the transformation example, the last two constraints could also be simplified. Please update them as well.
* A section to discuss and/or illustrate the applications
# The figure in this section needs to be labeled.
# The figure needs to be resized and perhaps aligned to the center.
* A conclusion section:
# Please avoid vague language such as: “This makes”.
# Please avoid opinionated statements: “one of the best ways”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# This Wiki has very few references. A quick Google Scholar search may provide relevant references.

== [[Adam]] ==

* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions
# Avoid inserting inline citations after words like “This article..” as it is a bit informal. This could be rephrased or changed to something like “According to author,^[2] …” with author name inserted.
* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section
* References
== [[A-star algorithm|a* algorithm]] ==

* Author list
* An introduction of the topic:
# Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.
# There are no citations in the introduction. Please cite every source.
* Theory, methodology, and/or algorithmic discussions
# Please add the mathematical description of the algorithm. (Insufficient)
# Please fix grammatical and spelling errors as (“from current position to the goal”, “There are a lot of discussions”, etc). Also, many hyphens are missing as “non playable”.
* At least one numerical example
# The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.
* A section to discuss and/or illustrate the applications
* A conclusion section
* References

== [[Job shop scheduling|Job-Shop Scheduling Problem]] ==

* An introduction of the topic
# The current introduction to the jobshop scheduling problem has only two sentences in addition to the parameter description. Introduction typically contains information about the problem, its importance in the real-world, and some information about the solution techniques and their types to solve the problem. Please add some information that covers the above.
* Theory, methodology, and/or algorithmic discussions
# It is unclear whether the assumptions stated in this section are required to apply the following solution techniques. Please clarify the same. Also use complete sentences to state them.
# The branch and bounds method described in this section only discusses the solution technique for problems with one machines. However, branch and bound is a general technique that can be applied to any MILP problems with varying scales. Please update the “methods” section to be as general as possible.
# Since this Wiki focuses on jobshop scheduling, at least two methods are expected. Branch and bound is a general MILP technique, so, it is recommended to add a tailored technique that can only solve specific jobshop scheduling problems. Solving the numerical example with this technique is not necessary.
# Reference to the branch and bound technique described in this section is a “youtube” video. Please add references in literature that describe this method in detail. The method used in this video is highly tailored for a single machine application. This is also an incorrect way to cite a reference. Please keep this section as general as possible.
# Use LaTex code or equation editor to display all equations and variables in this section and all other sections as well.
# Check grammar in this section. For example, phrases like “are as follows” need to be followed by a colon and not a period.
# Consider rewriting the assumptions as a list in this section.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# The example used in this section is exactly the same as the one in the youtube video. Please use a modification of this example or choose another example/method to demonstrate the solution technique. Your team should ideally create a numerical example independently. If you take a numerical example directly from a particular source, you will need to get explicit permission from the textbook author in writing and share that written permission with the instructors.
# The figure in this section is not numbered when all others are. Relabel this figure for consistency and its number to refer to it in-text.
# A numerical example should be simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments).
* A section to discuss and/or illustrate the applications
# This section should only focus on real-world applications of the jobshop scheduling problem. But currently, this section includes additional information on solution techniques/complexity that is appropriate for the Introduction section. Please discuss the applications of the problem in this section.
* A conclusion section
# The meaning of “Operations applications” is unclear. Please explain or update if necessary.
# The current conclusion section does not properly summarize the problem. Please refer to other Wiki examples for an idea to update the section accordingly.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please reference media sources like reference 5 appropriately.
# A simple Google Scholar search would give you many "formal" references.

== [[Optimization in game theory]] ==

* Author list: remove cornell IDs.
* An introduction of the topic
# References are not linked. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
* Theory, methodology, and/or algorithmic discussions
# Why only a subsection on "Nash Equilibrium" is included in "Theory" section? Please re-format.
# Please edit references.
# Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm.
# Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.
* At least one numerical example
# Please organize the last part in a more readable format. Questions may be in bold and numbered, answers are more direct, etc.
# Remember to cite all images and tables.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# Very good, link the reference and cite all sources.
* A conclusion section
# Please add more summarizing especially from theory sentences and avoid long sentences.
* References
# Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Reference primary sources rather than Wikipedia
# Incorrect reference style. Please correct.

== [[Trust-region methods]] ==
* An introduction of the topic
** Avoid pronouns such as “we”. This goes for all other sections as well.

* Theory, methodology, and/or algorithmic discussions
# Organization of ideas in this section needs work.
# You have not defined explicitly why the Cauchy point is important to compute beyond a vague allusion to performance improvements, which is also wrong (it is useful because of its guarantees for convergence, not performance) It is also misspelled.
# Please format the algorithm in proper algorithmic pseudocode format.
* References
# Incorrect reference style.

*There are numerous misspellings, grammatical errors, and incorrect claims. Please fix these.

== [[Momentum]] ==
* An introduction of the topic
# Apart from an explanation on momentum, it is necessary to briefly point out the limitations of SGD and why momentum could help with these limitations. Please update it accordingly.
# Remove bold on “Momentum”.
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
* Theory, methodology, and/or algorithmic discussions
#
# The definition of the update rule for SGD with momentum looks incorrect, specifically the first expression. Please fix it and also explain all the parameters used.
# Use LaTex code or equation editor to display all equations and variables (e.g., “W”, “V`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “you”.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step". Since writing all iterations is not feasible, at least present a few iterations for both cases.
# Please try to label the plots that explains what each line color means.
# Starting point for SGD with momentum is different in explanation and the table. Please fix the same.
* A section to discuss and/or illustrate the applications
# Please use correct terminology like “optimizing non-convex functions” and not “training non-convex models”.
* References
# Almost all references used are URLs. Please try to add journal/conference articles or books for references, instead of directly citing the URLs. Please check the list below and run a quick Google (Scholar) search to identify relevant literature.

== [[Stochastic dynamic programming|Stochastic Dynamic programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Discussion on applications should be moved to a separate section.
* Theory, methodology, and/or algorithmic discussions
# Remove the grey box background of equations.
* At least one numerical example
* A section to discuss and/or illustrate the applications
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Outer-approximation (OA)|Outer-approximation]] ==

* An introduction of the topic
# See formatting guideline below
# Avoid opinionated statements such as “MINLP problems are usually the hardest to solve”.
# Rearrange the text such that the MINLP formulation is in the theory section and keep the introduction in words only.
* Theory, methodology, and/or algorithmic discussions
# Consider left aligning equations and optimization problem formulations by the “=”. See [[Stochastic programming|https://optimization.cbe.cornell.edu/index.php?title=Stochastic_programming]] for an example
# The sentence “The Outer-Approximation (OA) algorithm was first proposed by Duran and and Grossmann in 1986 to solve MINLP problems.” needs a reference.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# “Minimize” and “subject to” should be “min” and “s.t.” in MathType
* A section to discuss and/or illustrate the applications
# Does not explicitly point out why OA is applicable (and/or preferred) in these applications, rather than other MINLP approaches (show that the problem formulations are amenable to a solution approach through OA)
# The sentence “... an active research area and there exists a vast number of applications in fields such as engineering, computational chemistry, and finance.” needs references.
# Posting GAMS code on the page is generally inappropriate and discouraged. Please check with the TAs or me if you have a strong desire to post GAMS codes on the Wiki page. A typical textbook should not be limited to a specific software package. If the GAMS code must be posted, please also post ALL other software implementation versions, such as Pyomo and JuliaOPT, among others.
# Consider reformatting to make steps more readable. Inserting spaces and breaking down steps would help.
* A conclusion section
# Too short. Consider discussion on future research direction and discussion on uncertainty
# Please review abbreviations throughout the page. Why is MINLP redefined here? “Outer-Approximation is a well known efficient approach for solving convex mixed-integer nonlinear programs (MINLP)”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove "Template:Reflist"

== [[Unit commitment problem]] ==

* Author list
* An introduction of the topic
# Please expand the introduction and avoid discussions of examples or specific applications in this section.
# The sentence “Nonlinear, Non-convex programming optimization problem.” doesn’t make sense by itself and Non-convex shouldn’t be capitalized.
* Theory, methodology, and/or algorithmic discussions
# Figure/image format should be revised to better display the content.
# Uppercase characters are used randomly (e.g., “non-convex transmission Constraints”) . Please follow correct language conventions for sentence structure.
# Avoid inserting inline citations after words like “written in matrix form as equation [3]..” or “presented in [3]...” as it is a bit informal when you don’t explicitly name the subject. Also these two sentences are grammatically incorrect and appear to be missing an ending period and comma, respectively.
# Don’t say “written in matrix form as equation..” and just cite the reference, actually write out the equation.
# Properly label the figure in this section with a figure number and improve visibility by making it larger.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Label the figures in this section properly with figure numbers.
# Fix typo “while minimize” to “while minimizing”.
# Avoid pronouns such as “we”.
# Use the equation editor when typing equations.
# A numerical example is simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments). There is an Application section where you discuss the applications.
# The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).
* A section to discuss and/or illustrate the applications:
# I suggest changing the order of the subtitles here. For example, Single-Period Unit Commitment.
* A conclusion section
* References

== [[Frank-Wolfe]] ==

* Author list:
* An introduction of the topic
# I suggest highlighting disadvantages along with advantages.
* Theory, methodology, and/or algorithmic discussions
# “[n x 1] matrix” please use the equation editor to express mathematical descriptions and symbols (p,b, etc)
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please show at least a few iterations. Even for smaller examples if needed. Report the final solution.
# Please use the LaTex code or equation editor for min and include s.t., etc.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps. For your example, please explicitly state that the derivative is taken etc.
* A section to discuss and/or illustrate the applications:
* A conclusion section
# Same as the introduction. Pros and cons should be evaluated together!
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Line search methods|Line Search Method]] ==

* Author list
* An introduction of the topic
# Expand the introduction and avoid discussion on some of the specific steps in the solution process.
# Provide references here.
* Theory, methodology, and/or algorithmic discussions
# The phrase “are as follows” in the steepest descent method discussion needs to be followed by a colon.
# Rephrase “has a nice convergence theory” and cite a reference for this claim.
# Avoid pronouns such as “we”.
# Add citation after “.. proposed by Phillip Wolfe in 1969.”
# Figure 1 is between two sections. Please fix this issue.
* At least one numerical example:
# Add some space between iterations or subsection break
* A section to discuss and/or illustrate the applications:
# Too few references in this section.
# Last paragraph makes some claims without references.
* A conclusion section
* References
# References should be properly formatted. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Piecewise linear approximation|Piecewise Linear Approximation]]==

* Author list
* An introduction of the topic
# The content of this section is good, but there are some issues with sentence clarity and some other grammatical errors. Please revisit this section and make changes accordingly.
* Theory, methodology, and/or algorithmic discussions
# Fix typo “to force the x’ values become associated with”.
* At least one numerical example
* A section to discuss and/or illustrate the applications
# Please aim for a maximum average sentence length of ~25 words. Some of these longer sentences are hard to read.
* A conclusion section
# Expand the conclusion section to be longer than one sentence. The conclusion section to include a brief summary of what was discussed above, an emphasis on it’s significance, and a brief discussion of future extensions and research direction if applicable.
* References
# Include hyperlinks to sources when possible.

== [[Mathematical programming with equilibrium constraints|Mathematical Programming with Equilibrium constraints]] ==

* An introduction of the topic
# This section includes several terms like variational inequalities, constraint qualifications that were not discussed in the class. Please add a sentence to explain them before using them.
* Theory, methodology, and/or algorithmic discussions
# The meaning of parameter vector x is unclear. Please add more information or update if necessary.
# Equations and symbols in the PIPA subsection are not formatted correctly. Please use the same formatting for all equations, so they read as mathematical equations and not text. This goes for all other sections as well.
# Use equations instead of images to represent math programs and equations in the Implicit Descent and SQP subsection.
# Apart from the steps for each solution technique, please also add a few sentences that describe each method.
* At least one numerical example
# Please define the terms like NCP, MP before abbreviating them. Also try not to unnecessarily abbreviate simple terms.
# Equations should be typed by LaTex. Images for equations are unacceptable.
# GAMS code is strongly discouraged. Please solve the problem "step-by-step".
# The selected numerical example is fine but is directly solved with the MPEC solver in GAMS. Try to solve it manually like the homework/in-class problems step by step using the steps described in the previous section by choosing any of the methods.
# Avoid using figures in the equations (subject to etc)
* A section to discuss and/or illustrate the applications
# Add references to “power management, highway pricing, chemical process engineering, and traffic planning.”
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# This Wiki contains very few references. Please check the list below and run a quick Google (Scholar) search to identify relevant literature.

== [[Wing shape optimization|Wing shape Optimization]] ==

* Author list: Remove cornell ID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC. Any formatting issue will incur a penalty in the grading.
* An introduction of the topic
# The introduction is missing several references (e.g., “software packages like computational fluid dynamics..”, sentences containing things that aren’t common knowledge, performance claims, etc.)
# Avoid discussion involving finer details of subject methods in this section.
# In the titles, please change the font from bold to normal to have consistent formatting in the site. Same applies to box of content!
* Theory, methodology, and/or algorithmic discussions
# Properly cite the CFD package, don’t just include a link.
# Properly label the figure with a figure number.
# Consider removing white space between isolated sentences to improve readability.
* At least one numerical example
# If you’ve already defined an abbreviation (CFD), there is no need to define it again. Just use the abbreviation.
# Avoid pronouns such as “we” or “they”.
# Phrases like “under the following” need to be followed by a colon.
# Properly label the figure with a figure number and consider making them larger to improve visibility. Call the reader's attention to the figures in text by referencing the figure number.
# “As seen in the video below” is stated yet there are only images present and it may be initially unclear to the reader which figure is being referenced here.
# Avoid inserting inline citations like “[4] introduces an..” as it is a bit informal when you don’t explicitly name the subject.
# Don’t just cite the reference when discussing the problem formulation, explicitly write the model formulation and solution process using LaTex or equation visual editor.
# Your team should ideally create a numerical example independently. If you take a numerical example directly from a textbook, etc., you will need to get explicit permission from the author in writing and share that written permission with me.
# A numerical example is simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments). There is an Application section where you discuss the applications.
# The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).
* A section to discuss and/or illustrate the applications
# Some characters are randomly capitalized in this section.
* A conclusion section
# These variables should be defined before the conclusion section, they are out of place here. Also, please use normal text when explaining variables except for the variable symbol.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Interior-point method for NLP|Interior point method for NLP]] ==

* Theory, methodology, and/or algorithmic discussions
** Need discussion about the concept of “central path” and the notion of self concordance
** Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
** Fix typo “optimisation”.
== [[AdaGrad|Adagrad]] ==
* At least one numerical example
# In the first sentence, “..take the following numerical example” should be followed by a colon.
* A section to discuss and/or illustrate the applications
# This section is too short; include specific applications in which input features are sparse and Adagrad excels.
*
* References

# References not properly formatted

== [[McCormick envelopes|McCormick Envelopes]] ==

* Author list: OK but I suggest removing NetID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# First sentence is hard to read. Please consider keeping sentences below 25-30 words.
# No references provided. Please cite all sources.
# Figure 1 is provided in the middle between two sections. Please include in the introduction section.
* Theory, methodology, and/or algorithmic discussions
# References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# When using mathematical expressions and symbols, please use the equation editor. (e.g., x*y, exy + y, sin (x+y) - x2)
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# The solution technique should be clearly presented, and solved "step-by-step".
# GAMS code is unnecessary. Please provide detailed step-by-step calculation results.
* A section to discuss and/or illustrate the applications
# Having a list is not enough. Please explain at least three applications in a few sentences each.
# This section should be at least a paragraph to discuss relevant applications. Each application should be explicitly linked to the page topic. A few keywords do not meet the requirement at all.
* A conclusion section:
* References
# References are not expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please follow the standard reference style - the current format is incorrect.

== [[Branch and bound (BB) for MINLP|Branch and Bound for MINLP]] ==

* Author list:
** Remove NetIDS
** Please remove abbreviations from the title (i.e. BB).
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# Please cite sources appropriately: References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Introduction is very short for a well-recognized topic. Please expand significantly. You may refer to the Wiki examples to get an idea on writing the Introduction to a topic.
# An illustration might be useful here.
* Theory, methodology, and/or algorithmic discussions
# The algorithm described here considers only binary integer variables. However, MINLP problems may include non-binary integer variables too. Please update the method or provide a short description of the assumptions that the MINLP problem needs to satisfy in order for the presented technique to be applicable.
# Use linked citations please as the Wiki template above.
# Please provide steps in a more organized way. Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
# Step 2 is missing yet it is referenced in the text multiple times. Please address this in addition to the above comment.
# An illustration might be useful here as well.
# Please explain what a Gomory Cut is. If the topic is available on optimization.cb.cornell.edu, you can link it.
# The current equations seem to be simple text written in Italics. All mathematical symbols and equations should be formatted via LaTex.
# Please format the math programs with equations and notations using formulations in lecture notes as templates.
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# Please show a step-by-step solution in the example. The solution is incomplete. The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).
# Please use the equation editor for equations or mathematical symbols. - All mathematical symbols and equations should be formatted via LaTex - this is a learning objective of the Wiki assignment. You can find some useful links on converting your equations/symbols into LaTex code here: (<nowiki>https://optimization.cbe.cornell.edu/index.php?title=Help:Contents</nowiki>). Again, any formatting issue will incur a "compound" penalty in the grading.
# This example does not follow the MINLP structure discussed in the above section since binary variables are missing. Branch and bound may not be appropriate for such problems. Please provide an appropriate numerical example and solve it according to the above comments.
# Make sure your example is not taken from a book as that is strictly disallowed.
* A section to discuss and/or illustrate the applications
# This section is not well-formatted. Please provide 3 applications and explain each in a few sentences and how BB for MINLP could be used. Also, please eliminate having multiple sections (Application, Mathematical problem, industrial application). All these could be merged together.
# This section should be at least a paragraph to discuss relevant applications. Each application should be explicitly linked to the page topic. A few keywords do not meet the requirement at all.
* A conclusion section:
# The sentence is hard to understand "a scheme that grows exponentially because" please use a simple language. Is it also theoretically correct? It is also not mentioned and explained earlier. Thus, please avoid introducing new concepts or terms at the end.
# Please use summarizing sentences to describe earlier sections instead of introducing new concepts/discussion.
* References
# Too few references overall, you should aggregate information from multiple sources. A quick Google scholar search could provide relevant references.
# References are not expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please follow the standard reference style - the current format is incorrect.

2021 Cornell Optimization Open Textbook Feedback

2021-12-07T15:33:51Z

Asa273: Moved comments on compressed sensing to Gdoc

== [[Lagrangean duality|Lagrangian duality]] ==
* Author list, sections and TOC
# Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.
# Remove cornell ID from Author list
* An introduction of the topic
# This section includes sentences on constructing the dual problem and is referred to as Lagrangian relaxation (LR). This is incorrect, please fix the definition of LR.
# Definitions of LR and its relation to duality should be double checked and re-written.
# Only one reference is present in this section. Please add more relevant references by expanding this section.
# Consider merging the “introduction” and “history” sections.
# In the titles, please change the font from bold to normal to have consistent formatting in the site.
* Theory, methodology, and/or algorithmic discussions
# The Lagrangian variables associated with equality constraints h(x) are unbounded but the Lagrangian dual problem states them as non-negative. Please fix the same.
# Also to construct a dual, we do not change minimization to maximization directly. We observed such things in the examples in lecture notes due to simplification. The lagrangian dual problem would be minimize (,).
# Adding to the previous point, the Lagrangian is a lower bound on the original objective; the solution to the primal and dual or only equivalent if the duality gap is 0. You reference this in one section, but this is after your statement “Hence, solving the dual problem, which is a function of the Lagrangian multipliers (𝜆*) yields the same solution as the primal problem, which is a function of the original variables (x*). “. Please clarify the specific conditions that must hold for the solution of the dual to be equal to the primal’s.
# You refer to the “Complementary Slackness Theorem”, but don’t actually write the mathematical representation of complementary slackness. Please fix this. Also consider including the derivation of the complementary slackness condition, as it is both easy and short. Boyd is a good reference for this.
# Last step of the “process” subsection also needs updating according to the previous comments.
# The inline notations should also be typed using LaTex.
# Please use the LaTex code or equation editor for min, s.t., etc.
* At least one numerical example
# Only one dual variable is associated with each constraint. The numerical example uses two for the first and second constraint which is unnecessary. Please update it accordingly for both constraints. This particular example will only have two dual variables instead of the five dual variables used currently.
# All consecutive steps need to be updated since the dual variables would be updated.
# After substitution the nonlinear function should be further simplified. The current expression reads like a highly nonlinear function but can be easily simplified.
# Similar to the comments in the methodology section, inverting minimize to maximize is incorrect. Please update the dual objective function and domain of dual variables accordingly.
# Please use the LaTex code or equation editor for min, s.t., etc.
* A section to discuss and/or illustrate the applications
# Bullet points could be used to state the last four real-world examples that explain the physical meaning of the primal and dual problems.
# Add references for the last set of applications.
* A conclusion section
# This section contains a few typos. Please fix the same.
* References
# Some citations' hyperlinks are displaying.

== [[Disjunctive inequalities|Disjunctive Inequalities]] ==

* Author list
# Missing course section and semester
# Remove cornell ID
* An introduction of the topic
# No citations are present in this section.
# “mixed-integer programming (MIP)” should be used instead of “multiple integer programming (MIP)”. Please fix this error.
* Theory, methodology, and/or algorithmic discussions
# The abbreviation MILP is not previously defined. Please fix this issue.
# You consistently use the negative sign instead of the NOT operator for y (-y instead of ¬y).
# Some inconsistencies with the spacing of variables, constraints, etc., under the “General” section that need to be fixed.
# Typo in “This is shown below by M1, M2, y1, and y1:” where y1 needs to be changed to y2. Why use two different Big-M variables here? Elsewhere in the Wiki you only use one so this could lead to confusion with a general audience. Also if this was taken from the lecture notes then it needs to be cited.
* At least one numerical example
# Please reformulate and solve a complete numerical example rather than just reformulating a general example. Demonstrate the use of Big-M and Convex Hull formulation in an optimization problem that provides details such as individual steps in the problem solving process and final results. The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results.
# Add space between vee (V) operator and brackets in first line of Latex
# Please format variables correctly, for example, use <math>x_1</math> instead of x1.
* A section to discuss and/or illustrate the applications
# Please format the equations appropriately either by using latex code or the visual editor. These images are NOT acceptable!
* A conclusion section
# There is no conclusion presented in this section at all.
* References
# The included references have NOT been used anywhere in the Wiki. Add references for sentences that are not common knowledge and please link them appropriately with the text in Wiki. If the figures used here were not original works, you must also cite them.
# There are many papers on this topic. A simple Google (Scholar) search could provide you with sufficient references to cite.
# Many important references of this topic are missing.
# Please consider linking the references as demonstrated in the Wiki tutorial on Canvas and in this template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

==[[Stochastic programming|Stochastic Programming]] ==

* Author list: Remove cornell IDs
* An introduction of the topic
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
# This section only includes two sentences on Stochastic programming (SP), while the rest gives examples of uncertainty. Please discuss the need for SP in the presence of uncertainty. Also, discussion on robust optimization and its limitations should be removed since it is out of place.
* Theory, methodology, and/or algorithmic discussions
# Please avoid direct inline linkbacks to Wikipedia.
# The symbol “xi” in the methodology subsection should be explained.
* At least one numerical example
# Copying a numerical example "entirely" from a textbook is inappropriate. Your team should come up with a "numerical" case.
# No specific application context is needed for a numerical example.
# The inline notations (`x1`, `s1`) should also be typed using LaTex.
# Label all tables with a table number for better readability.
# Properly format the solution table with the label attached rather than the following sentence. The solution table looks different from the others, please fix this for consistency.
* A section to discuss and/or illustrate the applications;
# I suggest eliminating citing the last name of the first author (i.e. Zhou et al.)
* A conclusion section
* References
# URLs of some citations are not properly formatted (not showing the hyperlinks).

== [[Exponential transformation|Exponential Transformation]] ==

* Author list
# Missing course section
# Remove cornell ID
* An introduction of the topic
# Please expand the introduction.
# Please aim for a maximum average sentence length of ~25 words. Last sentence with 51 words is hard to read.
# Second Sentence: please change the word “they” as it could make the meaning ambiguous
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
# If you use abbreviations, please introduce them (e.g. NLP,MINLP)
* Theory, methodology, and/or algorithmic discussions
# Please explain the transformation in words along with equations
# Terms like posynomial should be described in detail.
# Please move the numerical example to the section below
# The “(eq 1)” is not needed here.
# Please expand this section.
* At least one numerical example
# In the third equation of the numerical example, it is confusing to have coefficients after numbers. Some readers may read it as an exponent.
# Last equation in this section after “further linearization” is incorrect. This equation cannot be further linearized, please fix this.
# Please explain the steps in the numerical examples in detail. The step-by-step solution should be provided.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# Missing part of text: “Proof of convexity of with positive definite test of Hessian…”
# Applications are not numerical examples. Please refer to this link for example of applications: [[Duality|https://optimization.cbe.cornell.edu/index.php?title=Duality]]
# Citation 7 is missing in current applications
# The section current applications is redundant
# Please use the LaTex code or equation editor for min, s.t., etc.
# Under current applications, do not just use a hyperlink to describe an application. Actually describe it. And properly inline citation style should be used instead of the hyperlink.
# The convexification application of MINLP can be further simplified for binary variables. Please refer to the lecture slides for more information.
* A conclusion section
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
* References
# Please consider linking the references by using this as Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Citation 7 is missing in current applications

== [[Sparse Reconstruction with Compressed Sensing|Sparse reconstruction with Compressed Sensing]] ==

== [[Portfolio optimization|Portfolio Optimization]] ==

* Author list
# Remove cornell id
* An introduction of the topic
# The introductory sentence should be rephrased. The action of minimizing the risks does not inherently maximize the gains, rather PO aims to maximize gains whilst minimizing risks.
# Amount of whitespace can be reduced by changing the orientation of Figure 1 and the sentences in this section.
# Define terms such as risk, return, portfolio, etc., when you introduce them. Assume that the reader may not know much about finance. This goes for all other sections as well.
* Theory, methodology, and/or algorithmic discussions
# A brief mention of modern portfolio theory (i.e.. Markowitz) would be appropriate in this section.
# Several grammatical errors here involving sentence structure and clarity. Some questionable semantics (e.g., “The portfolio optimization mainly assumes two directions.”) and syntax (phrases such as “.. is as follows” should be followed by a colon). Misuse of commas and missing commas in this section. Two sentences introducing E(rp) and w should be combined into one.
# Use LaTex to distinguish variables written within a sentence, such as m and n.
# Rephrase “Cut the relevant information and conditions in the portfolio optimization, as well as the final requirements into the relevant variables, constraints and linear functions of the linear programming problem.”
# An explanation of a few common constraints would be helpful, rather than just including a table.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Solving the numerical example by GAMS is inappropriate. Please provide detailed step-by-step calculation results.
# All tables need to be labeled.
# Include figure number in label for consistency.
# Fix misspelling “dolling decision variables”.
# Use LaTex for all variables, equations, and constraints here.
# Example 2 table is hard to read, so making it bigger would help.
# Remove the “Using excel as the solver” part from the sentence before the solution discussion.
# Some grammatical errors here (phrases such as “.. is as follows” should be followed by a colon).
* A section to discuss and/or illustrate the applications
# Rephrase “Portfolio optimization can be used to screen investment projects that meet investors, rationally allocate investment amounts, etc.”
# Not sure “relevant” is the correct word choice here.
# You need more specific examples with the utility of portfolio optimization, this section is quite general as is. Some more detail and focus on real-world applications in the financial industry that relate to retirement planning, financial security, economic stability, etc., would be helpful.
* A conclusion section
# Need some commas here.
# The sentence “Linear programming has been around since the 1940’s and has such a wide base of applications” is not necessary.
* References
# Please consider linking the references as demonstrated in the Wiki tutorial on Canvas and in this template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove white space between end of sentences and reference numbers.

== [[Chance-constraint method|Chance constraint method]] ==

* Author list:
* An introduction of the topic
# Please consider correcting a few grammatical errors: “pre-planned for”, “god”, “certain levels of feasibility is guaranteed in what are”, and “Performance of a system”
# In “Chance-constraint”, it is capitalized randomly throughout the introduction. Please correct.
# Please use technical language to briefly introduce chance-constrained programming. Words like “acts of god”, “cost of doing business” are not appropriate for a technical Wiki.
* Theory, methodology, and/or algorithmic discussions
# Please add a citation to the first sentence.
# Xi is an uncertainty/randomness variable. It is better to use clear language.
# Please use the mathematical editor for adding explanations in the text. Using “ x is a decision variable” is hard to read. Same for f(x) and others.
# Theory is insufficient. Please expand and explain different approaches.
# Please add pros and cons explicitly as a list.
# Explain the physical meaning for examples of chance constraints along with all the notations used.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please remove this example as it is directly from this book. The example should be purely numerical without any background.
# Please use the equation editor for min, st., etc.
# Please use the mathematical editor for adding explanations in the text. Using “ x is a decision variable” is hard to read. Same for f(x) and others.
# Please change the table format so as not to confuse the reader.
# Multiple instances of [Chart to be added] are missing.
# Example is incomplete.
# Avoid pronouns such as “we”.
* A section to discuss and/or illustrate the applications
# Please connect several grammatical and spelling errors: “real life application”, Energy creation, particularly in renewable sources, have high variabilities”, and others
# “Zhao, Xue, Cao, and Zhang”. No need to list all authors within the article. Provide a reference is sufficient. If authors must be mentioned, (Zhao et al.) should be ok.
* A conclusion section
# Uniqueness and universality earlier are not clear to me. If they are not discussed earlier in the application, it would be better not to introduce new discussions in the conclusion.
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
* References
# References seem to vary in format. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Bayesian Optimization]] ==
* Section titles should not be "bold". Please double check using source editor on the section titles.
* Contents: The section titles should NOT be in bold to avoid strange format in TOC. Any formatting issue will incur a penalty in the grading.
* Author list: Remove cornell ID, Please check names
* Introduction
# The introduction is too general and not substantial enough. For example, simply saying BayesOpt is useful when the objective function is unknown obscures exactly HOW it is useful (namely, computational efficiency in applications where ground truth sampling is expensive). Discussion on applications should be moved to a separate section.
# Machine learning rarely includes black-box functions to be optimized. Bayesian optimization is almost never used for optimizing ML loss functions but can instead be used for hyperparameter optimization. Please update such claims in this section.
* Theory, methodology, and/or algorithmic discussions
# Captions need reformatting.
# Consider italicizing keywords rather than bolding.
# Please add a citation to the first sentence.
# Discussion on acquisition functions should include comparisons, tradeoffs, and reasons to use one over the other. Should also note that expected improvement is the most widely used in practice, and explain.
# Avoid pronouns such as “we”.
# Please write equations in the Wiki instead of attaching images for equations.
# Acquisition function figure could be made larger and clearer to improve readability.
* At least one numerical example
# Any references to functions or methods in code ‘e.g. fmin’ should be properly formatted as code-stylized text.
# Please use the equation editor for min, st., etc.
# Avoid including a figure of the code for this example and explicitly describe the steps to the modeling and solution process instead.
# Avoid pronouns such as “our” and “we”.
* A section to discuss and/or illustrate the applications
* A conclusion section
# Please do not use brackets to enclose lists.
# Some claims here should be supported by references. Please cite each source after its sentence.
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Try to avoid references to “pop” machine learning blogs where anyone can be an author. (e.g. towardsdatascience)
# All references are URLs. Please cite publications and literature.
# A simple Google Scholar search would give you many references.

Notes on grammar: Needs some work. Several instances where colons are inappropriately inserted mid sentence or in subheadings. Explanations are not terse. Several instances of switching between personal and impersonal style of writing, which is distracting.

== [[Conjugate gradient methods]] ==

* Author list: Remove cornell ID
* Introduction
# All inline notations (e.g., `x`, `A`) should be typed using LaTex.
* Theory, methodology, and/or algorithmic discussions
# All equations need to be better formatted.
# Is Gauss-Newton no longer referenced?
# Theorems listed in the first section should be accompanied with high level explanation, not just a list of the theorems themselves. The page should read like an article, with proper flow.
# Please indent equation blocks.
# Please properly format pseudocode.
* At least one numerical example
# Steps should be accompanied with explanation, or reference to the corresponding step in the pseudocode.
# Please properly format in a more organized manner, aligning equations appropriately and demarcating steps appropriately.
* A section to discuss and/or illustrate the applications
# Consider including 2 additional examples of applications
* A conclusion section
# Consider adding future research directions
* References
# Reference primary sources rather than Wikipedia
# Too few references.
# More references should be added. A simple Google Scholar search would give you many references.

== [[Geometric programming|Geometric Programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Examples of applications in this section use the same reference. Please cite their individual sources.
* Theory, methodology, and/or algorithmic discussions
# The symbol denoting the domain in the definition of a monomial is unclear. Please clarify it or fix this if it is incorrect.
# Definition of posynomial refers to section 2.1 which is missing from the Wiki (sections are not numbered in the main text).
# In the generalized posynomial subsection, bullet points do not tell us why h(x) is posynomial. Either provide reasons or simply state that h(x) is posynomial. Also explain why h3 is a generalized posynomial.
# Additional theory on the feasibility analysis could be provided in this section.
* At least one numerical example
# In the transformation example, the last two constraints could also be simplified. Please update them as well.
* A section to discuss and/or illustrate the applications
# The figure in this section needs to be labeled.
# The figure needs to be resized and perhaps aligned to the center.
* A conclusion section:
# Please avoid vague language such as: “This makes”.
# Please avoid opinionated statements: “one of the best ways”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# This Wiki has very few references. A quick Google Scholar search may provide relevant references.

== [[Adam]] ==

* Author list
* An introduction of the topic
# Some grammatical errors here, mostly related to the need for commas in certain places (e.g., “Before Adam..”).
# Some minor errors with parts of speech throughout the section, need to revisit phrases such as “which has broader scope in future for”, etc.
# Try splitting up some of the longer sentences in this section, a couple are hard to read.
# Avoid definitive statements about Adam being the best or always better solver, as this is simply not true (the choice of the “best” optimizer is setting-dependent). Use language such as “Research has shown that Adam has demonstrated superior experimental performance over..” and then cite academic references to back this claim.
# What does adam stand for? Introduction is insufficient. Please expand.
* Theory, methodology, and/or algorithmic discussions
# Revise grammar here, noticing some missing commas and uncapitalized word after period.
# Rephrase “second one is to update the old position with the updated position”.
# Use LaTex code or equation editor to display all equations and variables in this section, and actual subscripts instead of “m_t”, etc.
# Avoid inserting inline citations after words like “According to..” or “This article..” as it is a bit informal. This could be rephrased or changed to something like “According to author,^[2] …” with author name inserted.
# Remove white space before the period in RMSP discussion.
# Please provide a pseudocode.
# Please use list the two methods here “Adam is a combination of two gradient descent methods which are explained below”
# Please expand the theory section significantly. Theoretical convergence properties should be discussed, even if briefly.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
* A section to discuss and/or illustrate the applications
# Same comment as before, consider replacing inline citations after words like “According to..”.
* A conclusion section
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Try to avoid references to blogs and use peer-reviewed academic references instead.
# Too few references.
# More references should be added. A simple Google Scholar search would give you many references.

== [[A-star algorithm|a* algorithm]] ==

* Author list: Remove cornell ID
* Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.
* An introduction of the topic:
# Weird spacing between paragraphs. Please fix this issue.
# In the titles, please change the font from bold to normal to have consistent formatting in the site.
# Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.
# There are no citations in the introduction. Please cite every source.
* Theory, methodology, and/or algorithmic discussions
# Please add the mathematical description of the algorithm.
# Reference style varies in sentences. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please fix grammatical and spelling errors as (“from current position to the goal”, “There are a lot of discussions”, etc). Also, many hyphens are missing as “non playable”.
# In algorithms, it is a standard to add high-level description (i.e. pseudocode or flowchart). Please incorporate it.
# Use LaTex code or equation editor to display all equations and variables in this section (e.g., “f(n)...”, “h(n)..”, etc.). This goes for other sections as well.
* At least one numerical example
# The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.
# Instead of writing things like “The above image..”, label each figure and use the figure number to refer to it in text.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# No references in the applications. Please cite every source
# Preferably, add at least an additional application.
* A conclusion section
# Conclusion should summarize descriptions. Please modify it to provide a summary.
# Please pay attention to the length and structure of sentences here and in the full page. First sentence is hard to read.
* References
# References seem to vary in format and are not linked correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Incorrect reference style. Please follow the example and use the template.

== [[Job shop scheduling|Job-Shop Scheduling Problem]] ==

* An introduction of the topic
# The current introduction to the jobshop scheduling problem has only two sentences in addition to the parameter description. Introduction typically contains information about the problem, its importance in the real-world, and some information about the solution techniques and their types to solve the problem. Please add some information that covers the above.
* Theory, methodology, and/or algorithmic discussions
# It is unclear whether the assumptions stated in this section are required to apply the following solution techniques. Please clarify the same. Also use complete sentences to state them.
# The branch and bounds method described in this section only discusses the solution technique for problems with one machines. However, branch and bound is a general technique that can be applied to any MILP problems with varying scales. Please update the “methods” section to be as general as possible.
# Since this Wiki focuses on jobshop scheduling, at least two methods are expected. Branch and bound is a general MILP technique, so, it is recommended to add a tailored technique that can only solve specific jobshop scheduling problems. Solving the numerical example with this technique is not necessary.
# Reference to the branch and bound technique described in this section is a “youtube” video. Please add references in literature that describe this method in detail. The method used in this video is highly tailored for a single machine application. This is also an incorrect way to cite a reference. Please keep this section as general as possible.
# Use LaTex code or equation editor to display all equations and variables in this section and all other sections as well.
# Check grammar in this section. For example, phrases like “are as follows” need to be followed by a colon and not a period.
# Consider rewriting the assumptions as a list in this section.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# The example used in this section is exactly the same as the one in the youtube video. Please use a modification of this example or choose another example/method to demonstrate the solution technique. Your team should ideally create a numerical example independently. If you take a numerical example directly from a particular source, you will need to get explicit permission from the textbook author in writing and share that written permission with the instructors.
# The figure in this section is not numbered when all others are. Relabel this figure for consistency and its number to refer to it in-text.
# A numerical example should be simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments).
* A section to discuss and/or illustrate the applications
# This section should only focus on real-world applications of the jobshop scheduling problem. But currently, this section includes additional information on solution techniques/complexity that is appropriate for the Introduction section. Please discuss the applications of the problem in this section.
* A conclusion section
# The meaning of “Operations applications” is unclear. Please explain or update if necessary.
# The current conclusion section does not properly summarize the problem. Please refer to other Wiki examples for an idea to update the section accordingly.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please reference media sources like reference 5 appropriately.
# A simple Google Scholar search would give you many "formal" references.

== [[Optimization in game theory]] ==

* Author list: remove cornell IDs.
* An introduction of the topic
# References are not linked. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
* Theory, methodology, and/or algorithmic discussions
# Why only a subsection on "Nash Equilibrium" is included in "Theory" section? Please re-format.
# Please edit references.
# Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm.
# Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.
* At least one numerical example
# Please organize the last part in a more readable format. Questions may be in bold and numbered, answers are more direct, etc.
# Remember to cite all images and tables.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# Very good, link the reference and cite all sources.
* A conclusion section
# Please add more summarizing especially from theory sentences and avoid long sentences.
* References
# Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Reference primary sources rather than Wikipedia
# Incorrect reference style. Please correct.

== [[Trust-region methods]] ==

* Author list:
# Remove cornell IDs. Author is also spelled incorrectly.
# Add the course section.
* An introduction of the topic
# References are not linked. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Use LaTex code or equation editor to display all equations and variables (e.g., “xk”, “f`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “we”. This goes for all other sections as well.
* Theory, methodology, and/or algorithmic discussions
# Organization of ideas in this section needs work.
# You have not defined explicitly why the Cauchy point is important to compute beyond a vague allusion to performance improvements, which is also wrong (it is useful because of its guarantees for convergence, not performance) It is also misspelled.
# Each approach should have accompanying explanation and motivation for why it is being discussed. It is not enough to outline the algorithm.
# Please make sure symbols are properly subscripted and superscripted (e.g. “pk” should be “p_k”
# Please format the algorithm in proper algorithmic pseudocode format.
# Little to no discussion on global convergence guarantees
# Please include discussion about the advantages and disadvantages of the algorithm
# Fix typo “couchy point”.
* At least one numerical example
# Any code functions (uminfunc) should have proper text formatting.
# The graph needs a better caption explaining how the axes are labeled and what data points are being shown.
# Please increase the quality of the figure. It is hard to see the red line.
# Add citation to “The Rosenbrock function is a non-convex function, introduced by Howard H. Rosenbrock in 1960, which is often used as a performance test problem for optimization algorithms.”
* A section to discuss and/or illustrate the applications
# The content in this section as it is currently does NOT describe applications, but rather different approaches within the trust region methodology. Please provide specific applications (e.g. TRPO in reinforcement learning).
* A conclusion section
# Please add more summary, future research directions for example is a good start.
* References
# Incorrect reference style.
# Please consider having the references as this Wiki template, <nowiki>https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization</nowiki>
# More references should be added. A simple Google Scholar search would give you many references.

*There are numerous misspellings, grammatical errors, and incorrect claims. Please fix these.

== [[Momentum]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Apart from an explanation on momentum, it is necessary to briefly point out the limitations of SGD and why momentum could help with these limitations. Please update it accordingly.
# Remove bold on “Momentum”.
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
* Theory, methodology, and/or algorithmic discussions
# Equation formatting is very poor and should be formalized.
# It is important to use technical language for this Wiki. Although a layman’s explanation is appreciated, it would be better to skip using words like “zig zagging”. Try to explain all concepts in a technical language with few simplifications but NOT vice versa.
# The definition of the update rule for SGD with momentum looks incorrect, specifically the first expression. Please fix it and also explain all the parameters used.
# Use LaTex code or equation editor to display all equations and variables (e.g., “W”, “V`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “you”.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step". Since writing all iterations is not feasible, at least present a few iterations for both cases.
# Please try to label the plots that explains what each line color means.
# Starting point for SGD with momentum is different in explanation and the table. Please fix the same.
* A section to discuss and/or illustrate the applications
# Please use correct terminology like “optimizing non-convex functions” and not “training non-convex models”.
# Adam, Adadelta, and RMSprop are variants of SGD that already use momentum. Please double check the writing and update if necessary.
* A conclusion section
# Please refrain from using words like “zig zag” effects.
* References
# Almost all references used are URLs. Please try to add journal/conference articles or books for references, instead of directly citing the URLs. Please check the list below and run a quick Google (Scholar) search to identify relevant literature.

== [[Stochastic dynamic programming|Stochastic Dynamic programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Discussion on applications should be moved to a separate section.
* Theory, methodology, and/or algorithmic discussions
# Remove the grey box background of equations.
* At least one numerical example
* A section to discuss and/or illustrate the applications
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Outer-approximation (OA)|Outer-approximation]] ==

* An introduction of the topic
# See formatting guideline below
# Avoid opinionated statements such as “MINLP problems are usually the hardest to solve”.
# Rearrange the text such that the MINLP formulation is in the theory section and keep the introduction in words only.
* Theory, methodology, and/or algorithmic discussions
# Consider left aligning equations and optimization problem formulations by the “=”. See [[Stochastic programming|https://optimization.cbe.cornell.edu/index.php?title=Stochastic_programming]] for an example
# The sentence “The Outer-Approximation (OA) algorithm was first proposed by Duran and and Grossmann in 1986 to solve MINLP problems.” needs a reference.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# “Minimize” and “subject to” should be “min” and “s.t.” in MathType
* A section to discuss and/or illustrate the applications
# Does not explicitly point out why OA is applicable (and/or preferred) in these applications, rather than other MINLP approaches (show that the problem formulations are amenable to a solution approach through OA)
# The sentence “... an active research area and there exists a vast number of applications in fields such as engineering, computational chemistry, and finance.” needs references.
# Posting GAMS code on the page is generally inappropriate and discouraged. Please check with the TAs or me if you have a strong desire to post GAMS codes on the Wiki page. A typical textbook should not be limited to a specific software package. If the GAMS code must be posted, please also post ALL other software implementation versions, such as Pyomo and JuliaOPT, among others.
# Consider reformatting to make steps more readable. Inserting spaces and breaking down steps would help.
* A conclusion section
# Too short. Consider discussion on future research direction and discussion on uncertainty
# Please review abbreviations throughout the page. Why is MINLP redefined here? “Outer-Approximation is a well known efficient approach for solving convex mixed-integer nonlinear programs (MINLP)”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove "Template:Reflist"

== [[Unit commitment problem]] ==

* Author list
* An introduction of the topic
# Please expand the introduction and avoid discussions of examples or specific applications in this section.
# The sentence “Nonlinear, Non-convex programming optimization problem.” doesn’t make sense by itself and Non-convex shouldn’t be capitalized.
* Theory, methodology, and/or algorithmic discussions
# Figure/image format should be revised to better display the content.
# Uppercase characters are used randomly (e.g., “non-convex transmission Constraints”) . Please follow correct language conventions for sentence structure.
# Avoid inserting inline citations after words like “written in matrix form as equation [3]..” or “presented in [3]...” as it is a bit informal when you don’t explicitly name the subject. Also these two sentences are grammatically incorrect and appear to be missing an ending period and comma, respectively.
# Don’t say “written in matrix form as equation..” and just cite the reference, actually write out the equation.
# Properly label the figure in this section with a figure number and improve visibility by making it larger.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Label the figures in this section properly with figure numbers.
# Fix typo “while minimize” to “while minimizing”.
# Avoid pronouns such as “we”.
# Use the equation editor when typing equations.
# A numerical example is simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments). There is an Application section where you discuss the applications.
# The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).
* A section to discuss and/or illustrate the applications:
# I suggest changing the order of the subtitles here. For example, Single-Period Unit Commitment.
* A conclusion section
* References

== [[Frank-Wolfe]] ==

* Author list:
* An introduction of the topic
# I suggest highlighting disadvantages along with advantages.
* Theory, methodology, and/or algorithmic discussions
# “[n x 1] matrix” please use the equation editor to express mathematical descriptions and symbols (p,b, etc)
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please show at least a few iterations. Even for smaller examples if needed. Report the final solution.
# Please use the LaTex code or equation editor for min and include s.t., etc.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps. For your example, please explicitly state that the derivative is taken etc.
* A section to discuss and/or illustrate the applications:
* A conclusion section
# Same as the introduction. Pros and cons should be evaluated together!
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Line search methods|Line Search Method]] ==

* Author list
* An introduction of the topic
# Expand the introduction and avoid discussion on some of the specific steps in the solution process.
# Provide references here.
* Theory, methodology, and/or algorithmic discussions
# The phrase “are as follows” in the steepest descent method discussion needs to be followed by a colon.
# Rephrase “has a nice convergence theory” and cite a reference for this claim.
# Avoid pronouns such as “we”.
# Add citation after “.. proposed by Phillip Wolfe in 1969.”
# Figure 1 is between two sections. Please fix this issue.
* At least one numerical example:
# Add some space between iterations or subsection break
* A section to discuss and/or illustrate the applications:
# Too few references in this section.
# Last paragraph makes some claims without references.
* A conclusion section
* References
# References should be properly formatted. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Piecewise linear approximation|Piecewise Linear Approximation]]==

* Author list
* An introduction of the topic
# The content of this section is good, but there are some issues with sentence clarity and some other grammatical errors. Please revisit this section and make changes accordingly.
* Theory, methodology, and/or algorithmic discussions
# Fix typo “to force the x’ values become associated with”.
* At least one numerical example
* A section to discuss and/or illustrate the applications
# Please aim for a maximum average sentence length of ~25 words. Some of these longer sentences are hard to read.
* A conclusion section
# Expand the conclusion section to be longer than one sentence. The conclusion section to include a brief summary of what was discussed above, an emphasis on it’s significance, and a brief discussion of future extensions and research direction if applicable.
* References
# Include hyperlinks to sources when possible.

== [[Mathematical programming with equilibrium constraints|Mathematical Programming with Equilibrium constraints]] ==

* An introduction of the topic
# This section includes several terms like variational inequalities, constraint qualifications that were not discussed in the class. Please add a sentence to explain them before using them.
* Theory, methodology, and/or algorithmic discussions
# The meaning of parameter vector x is unclear. Please add more information or update if necessary.
# Equations and symbols in the PIPA subsection are not formatted correctly. Please use the same formatting for all equations, so they read as mathematical equations and not text. This goes for all other sections as well.
# Use equations instead of images to represent math programs and equations in the Implicit Descent and SQP subsection.
# Apart from the steps for each solution technique, please also add a few sentences that describe each method.
* At least one numerical example
# Please define the terms like NCP, MP before abbreviating them. Also try not to unnecessarily abbreviate simple terms.
# Equations should be typed by LaTex. Images for equations are unacceptable.
# GAMS code is strongly discouraged. Please solve the problem "step-by-step".
# The selected numerical example is fine but is directly solved with the MPEC solver in GAMS. Try to solve it manually like the homework/in-class problems step by step using the steps described in the previous section by choosing any of the methods.
# Avoid using figures in the equations (subject to etc)
* A section to discuss and/or illustrate the applications
# Add references to “power management, highway pricing, chemical process engineering, and traffic planning.”
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# This Wiki contains very few references. Please check the list below and run a quick Google (Scholar) search to identify relevant literature.

== [[Wing shape optimization|Wing shape Optimization]] ==

* Author list: Remove cornell ID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC. Any formatting issue will incur a penalty in the grading.
* An introduction of the topic
# The introduction is missing several references (e.g., “software packages like computational fluid dynamics..”, sentences containing things that aren’t common knowledge, performance claims, etc.)
# Avoid discussion involving finer details of subject methods in this section.
# In the titles, please change the font from bold to normal to have consistent formatting in the site. Same applies to box of content!
* Theory, methodology, and/or algorithmic discussions
# Properly cite the CFD package, don’t just include a link.
# Properly label the figure with a figure number.
# Consider removing white space between isolated sentences to improve readability.
* At least one numerical example
# If you’ve already defined an abbreviation (CFD), there is no need to define it again. Just use the abbreviation.
# Avoid pronouns such as “we” or “they”.
# Phrases like “under the following” need to be followed by a colon.
# Properly label the figure with a figure number and consider making them larger to improve visibility. Call the reader's attention to the figures in text by referencing the figure number.
# “As seen in the video below” is stated yet there are only images present and it may be initially unclear to the reader which figure is being referenced here.
# Avoid inserting inline citations like “[4] introduces an..” as it is a bit informal when you don’t explicitly name the subject.
# Don’t just cite the reference when discussing the problem formulation, explicitly write the model formulation and solution process using LaTex or equation visual editor.
# Your team should ideally create a numerical example independently. If you take a numerical example directly from a textbook, etc., you will need to get explicit permission from the author in writing and share that written permission with me.
# A numerical example is simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments). There is an Application section where you discuss the applications.
# The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).
* A section to discuss and/or illustrate the applications
# Some characters are randomly capitalized in this section.
* A conclusion section
# These variables should be defined before the conclusion section, they are out of place here. Also, please use normal text when explaining variables except for the variable symbol.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Interior-point method for NLP|Interior point method for NLP]] ==

* An introduction of the topic:
* Theory, methodology, and/or algorithmic discussions
# Primal-Dual formulation and comparison to the Barrier Method is not discussed.
# Include brief discussion about big O convergence rates.
# Need discussion about the concept of “central path” and the notion of self concordance
# Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
# Graphs and images are incorrectly formatted to the page. Consider proper alignment with respect to the text body.
# Use explicitly typed Latex equations instead of images to represent math programs and equations.
# Fix typo “optimisation”.
# Use LaTex code or equation editor to display all equations and variables (e.g., “xi ”, “μ”, etc.).
* At least one numerical example:
# There are formatting issues with figures 2,3. Please make sure to embed them within their respective sections.
* A section to discuss and/or illustrate the applications
* A conclusion section
# Minor character code typos in the conclusion.
# Also, please add more discussion in this section. Future research directions is a good start.
# There is a box "􏰐"
* References

== [[AdaGrad|Adagrad]] ==

* An introduction of the topic:
* Theory, methodology, and/or algorithmic discussions
# Include discussion on its variants (most important is AdaDelta).
# Include disadvantages of Adagrad, since this provides motivation for the discussion on the variants and improvements of Adagrad
# Include comparisons to other popular optimizers (particularly important is comparisons to regular SGD and Adam)
# Different convergence rates are possible depending on the setting where Adagrad is used, but this is not mentioned on the page currently. As such the regret bound section should be more thoroughly explained.
# Algorithm image is blurry. Either increase the fidelity or write the pseudocode directly in the wiki editor.
* At least one numerical example
# In the first sentence, “..take the following numerical example” should be followed by a colon.
# Fix typo “trayectory”.
* A section to discuss and/or illustrate the applications
# This section is too short; include specific applications in which input features are sparse and Adagrad excels.
# Add reference to the claim “Mainly, it is a good choice for deep learning models with sparse input features”.
* A conclusion section
* References

# Too few references overall, you should aggregate information from multiple sources (even if the base algorithm itself comes from a singular paper)

== [[McCormick envelopes|McCormick Envelopes]] ==

* Author list: OK but I suggest removing NetID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# First sentence is hard to read. Please consider keeping sentences below 25-30 words.
# No references provided. Please cite all sources.
# Figure 1 is provided in the middle between two sections. Please include in the introduction section.
* Theory, methodology, and/or algorithmic discussions
# References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# When using mathematical expressions and symbols, please use the equation editor. (e.g., x*y, exy + y, sin (x+y) - x2)
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# The solution technique should be clearly presented, and solved "step-by-step".
# GAMS code is unnecessary. Please provide detailed step-by-step calculation results.
* A section to discuss and/or illustrate the applications
# Having a list is not enough. Please explain at least three applications in a few sentences each.
# This section should be at least a paragraph to discuss relevant applications. Each application should be explicitly linked to the page topic. A few keywords do not meet the requirement at all.
* A conclusion section:
* References
# References are not expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please follow the standard reference style - the current format is incorrect.

== [[Branch and bound (BB) for MINLP|Branch and Bound for MINLP]] ==

* Author list:
** Remove NetIDS
** Please remove abbreviations from the title (i.e. BB).
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# Please cite sources appropriately: References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Introduction is very short for a well-recognized topic. Please expand significantly. You may refer to the Wiki examples to get an idea on writing the Introduction to a topic.
# An illustration might be useful here.
* Theory, methodology, and/or algorithmic discussions
# The algorithm described here considers only binary integer variables. However, MINLP problems may include non-binary integer variables too. Please update the method or provide a short description of the assumptions that the MINLP problem needs to satisfy in order for the presented technique to be applicable.
# Use linked citations please as the Wiki template above.
# Please provide steps in a more organized way. Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
# Step 2 is missing yet it is referenced in the text multiple times. Please address this in addition to the above comment.
# An illustration might be useful here as well.
# Please explain what a Gomory Cut is. If the topic is available on optimization.cb.cornell.edu, you can link it.
# The current equations seem to be simple text written in Italics. All mathematical symbols and equations should be formatted via LaTex.
# Please format the math programs with equations and notations using formulations in lecture notes as templates.
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# Please show a step-by-step solution in the example. The solution is incomplete. The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).
# Please use the equation editor for equations or mathematical symbols. - All mathematical symbols and equations should be formatted via LaTex - this is a learning objective of the Wiki assignment. You can find some useful links on converting your equations/symbols into LaTex code here: (<nowiki>https://optimization.cbe.cornell.edu/index.php?title=Help:Contents</nowiki>). Again, any formatting issue will incur a "compound" penalty in the grading.
# This example does not follow the MINLP structure discussed in the above section since binary variables are missing. Branch and bound may not be appropriate for such problems. Please provide an appropriate numerical example and solve it according to the above comments.
# Make sure your example is not taken from a book as that is strictly disallowed.
* A section to discuss and/or illustrate the applications
# This section is not well-formatted. Please provide 3 applications and explain each in a few sentences and how BB for MINLP could be used. Also, please eliminate having multiple sections (Application, Mathematical problem, industrial application). All these could be merged together.
# This section should be at least a paragraph to discuss relevant applications. Each application should be explicitly linked to the page topic. A few keywords do not meet the requirement at all.
* A conclusion section:
# The sentence is hard to understand "a scheme that grows exponentially because" please use a simple language. Is it also theoretically correct? It is also not mentioned and explained earlier. Thus, please avoid introducing new concepts or terms at the end.
# Please use summarizing sentences to describe earlier sections instead of introducing new concepts/discussion.
* References
# Too few references overall, you should aggregate information from multiple sources. A quick Google scholar search could provide relevant references.
# References are not expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please follow the standard reference style - the current format is incorrect.

2021 Cornell Optimization Open Textbook Feedback

2021-12-07T05:12:37Z

Asa273: /* Geometric Programming */

== [[Lagrangean duality|Lagrangian duality]] ==
* Author list, sections and TOC
# Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.
# Remove cornell ID from Author list
* An introduction of the topic
# This section includes sentences on constructing the dual problem and is referred to as Lagrangian relaxation (LR). This is incorrect, please fix the definition of LR.
# Definitions of LR and its relation to duality should be double checked and re-written.
# Only one reference is present in this section. Please add more relevant references by expanding this section.
# Consider merging the “introduction” and “history” sections.
# In the titles, please change the font from bold to normal to have consistent formatting in the site.
* Theory, methodology, and/or algorithmic discussions
# The Lagrangian variables associated with equality constraints h(x) are unbounded but the Lagrangian dual problem states them as non-negative. Please fix the same.
# Also to construct a dual, we do not change minimization to maximization directly. We observed such things in the examples in lecture notes due to simplification. The lagrangian dual problem would be minimize (,).
# Adding to the previous point, the Lagrangian is a lower bound on the original objective; the solution to the primal and dual or only equivalent if the duality gap is 0. You reference this in one section, but this is after your statement “Hence, solving the dual problem, which is a function of the Lagrangian multipliers (𝜆*) yields the same solution as the primal problem, which is a function of the original variables (x*). “. Please clarify the specific conditions that must hold for the solution of the dual to be equal to the primal’s.
# You refer to the “Complementary Slackness Theorem”, but don’t actually write the mathematical representation of complementary slackness. Please fix this. Also consider including the derivation of the complementary slackness condition, as it is both easy and short. Boyd is a good reference for this.
# Last step of the “process” subsection also needs updating according to the previous comments.
# The inline notations should also be typed using LaTex.
# Please use the LaTex code or equation editor for min, s.t., etc.
* At least one numerical example
# Only one dual variable is associated with each constraint. The numerical example uses two for the first and second constraint which is unnecessary. Please update it accordingly for both constraints. This particular example will only have two dual variables instead of the five dual variables used currently.
# All consecutive steps need to be updated since the dual variables would be updated.
# After substitution the nonlinear function should be further simplified. The current expression reads like a highly nonlinear function but can be easily simplified.
# Similar to the comments in the methodology section, inverting minimize to maximize is incorrect. Please update the dual objective function and domain of dual variables accordingly.
# Please use the LaTex code or equation editor for min, s.t., etc.
* A section to discuss and/or illustrate the applications
# Bullet points could be used to state the last four real-world examples that explain the physical meaning of the primal and dual problems.
# Add references for the last set of applications.
* A conclusion section
# This section contains a few typos. Please fix the same.
* References
# Some citations' hyperlinks are displaying.

== [[Disjunctive inequalities|Disjunctive Inequalities]] ==

* Author list
# Missing course section and semester
# Remove cornell ID
* An introduction of the topic
# No citations are present in this section.
# “mixed-integer programming (MIP)” should be used instead of “multiple integer programming (MIP)”. Please fix this error.
* Theory, methodology, and/or algorithmic discussions
# The abbreviation MILP is not previously defined. Please fix this issue.
# You consistently use the negative sign instead of the NOT operator for y (-y instead of ¬y).
# Some inconsistencies with the spacing of variables, constraints, etc., under the “General” section that need to be fixed.
# Typo in “This is shown below by M1, M2, y1, and y1:” where y1 needs to be changed to y2. Why use two different Big-M variables here? Elsewhere in the Wiki you only use one so this could lead to confusion with a general audience. Also if this was taken from the lecture notes then it needs to be cited.
* At least one numerical example
# Please reformulate and solve a complete numerical example rather than just reformulating a general example. Demonstrate the use of Big-M and Convex Hull formulation in an optimization problem that provides details such as individual steps in the problem solving process and final results. The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results.
# Add space between vee (V) operator and brackets in first line of Latex
# Please format variables correctly, for example, use <math>x_1</math> instead of x1.
* A section to discuss and/or illustrate the applications
# Please format the equations appropriately either by using latex code or the visual editor. These images are NOT acceptable!
* A conclusion section
# There is no conclusion presented in this section at all.
* References
# The included references have NOT been used anywhere in the Wiki. Add references for sentences that are not common knowledge and please link them appropriately with the text in Wiki. If the figures used here were not original works, you must also cite them.
# There are many papers on this topic. A simple Google (Scholar) search could provide you with sufficient references to cite.
# Many important references of this topic are missing.
# Please consider linking the references as demonstrated in the Wiki tutorial on Canvas and in this template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

==[[Stochastic programming|Stochastic Programming]] ==

* Author list: Remove cornell IDs
* An introduction of the topic
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
# This section only includes two sentences on Stochastic programming (SP), while the rest gives examples of uncertainty. Please discuss the need for SP in the presence of uncertainty. Also, discussion on robust optimization and its limitations should be removed since it is out of place.
* Theory, methodology, and/or algorithmic discussions
# Please avoid direct inline linkbacks to Wikipedia.
# The symbol “xi” in the methodology subsection should be explained.
* At least one numerical example
# Copying a numerical example "entirely" from a textbook is inappropriate. Your team should come up with a "numerical" case.
# No specific application context is needed for a numerical example.
# The inline notations (`x1`, `s1`) should also be typed using LaTex.
# Label all tables with a table number for better readability.
# Properly format the solution table with the label attached rather than the following sentence. The solution table looks different from the others, please fix this for consistency.
* A section to discuss and/or illustrate the applications;
# I suggest eliminating citing the last name of the first author (i.e. Zhou et al.)
* A conclusion section
* References
# URLs of some citations are not properly formatted (not showing the hyperlinks).

== [[Exponential transformation|Exponential Transformation]] ==

* Author list
# Missing course section
# Remove cornell ID
* An introduction of the topic
# Please expand the introduction.
# Please aim for a maximum average sentence length of ~25 words. Last sentence with 51 words is hard to read.
# Second Sentence: please change the word “they” as it could make the meaning ambiguous
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
# If you use abbreviations, please introduce them (e.g. NLP,MINLP)
* Theory, methodology, and/or algorithmic discussions
# Please explain the transformation in words along with equations
# Terms like posynomial should be described in detail.
# Please move the numerical example to the section below
# The “(eq 1)” is not needed here.
# Please expand this section.
* At least one numerical example
# In the third equation of the numerical example, it is confusing to have coefficients after numbers. Some readers may read it as an exponent.
# Last equation in this section after “further linearization” is incorrect. This equation cannot be further linearized, please fix this.
# Please explain the steps in the numerical examples in detail. The step-by-step solution should be provided.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# Missing part of text: “Proof of convexity of with positive definite test of Hessian…”
# Applications are not numerical examples. Please refer to this link for example of applications: [[Duality|https://optimization.cbe.cornell.edu/index.php?title=Duality]]
# Citation 7 is missing in current applications
# The section current applications is redundant
# Please use the LaTex code or equation editor for min, s.t., etc.
# Under current applications, do not just use a hyperlink to describe an application. Actually describe it. And properly inline citation style should be used instead of the hyperlink.
# The convexification application of MINLP can be further simplified for binary variables. Please refer to the lecture slides for more information.
* A conclusion section
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
* References
# Please consider linking the references by using this as Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Citation 7 is missing in current applications

== [[Sparse Reconstruction with Compressed Sensing|Sparse reconstruction with Compressed Sensing]] ==
This Wiki needs a significant rewrite. Please go through the comments for details.

* An introduction of the topic
# The introduction section should include information about the problem and its implications presented briefly. Please use full sentences to write this Wiki. You may use tools like Grammarly to check sentence formation and grammar.
# This section includes several typos like “sub modual”. Please fix them throughout the wiki and delete them if not required.
# Many abbreviations are used before previously defining them. Please define these abbreviations before using them in the text.
# This section is incomprehensible in its current form. Please rewrite with proper comprehension.
# Equations and math symbols need proper reformatting. The current version reads like text (along with equations) copy-pasted from a specific source. All mathematical symbols and equations should be formatted via LaTex - this is a learning objective of the Wiki assignment. You can find some useful links on converting your equations/symbols into LaTex code here: (https://optimization.cbe.cornell.edu/index.php?title=Help:Contents).
# Try to place the figure at the top of the Wiki between the main text.
# Avoid pronouns such as “we”.
# I suggest the use of more formal abstract illustrations.
* Theory, methodology, and/or algorithmic discussions
# Equations and symbols need proper reformatting.
# Lemmas and theorems are not expected for this Wiki. Sparse reconstruction is a straightforward concept but is unnecessarily complicated here. Please refer to other Wiki examples to get an idea of what the Wiki should convey.
# All equations need to be better formatted.

* At least one numerical example
# Numerical example is missing.
# Every iteration should be clearly presented, and solved "step-by-step".
* A section to discuss and/or illustrate the applications
# Having a list is not enough. Please explain at least three applications in a few sentences each.
* A conclusion section
# Conclusion section is missing.
* References
# The current reference list is not correctly formatted. References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Portfolio optimization|Portfolio Optimization]] ==

* Author list
# Remove cornell id
* An introduction of the topic
# The introductory sentence should be rephrased. The action of minimizing the risks does not inherently maximize the gains, rather PO aims to maximize gains whilst minimizing risks.
# Amount of whitespace can be reduced by changing the orientation of Figure 1 and the sentences in this section.
# Define terms such as risk, return, portfolio, etc., when you introduce them. Assume that the reader may not know much about finance. This goes for all other sections as well.
* Theory, methodology, and/or algorithmic discussions
# A brief mention of modern portfolio theory (i.e.. Markowitz) would be appropriate in this section.
# Several grammatical errors here involving sentence structure and clarity. Some questionable semantics (e.g., “The portfolio optimization mainly assumes two directions.”) and syntax (phrases such as “.. is as follows” should be followed by a colon). Misuse of commas and missing commas in this section. Two sentences introducing E(rp) and w should be combined into one.
# Use LaTex to distinguish variables written within a sentence, such as m and n.
# Rephrase “Cut the relevant information and conditions in the portfolio optimization, as well as the final requirements into the relevant variables, constraints and linear functions of the linear programming problem.”
# An explanation of a few common constraints would be helpful, rather than just including a table.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Solving the numerical example by GAMS is inappropriate. Please provide detailed step-by-step calculation results.
# All tables need to be labeled.
# Include figure number in label for consistency.
# Fix misspelling “dolling decision variables”.
# Use LaTex for all variables, equations, and constraints here.
# Example 2 table is hard to read, so making it bigger would help.
# Remove the “Using excel as the solver” part from the sentence before the solution discussion.
# Some grammatical errors here (phrases such as “.. is as follows” should be followed by a colon).
* A section to discuss and/or illustrate the applications
# Rephrase “Portfolio optimization can be used to screen investment projects that meet investors, rationally allocate investment amounts, etc.”
# Not sure “relevant” is the correct word choice here.
# You need more specific examples with the utility of portfolio optimization, this section is quite general as is. Some more detail and focus on real-world applications in the financial industry that relate to retirement planning, financial security, economic stability, etc., would be helpful.
* A conclusion section
# Need some commas here.
# The sentence “Linear programming has been around since the 1940’s and has such a wide base of applications” is not necessary.
* References
# Please consider linking the references as demonstrated in the Wiki tutorial on Canvas and in this template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove white space between end of sentences and reference numbers.

== [[Chance-constraint method|Chance constraint method]] ==

* Author list:
* An introduction of the topic
# Please consider correcting a few grammatical errors: “pre-planned for”, “god”, “certain levels of feasibility is guaranteed in what are”, and “Performance of a system”
# In “Chance-constraint”, it is capitalized randomly throughout the introduction. Please correct.
# Please use technical language to briefly introduce chance-constrained programming. Words like “acts of god”, “cost of doing business” are not appropriate for a technical Wiki.
* Theory, methodology, and/or algorithmic discussions
# Please add a citation to the first sentence.
# Xi is an uncertainty/randomness variable. It is better to use clear language.
# Please use the mathematical editor for adding explanations in the text. Using “ x is a decision variable” is hard to read. Same for f(x) and others.
# Theory is insufficient. Please expand and explain different approaches.
# Please add pros and cons explicitly as a list.
# Explain the physical meaning for examples of chance constraints along with all the notations used.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please remove this example as it is directly from this book. The example should be purely numerical without any background.
# Please use the equation editor for min, st., etc.
# Please use the mathematical editor for adding explanations in the text. Using “ x is a decision variable” is hard to read. Same for f(x) and others.
# Please change the table format so as not to confuse the reader.
# Multiple instances of [Chart to be added] are missing.
# Example is incomplete.
# Avoid pronouns such as “we”.
* A section to discuss and/or illustrate the applications
# Please connect several grammatical and spelling errors: “real life application”, Energy creation, particularly in renewable sources, have high variabilities”, and others
# “Zhao, Xue, Cao, and Zhang”. No need to list all authors within the article. Provide a reference is sufficient. If authors must be mentioned, (Zhao et al.) should be ok.
* A conclusion section
# Uniqueness and universality earlier are not clear to me. If they are not discussed earlier in the application, it would be better not to introduce new discussions in the conclusion.
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
* References
# References seem to vary in format. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Bayesian Optimization]] ==
* Section titles should not be "bold". Please double check using source editor on the section titles.
* Contents: The section titles should NOT be in bold to avoid strange format in TOC. Any formatting issue will incur a penalty in the grading.
* Author list: Remove cornell ID, Please check names
* Introduction
# The introduction is too general and not substantial enough. For example, simply saying BayesOpt is useful when the objective function is unknown obscures exactly HOW it is useful (namely, computational efficiency in applications where ground truth sampling is expensive). Discussion on applications should be moved to a separate section.
# Machine learning rarely includes black-box functions to be optimized. Bayesian optimization is almost never used for optimizing ML loss functions but can instead be used for hyperparameter optimization. Please update such claims in this section.
* Theory, methodology, and/or algorithmic discussions
# Captions need reformatting.
# Consider italicizing keywords rather than bolding.
# Please add a citation to the first sentence.
# Discussion on acquisition functions should include comparisons, tradeoffs, and reasons to use one over the other. Should also note that expected improvement is the most widely used in practice, and explain.
# Avoid pronouns such as “we”.
# Please write equations in the Wiki instead of attaching images for equations.
# Acquisition function figure could be made larger and clearer to improve readability.
* At least one numerical example
# Any references to functions or methods in code ‘e.g. fmin’ should be properly formatted as code-stylized text.
# Please use the equation editor for min, st., etc.
# Avoid including a figure of the code for this example and explicitly describe the steps to the modeling and solution process instead.
# Avoid pronouns such as “our” and “we”.
* A section to discuss and/or illustrate the applications
* A conclusion section
# Please do not use brackets to enclose lists.
# Some claims here should be supported by references. Please cite each source after its sentence.
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Try to avoid references to “pop” machine learning blogs where anyone can be an author. (e.g. towardsdatascience)
# All references are URLs. Please cite publications and literature.
# A simple Google Scholar search would give you many references.

Notes on grammar: Needs some work. Several instances where colons are inappropriately inserted mid sentence or in subheadings. Explanations are not terse. Several instances of switching between personal and impersonal style of writing, which is distracting.

== [[Conjugate gradient methods]] ==

* Author list: Remove cornell ID
* Introduction
# All inline notations (e.g., `x`, `A`) should be typed using LaTex.
* Theory, methodology, and/or algorithmic discussions
# All equations need to be better formatted.
# Is Gauss-Newton no longer referenced?
# Theorems listed in the first section should be accompanied with high level explanation, not just a list of the theorems themselves. The page should read like an article, with proper flow.
# Please indent equation blocks.
# Please properly format pseudocode.
* At least one numerical example
# Steps should be accompanied with explanation, or reference to the corresponding step in the pseudocode.
# Please properly format in a more organized manner, aligning equations appropriately and demarcating steps appropriately.
* A section to discuss and/or illustrate the applications
# Consider including 2 additional examples of applications
* A conclusion section
# Consider adding future research directions
* References
# Reference primary sources rather than Wikipedia
# Too few references.
# More references should be added. A simple Google Scholar search would give you many references.

== [[Geometric programming|Geometric Programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Examples of applications in this section use the same reference. Please cite their individual sources.
* Theory, methodology, and/or algorithmic discussions
# The symbol denoting the domain in the definition of a monomial is unclear. Please clarify it or fix this if it is incorrect.
# Definition of posynomial refers to section 2.1 which is missing from the Wiki (sections are not numbered in the main text).
# In the generalized posynomial subsection, bullet points do not tell us why h(x) is posynomial. Either provide reasons or simply state that h(x) is posynomial. Also explain why h3 is a generalized posynomial.
# Additional theory on the feasibility analysis could be provided in this section.
* At least one numerical example
# In the transformation example, the last two constraints could also be simplified. Please update them as well.
* A section to discuss and/or illustrate the applications
# The figure in this section needs to be labeled.
# The figure needs to be resized and perhaps aligned to the center.
* A conclusion section:
# Please avoid vague language such as: “This makes”.
# Please avoid opinionated statements: “one of the best ways”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# This Wiki has very few references. A quick Google Scholar search may provide relevant references.

== [[Adam]] ==

* Author list
* An introduction of the topic
# Some grammatical errors here, mostly related to the need for commas in certain places (e.g., “Before Adam..”).
# Some minor errors with parts of speech throughout the section, need to revisit phrases such as “which has broader scope in future for”, etc.
# Try splitting up some of the longer sentences in this section, a couple are hard to read.
# Avoid definitive statements about Adam being the best or always better solver, as this is simply not true (the choice of the “best” optimizer is setting-dependent). Use language such as “Research has shown that Adam has demonstrated superior experimental performance over..” and then cite academic references to back this claim.
# What does adam stand for? Introduction is insufficient. Please expand.
* Theory, methodology, and/or algorithmic discussions
# Revise grammar here, noticing some missing commas and uncapitalized word after period.
# Rephrase “second one is to update the old position with the updated position”.
# Use LaTex code or equation editor to display all equations and variables in this section, and actual subscripts instead of “m_t”, etc.
# Avoid inserting inline citations after words like “According to..” or “This article..” as it is a bit informal. This could be rephrased or changed to something like “According to author,^[2] …” with author name inserted.
# Remove white space before the period in RMSP discussion.
# Please provide a pseudocode.
# Please use list the two methods here “Adam is a combination of two gradient descent methods which are explained below”
# Please expand the theory section significantly. Theoretical convergence properties should be discussed, even if briefly.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
* A section to discuss and/or illustrate the applications
# Same comment as before, consider replacing inline citations after words like “According to..”.
* A conclusion section
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Try to avoid references to blogs and use peer-reviewed academic references instead.
# Too few references.
# More references should be added. A simple Google Scholar search would give you many references.

== [[A-star algorithm|a* algorithm]] ==

* Author list: Remove cornell ID
* Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.
* An introduction of the topic:
# Weird spacing between paragraphs. Please fix this issue.
# In the titles, please change the font from bold to normal to have consistent formatting in the site.
# Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.
# There are no citations in the introduction. Please cite every source.
* Theory, methodology, and/or algorithmic discussions
# Please add the mathematical description of the algorithm.
# Reference style varies in sentences. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please fix grammatical and spelling errors as (“from current position to the goal”, “There are a lot of discussions”, etc). Also, many hyphens are missing as “non playable”.
# In algorithms, it is a standard to add high-level description (i.e. pseudocode or flowchart). Please incorporate it.
# Use LaTex code or equation editor to display all equations and variables in this section (e.g., “f(n)...”, “h(n)..”, etc.). This goes for other sections as well.
* At least one numerical example
# The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.
# Instead of writing things like “The above image..”, label each figure and use the figure number to refer to it in text.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# No references in the applications. Please cite every source
# Preferably, add at least an additional application.
* A conclusion section
# Conclusion should summarize descriptions. Please modify it to provide a summary.
# Please pay attention to the length and structure of sentences here and in the full page. First sentence is hard to read.
* References
# References seem to vary in format and are not linked correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Incorrect reference style. Please follow the example and use the template.

== [[Job shop scheduling|Job-Shop Scheduling Problem]] ==

* An introduction of the topic
# The current introduction to the jobshop scheduling problem has only two sentences in addition to the parameter description. Introduction typically contains information about the problem, its importance in the real-world, and some information about the solution techniques and their types to solve the problem. Please add some information that covers the above.
* Theory, methodology, and/or algorithmic discussions
# It is unclear whether the assumptions stated in this section are required to apply the following solution techniques. Please clarify the same. Also use complete sentences to state them.
# The branch and bounds method described in this section only discusses the solution technique for problems with one machines. However, branch and bound is a general technique that can be applied to any MILP problems with varying scales. Please update the “methods” section to be as general as possible.
# Since this Wiki focuses on jobshop scheduling, at least two methods are expected. Branch and bound is a general MILP technique, so, it is recommended to add a tailored technique that can only solve specific jobshop scheduling problems. Solving the numerical example with this technique is not necessary.
# Reference to the branch and bound technique described in this section is a “youtube” video. Please add references in literature that describe this method in detail. The method used in this video is highly tailored for a single machine application. This is also an incorrect way to cite a reference. Please keep this section as general as possible.
# Use LaTex code or equation editor to display all equations and variables in this section and all other sections as well.
# Check grammar in this section. For example, phrases like “are as follows” need to be followed by a colon and not a period.
# Consider rewriting the assumptions as a list in this section.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# The example used in this section is exactly the same as the one in the youtube video. Please use a modification of this example or choose another example/method to demonstrate the solution technique. Your team should ideally create a numerical example independently. If you take a numerical example directly from a particular source, you will need to get explicit permission from the textbook author in writing and share that written permission with the instructors.
# The figure in this section is not numbered when all others are. Relabel this figure for consistency and its number to refer to it in-text.
# A numerical example should be simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments).
* A section to discuss and/or illustrate the applications
# This section should only focus on real-world applications of the jobshop scheduling problem. But currently, this section includes additional information on solution techniques/complexity that is appropriate for the Introduction section. Please discuss the applications of the problem in this section.
* A conclusion section
# The meaning of “Operations applications” is unclear. Please explain or update if necessary.
# The current conclusion section does not properly summarize the problem. Please refer to other Wiki examples for an idea to update the section accordingly.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please reference media sources like reference 5 appropriately.
# A simple Google Scholar search would give you many "formal" references.

== [[Optimization in game theory]] ==

* Author list: remove cornell IDs.
* An introduction of the topic
# References are not linked. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
* Theory, methodology, and/or algorithmic discussions
# Why only a subsection on "Nash Equilibrium" is included in "Theory" section? Please re-format.
# Please edit references.
# Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm.
# Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.
* At least one numerical example
# Please organize the last part in a more readable format. Questions may be in bold and numbered, answers are more direct, etc.
# Remember to cite all images and tables.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# Very good, link the reference and cite all sources.
* A conclusion section
# Please add more summarizing especially from theory sentences and avoid long sentences.
* References
# Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Reference primary sources rather than Wikipedia
# Incorrect reference style. Please correct.

== [[Trust-region methods]] ==

* Author list:
# Remove cornell IDs. Author is also spelled incorrectly.
# Add the course section.
* An introduction of the topic
# References are not linked. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Use LaTex code or equation editor to display all equations and variables (e.g., “xk”, “f`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “we”. This goes for all other sections as well.
* Theory, methodology, and/or algorithmic discussions
# Organization of ideas in this section needs work.
# You have not defined explicitly why the Cauchy point is important to compute beyond a vague allusion to performance improvements, which is also wrong (it is useful because of its guarantees for convergence, not performance) It is also misspelled.
# Each approach should have accompanying explanation and motivation for why it is being discussed. It is not enough to outline the algorithm.
# Please make sure symbols are properly subscripted and superscripted (e.g. “pk” should be “p_k”
# Please format the algorithm in proper algorithmic pseudocode format.
# Little to no discussion on global convergence guarantees
# Please include discussion about the advantages and disadvantages of the algorithm
# Fix typo “couchy point”.
* At least one numerical example
# Any code functions (uminfunc) should have proper text formatting.
# The graph needs a better caption explaining how the axes are labeled and what data points are being shown.
# Please increase the quality of the figure. It is hard to see the red line.
# Add citation to “The Rosenbrock function is a non-convex function, introduced by Howard H. Rosenbrock in 1960, which is often used as a performance test problem for optimization algorithms.”
* A section to discuss and/or illustrate the applications
# The content in this section as it is currently does NOT describe applications, but rather different approaches within the trust region methodology. Please provide specific applications (e.g. TRPO in reinforcement learning).
* A conclusion section
# Please add more summary, future research directions for example is a good start.
* References
# Incorrect reference style.
# Please consider having the references as this Wiki template, <nowiki>https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization</nowiki>
# More references should be added. A simple Google Scholar search would give you many references.

*There are numerous misspellings, grammatical errors, and incorrect claims. Please fix these.

== [[Momentum]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Apart from an explanation on momentum, it is necessary to briefly point out the limitations of SGD and why momentum could help with these limitations. Please update it accordingly.
# Remove bold on “Momentum”.
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
* Theory, methodology, and/or algorithmic discussions
# Equation formatting is very poor and should be formalized.
# It is important to use technical language for this Wiki. Although a layman’s explanation is appreciated, it would be better to skip using words like “zig zagging”. Try to explain all concepts in a technical language with few simplifications but NOT vice versa.
# The definition of the update rule for SGD with momentum looks incorrect, specifically the first expression. Please fix it and also explain all the parameters used.
# Use LaTex code or equation editor to display all equations and variables (e.g., “W”, “V`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “you”.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step". Since writing all iterations is not feasible, at least present a few iterations for both cases.
# Please try to label the plots that explains what each line color means.
# Starting point for SGD with momentum is different in explanation and the table. Please fix the same.
* A section to discuss and/or illustrate the applications
# Please use correct terminology like “optimizing non-convex functions” and not “training non-convex models”.
# Adam, Adadelta, and RMSprop are variants of SGD that already use momentum. Please double check the writing and update if necessary.
* A conclusion section
# Please refrain from using words like “zig zag” effects.
* References
# Almost all references used are URLs. Please try to add journal/conference articles or books for references, instead of directly citing the URLs. Please check the list below and run a quick Google (Scholar) search to identify relevant literature.

== [[Stochastic dynamic programming|Stochastic Dynamic programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Discussion on applications should be moved to a separate section.
* Theory, methodology, and/or algorithmic discussions
# Remove the grey box background of equations.
* At least one numerical example
* A section to discuss and/or illustrate the applications
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Outer-approximation (OA)|Outer-approximation]] ==

* An introduction of the topic
# See formatting guideline below
# Avoid opinionated statements such as “MINLP problems are usually the hardest to solve”.
# Rearrange the text such that the MINLP formulation is in the theory section and keep the introduction in words only.
* Theory, methodology, and/or algorithmic discussions
# Consider left aligning equations and optimization problem formulations by the “=”. See [[Stochastic programming|https://optimization.cbe.cornell.edu/index.php?title=Stochastic_programming]] for an example
# The sentence “The Outer-Approximation (OA) algorithm was first proposed by Duran and and Grossmann in 1986 to solve MINLP problems.” needs a reference.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# “Minimize” and “subject to” should be “min” and “s.t.” in MathType
* A section to discuss and/or illustrate the applications
# Does not explicitly point out why OA is applicable (and/or preferred) in these applications, rather than other MINLP approaches (show that the problem formulations are amenable to a solution approach through OA)
# The sentence “... an active research area and there exists a vast number of applications in fields such as engineering, computational chemistry, and finance.” needs references.
# Posting GAMS code on the page is generally inappropriate and discouraged. Please check with the TAs or me if you have a strong desire to post GAMS codes on the Wiki page. A typical textbook should not be limited to a specific software package. If the GAMS code must be posted, please also post ALL other software implementation versions, such as Pyomo and JuliaOPT, among others.
# Consider reformatting to make steps more readable. Inserting spaces and breaking down steps would help.
* A conclusion section
# Too short. Consider discussion on future research direction and discussion on uncertainty
# Please review abbreviations throughout the page. Why is MINLP redefined here? “Outer-Approximation is a well known efficient approach for solving convex mixed-integer nonlinear programs (MINLP)”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove "Template:Reflist"

== [[Unit commitment problem]] ==

* Author list
* An introduction of the topic
# Please expand the introduction and avoid discussions of examples or specific applications in this section.
# The sentence “Nonlinear, Non-convex programming optimization problem.” doesn’t make sense by itself and Non-convex shouldn’t be capitalized.
* Theory, methodology, and/or algorithmic discussions
# Figure/image format should be revised to better display the content.
# Uppercase characters are used randomly (e.g., “non-convex transmission Constraints”) . Please follow correct language conventions for sentence structure.
# Avoid inserting inline citations after words like “written in matrix form as equation [3]..” or “presented in [3]...” as it is a bit informal when you don’t explicitly name the subject. Also these two sentences are grammatically incorrect and appear to be missing an ending period and comma, respectively.
# Don’t say “written in matrix form as equation..” and just cite the reference, actually write out the equation.
# Properly label the figure in this section with a figure number and improve visibility by making it larger.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Label the figures in this section properly with figure numbers.
# Fix typo “while minimize” to “while minimizing”.
# Avoid pronouns such as “we”.
# Use the equation editor when typing equations.
# A numerical example is simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments). There is an Application section where you discuss the applications.
# The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).
* A section to discuss and/or illustrate the applications:
# I suggest changing the order of the subtitles here. For example, Single-Period Unit Commitment.
* A conclusion section
* References

== [[Frank-Wolfe]] ==

* Author list:
* An introduction of the topic
# I suggest highlighting disadvantages along with advantages.
* Theory, methodology, and/or algorithmic discussions
# “[n x 1] matrix” please use the equation editor to express mathematical descriptions and symbols (p,b, etc)
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please show at least a few iterations. Even for smaller examples if needed. Report the final solution.
# Please use the LaTex code or equation editor for min and include s.t., etc.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps. For your example, please explicitly state that the derivative is taken etc.
* A section to discuss and/or illustrate the applications:
* A conclusion section
# Same as the introduction. Pros and cons should be evaluated together!
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Line search methods|Line Search Method]] ==

* Author list
* An introduction of the topic
# Expand the introduction and avoid discussion on some of the specific steps in the solution process.
# Provide references here.
* Theory, methodology, and/or algorithmic discussions
# The phrase “are as follows” in the steepest descent method discussion needs to be followed by a colon.
# Rephrase “has a nice convergence theory” and cite a reference for this claim.
# Avoid pronouns such as “we”.
# Add citation after “.. proposed by Phillip Wolfe in 1969.”
# Figure 1 is between two sections. Please fix this issue.
* At least one numerical example:
# Add some space between iterations or subsection break
* A section to discuss and/or illustrate the applications:
# Too few references in this section.
# Last paragraph makes some claims without references.
* A conclusion section
* References
# References should be properly formatted. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Piecewise linear approximation|Piecewise Linear Approximation]]==

* Author list
* An introduction of the topic
# The content of this section is good, but there are some issues with sentence clarity and some other grammatical errors. Please revisit this section and make changes accordingly.
* Theory, methodology, and/or algorithmic discussions
# Fix typo “to force the x’ values become associated with”.
* At least one numerical example
* A section to discuss and/or illustrate the applications
# Please aim for a maximum average sentence length of ~25 words. Some of these longer sentences are hard to read.
* A conclusion section
# Expand the conclusion section to be longer than one sentence. The conclusion section to include a brief summary of what was discussed above, an emphasis on it’s significance, and a brief discussion of future extensions and research direction if applicable.
* References
# Include hyperlinks to sources when possible.

== [[Mathematical programming with equilibrium constraints|Mathematical Programming with Equilibrium constraints]] ==

* An introduction of the topic
# This section includes several terms like variational inequalities, constraint qualifications that were not discussed in the class. Please add a sentence to explain them before using them.
* Theory, methodology, and/or algorithmic discussions
# The meaning of parameter vector x is unclear. Please add more information or update if necessary.
# Equations and symbols in the PIPA subsection are not formatted correctly. Please use the same formatting for all equations, so they read as mathematical equations and not text. This goes for all other sections as well.
# Use equations instead of images to represent math programs and equations in the Implicit Descent and SQP subsection.
# Apart from the steps for each solution technique, please also add a few sentences that describe each method.
* At least one numerical example
# Please define the terms like NCP, MP before abbreviating them. Also try not to unnecessarily abbreviate simple terms.
# Equations should be typed by LaTex. Images for equations are unacceptable.
# GAMS code is strongly discouraged. Please solve the problem "step-by-step".
# The selected numerical example is fine but is directly solved with the MPEC solver in GAMS. Try to solve it manually like the homework/in-class problems step by step using the steps described in the previous section by choosing any of the methods.
# Avoid using figures in the equations (subject to etc)
* A section to discuss and/or illustrate the applications
# Add references to “power management, highway pricing, chemical process engineering, and traffic planning.”
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# This Wiki contains very few references. Please check the list below and run a quick Google (Scholar) search to identify relevant literature.

== [[Wing shape optimization|Wing shape Optimization]] ==

* Author list: Remove cornell ID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC. Any formatting issue will incur a penalty in the grading.
* An introduction of the topic
# The introduction is missing several references (e.g., “software packages like computational fluid dynamics..”, sentences containing things that aren’t common knowledge, performance claims, etc.)
# Avoid discussion involving finer details of subject methods in this section.
# In the titles, please change the font from bold to normal to have consistent formatting in the site. Same applies to box of content!
* Theory, methodology, and/or algorithmic discussions
# Properly cite the CFD package, don’t just include a link.
# Properly label the figure with a figure number.
# Consider removing white space between isolated sentences to improve readability.
* At least one numerical example
# If you’ve already defined an abbreviation (CFD), there is no need to define it again. Just use the abbreviation.
# Avoid pronouns such as “we” or “they”.
# Phrases like “under the following” need to be followed by a colon.
# Properly label the figure with a figure number and consider making them larger to improve visibility. Call the reader's attention to the figures in text by referencing the figure number.
# “As seen in the video below” is stated yet there are only images present and it may be initially unclear to the reader which figure is being referenced here.
# Avoid inserting inline citations like “[4] introduces an..” as it is a bit informal when you don’t explicitly name the subject.
# Don’t just cite the reference when discussing the problem formulation, explicitly write the model formulation and solution process using LaTex or equation visual editor.
# Your team should ideally create a numerical example independently. If you take a numerical example directly from a textbook, etc., you will need to get explicit permission from the author in writing and share that written permission with me.
# A numerical example is simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments). There is an Application section where you discuss the applications.
# The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).
* A section to discuss and/or illustrate the applications
# Some characters are randomly capitalized in this section.
* A conclusion section
# These variables should be defined before the conclusion section, they are out of place here. Also, please use normal text when explaining variables except for the variable symbol.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Interior-point method for NLP|Interior point method for NLP]] ==

* An introduction of the topic:
* Theory, methodology, and/or algorithmic discussions
# Primal-Dual formulation and comparison to the Barrier Method is not discussed.
# Include brief discussion about big O convergence rates.
# Need discussion about the concept of “central path” and the notion of self concordance
# Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
# Graphs and images are incorrectly formatted to the page. Consider proper alignment with respect to the text body.
# Use explicitly typed Latex equations instead of images to represent math programs and equations.
# Fix typo “optimisation”.
# Use LaTex code or equation editor to display all equations and variables (e.g., “xi ”, “μ”, etc.).
* At least one numerical example:
# There are formatting issues with figures 2,3. Please make sure to embed them within their respective sections.
* A section to discuss and/or illustrate the applications
* A conclusion section
# Minor character code typos in the conclusion.
# Also, please add more discussion in this section. Future research directions is a good start.
# There is a box "􏰐"
* References

== [[AdaGrad|Adagrad]] ==

* An introduction of the topic:
* Theory, methodology, and/or algorithmic discussions
# Include discussion on its variants (most important is AdaDelta).
# Include disadvantages of Adagrad, since this provides motivation for the discussion on the variants and improvements of Adagrad
# Include comparisons to other popular optimizers (particularly important is comparisons to regular SGD and Adam)
# Different convergence rates are possible depending on the setting where Adagrad is used, but this is not mentioned on the page currently. As such the regret bound section should be more thoroughly explained.
# Algorithm image is blurry. Either increase the fidelity or write the pseudocode directly in the wiki editor.
* At least one numerical example
# In the first sentence, “..take the following numerical example” should be followed by a colon.
# Fix typo “trayectory”.
* A section to discuss and/or illustrate the applications
# This section is too short; include specific applications in which input features are sparse and Adagrad excels.
# Add reference to the claim “Mainly, it is a good choice for deep learning models with sparse input features”.
* A conclusion section
* References

# Too few references overall, you should aggregate information from multiple sources (even if the base algorithm itself comes from a singular paper)

== [[McCormick envelopes|McCormick Envelopes]] ==

* Author list: OK but I suggest removing NetID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# First sentence is hard to read. Please consider keeping sentences below 25-30 words.
# No references provided. Please cite all sources.
# Figure 1 is provided in the middle between two sections. Please include in the introduction section.
* Theory, methodology, and/or algorithmic discussions
# References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# When using mathematical expressions and symbols, please use the equation editor. (e.g., x*y, exy + y, sin (x+y) - x2)
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# The solution technique should be clearly presented, and solved "step-by-step".
# GAMS code is unnecessary. Please provide detailed step-by-step calculation results.
* A section to discuss and/or illustrate the applications
# Having a list is not enough. Please explain at least three applications in a few sentences each.
# This section should be at least a paragraph to discuss relevant applications. Each application should be explicitly linked to the page topic. A few keywords do not meet the requirement at all.
* A conclusion section:
* References
# References are not expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please follow the standard reference style - the current format is incorrect.

== [[Branch and bound (BB) for MINLP|Branch and Bound for MINLP]] ==

* Author list:
** Remove NetIDS
** Please remove abbreviations from the title (i.e. BB).
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# Please cite sources appropriately: References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Introduction is very short for a well-recognized topic. Please expand significantly. You may refer to the Wiki examples to get an idea on writing the Introduction to a topic.
# An illustration might be useful here.
* Theory, methodology, and/or algorithmic discussions
# The algorithm described here considers only binary integer variables. However, MINLP problems may include non-binary integer variables too. Please update the method or provide a short description of the assumptions that the MINLP problem needs to satisfy in order for the presented technique to be applicable.
# Use linked citations please as the Wiki template above.
# Please provide steps in a more organized way. Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
# Step 2 is missing yet it is referenced in the text multiple times. Please address this in addition to the above comment.
# An illustration might be useful here as well.
# Please explain what a Gomory Cut is. If the topic is available on optimization.cb.cornell.edu, you can link it.
# The current equations seem to be simple text written in Italics. All mathematical symbols and equations should be formatted via LaTex.
# Please format the math programs with equations and notations using formulations in lecture notes as templates.
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# Please show a step-by-step solution in the example. The solution is incomplete. The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).
# Please use the equation editor for equations or mathematical symbols. - All mathematical symbols and equations should be formatted via LaTex - this is a learning objective of the Wiki assignment. You can find some useful links on converting your equations/symbols into LaTex code here: (<nowiki>https://optimization.cbe.cornell.edu/index.php?title=Help:Contents</nowiki>). Again, any formatting issue will incur a "compound" penalty in the grading.
# This example does not follow the MINLP structure discussed in the above section since binary variables are missing. Branch and bound may not be appropriate for such problems. Please provide an appropriate numerical example and solve it according to the above comments.
# Make sure your example is not taken from a book as that is strictly disallowed.
* A section to discuss and/or illustrate the applications
# This section is not well-formatted. Please provide 3 applications and explain each in a few sentences and how BB for MINLP could be used. Also, please eliminate having multiple sections (Application, Mathematical problem, industrial application). All these could be merged together.
# This section should be at least a paragraph to discuss relevant applications. Each application should be explicitly linked to the page topic. A few keywords do not meet the requirement at all.
* A conclusion section:
# The sentence is hard to understand "a scheme that grows exponentially because" please use a simple language. Is it also theoretically correct? It is also not mentioned and explained earlier. Thus, please avoid introducing new concepts or terms at the end.
# Please use summarizing sentences to describe earlier sections instead of introducing new concepts/discussion.
* References
# Too few references overall, you should aggregate information from multiple sources. A quick Google scholar search could provide relevant references.
# References are not expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please follow the standard reference style - the current format is incorrect.

2021 Cornell Optimization Open Textbook Feedback

2021-12-06T03:10:32Z

Asa273: /* McCormick Envelopes */

== [[Lagrangean duality|Lagrangian duality]] ==
* Author list, sections and TOC
# Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.
# Remove cornell ID from Author list
* An introduction of the topic
# This section includes sentences on constructing the dual problem and is referred to as Lagrangian relaxation (LR). This is incorrect, please fix the definition of LR.
# Definitions of LR and its relation to duality should be double checked and re-written.
# Only one reference is present in this section. Please add more relevant references by expanding this section.
# Consider merging the “introduction” and “history” sections.
# In the titles, please change the font from bold to normal to have consistent formatting in the site.
* Theory, methodology, and/or algorithmic discussions
# The Lagrangian variables associated with equality constraints h(x) are unbounded but the Lagrangian dual problem states them as non-negative. Please fix the same.
# Also to construct a dual, we do not change minimization to maximization directly. We observed such things in the examples in lecture notes due to simplification. The lagrangian dual problem would be minimize (,).
# Adding to the previous point, the Lagrangian is a lower bound on the original objective; the solution to the primal and dual or only equivalent if the duality gap is 0. You reference this in one section, but this is after your statement “Hence, solving the dual problem, which is a function of the Lagrangian multipliers (𝜆*) yields the same solution as the primal problem, which is a function of the original variables (x*). “. Please clarify the specific conditions that must hold for the solution of the dual to be equal to the primal’s.
# You refer to the “Complementary Slackness Theorem”, but don’t actually write the mathematical representation of complementary slackness. Please fix this. Also consider including the derivation of the complementary slackness condition, as it is both easy and short. Boyd is a good reference for this.
# Last step of the “process” subsection also needs updating according to the previous comments.
# The inline notations should also be typed using LaTex.
# Please use the LaTex code or equation editor for min, s.t., etc.
* At least one numerical example
# Only one dual variable is associated with each constraint. The numerical example uses two for the first and second constraint which is unnecessary. Please update it accordingly for both constraints. This particular example will only have two dual variables instead of the five dual variables used currently.
# All consecutive steps need to be updated since the dual variables would be updated.
# After substitution the nonlinear function should be further simplified. The current expression reads like a highly nonlinear function but can be easily simplified.
# Similar to the comments in the methodology section, inverting minimize to maximize is incorrect. Please update the dual objective function and domain of dual variables accordingly.
# Please use the LaTex code or equation editor for min, s.t., etc.
* A section to discuss and/or illustrate the applications
# Bullet points could be used to state the last four real-world examples that explain the physical meaning of the primal and dual problems.
# Add references for the last set of applications.
* A conclusion section
# This section contains a few typos. Please fix the same.
* References
# Some citations' hyperlinks are displaying.

== [[Disjunctive inequalities|Disjunctive Inequalities]] ==

* Author list
# Missing course section and semester
# Remove cornell ID
* An introduction of the topic
# No citations are present in this section.
# “mixed-integer programming (MIP)” should be used instead of “multiple integer programming (MIP)”. Please fix this error.
* Theory, methodology, and/or algorithmic discussions
# The abbreviation MILP is not previously defined. Please fix this issue.
# You consistently use the negative sign instead of the NOT operator for y (-y instead of ¬y).
# Some inconsistencies with the spacing of variables, constraints, etc., under the “General” section that need to be fixed.
# Typo in “This is shown below by M1, M2, y1, and y1:” where y1 needs to be changed to y2. Why use two different Big-M variables here? Elsewhere in the Wiki you only use one so this could lead to confusion with a general audience. Also if this was taken from the lecture notes then it needs to be cited.
* At least one numerical example
# Please reformulate and solve a complete numerical example rather than just reformulating a general example. Demonstrate the use of Big-M and Convex Hull formulation in an optimization problem that provides details such as individual steps in the problem solving process and final results. The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results.
# Add space between vee (V) operator and brackets in first line of Latex
# Please format variables correctly, for example, use <math>x_1</math> instead of x1.
* A section to discuss and/or illustrate the applications
# Please format the equations appropriately either by using latex code or the visual editor. These images are NOT acceptable!
* A conclusion section
# There is no conclusion presented in this section at all.
* References
# The included references have NOT been used anywhere in the Wiki. Add references for sentences that are not common knowledge and please link them appropriately with the text in Wiki. If the figures used here were not original works, you must also cite them.
# There are many papers on this topic. A simple Google (Scholar) search could provide you with sufficient references to cite.
# Many important references of this topic are missing.
# Please consider linking the references as demonstrated in the Wiki tutorial on Canvas and in this template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

==[[Stochastic programming|Stochastic Programming]] ==

* Author list: Remove cornell IDs
* An introduction of the topic
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
# This section only includes two sentences on Stochastic programming (SP), while the rest gives examples of uncertainty. Please discuss the need for SP in the presence of uncertainty. Also, discussion on robust optimization and its limitations should be removed since it is out of place.
* Theory, methodology, and/or algorithmic discussions
# Please avoid direct inline linkbacks to Wikipedia.
# The symbol “xi” in the methodology subsection should be explained.
* At least one numerical example
# Copying a numerical example "entirely" from a textbook is inappropriate. Your team should come up with a "numerical" case.
# No specific application context is needed for a numerical example.
# The inline notations (`x1`, `s1`) should also be typed using LaTex.
# Label all tables with a table number for better readability.
# Properly format the solution table with the label attached rather than the following sentence. The solution table looks different from the others, please fix this for consistency.
* A section to discuss and/or illustrate the applications;
# I suggest eliminating citing the last name of the first author (i.e. Zhou et al.)
* A conclusion section
* References
# URLs of some citations are not properly formatted (not showing the hyperlinks).

== [[Exponential transformation|Exponential Transformation]] ==

* Author list
# Missing course section
# Remove cornell ID
* An introduction of the topic
# Please expand the introduction.
# Please aim for a maximum average sentence length of ~25 words. Last sentence with 51 words is hard to read.
# Second Sentence: please change the word “they” as it could make the meaning ambiguous
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
# If you use abbreviations, please introduce them (e.g. NLP,MINLP)
* Theory, methodology, and/or algorithmic discussions
# Please explain the transformation in words along with equations
# Terms like posynomial should be described in detail.
# Please move the numerical example to the section below
# The “(eq 1)” is not needed here.
# Please expand this section.
* At least one numerical example
# In the third equation of the numerical example, it is confusing to have coefficients after numbers. Some readers may read it as an exponent.
# Last equation in this section after “further linearization” is incorrect. This equation cannot be further linearized, please fix this.
# Please explain the steps in the numerical examples in detail. The step-by-step solution should be provided.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# Missing part of text: “Proof of convexity of with positive definite test of Hessian…”
# Applications are not numerical examples. Please refer to this link for example of applications: [[Duality|https://optimization.cbe.cornell.edu/index.php?title=Duality]]
# Citation 7 is missing in current applications
# The section current applications is redundant
# Please use the LaTex code or equation editor for min, s.t., etc.
# Under current applications, do not just use a hyperlink to describe an application. Actually describe it. And properly inline citation style should be used instead of the hyperlink.
# The convexification application of MINLP can be further simplified for binary variables. Please refer to the lecture slides for more information.
* A conclusion section
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
* References
# Please consider linking the references by using this as Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Citation 7 is missing in current applications

== [[Sparse Reconstruction with Compressed Sensing|Sparse reconstruction with Compressed Sensing]] ==
This Wiki needs a significant rewrite. Please go through the comments for details.

* An introduction of the topic
# The introduction section should include information about the problem and its implications presented briefly. Please use full sentences to write this Wiki. You may use tools like Grammarly to check sentence formation and grammar.
# This section includes several typos like “sub modual”. Please fix them throughout the wiki and delete them if not required.
# Many abbreviations are used before previously defining them. Please define these abbreviations before using them in the text.
# This section is incomprehensible in its current form. Please rewrite with proper comprehension.
# Equations and math symbols need proper reformatting. The current version reads like text (along with equations) copy-pasted from a specific source. All mathematical symbols and equations should be formatted via LaTex - this is a learning objective of the Wiki assignment. You can find some useful links on converting your equations/symbols into LaTex code here: (https://optimization.cbe.cornell.edu/index.php?title=Help:Contents).
# Try to place the figure at the top of the Wiki between the main text.
# Avoid pronouns such as “we”.
# I suggest the use of more formal abstract illustrations.
* Theory, methodology, and/or algorithmic discussions
# Equations and symbols need proper reformatting.
# Lemmas and theorems are not expected for this Wiki. Sparse reconstruction is a straightforward concept but is unnecessarily complicated here. Please refer to other Wiki examples to get an idea of what the Wiki should convey.
# All equations need to be better formatted.

* At least one numerical example
# Numerical example is missing.
# Every iteration should be clearly presented, and solved "step-by-step".
* A section to discuss and/or illustrate the applications
# Having a list is not enough. Please explain at least three applications in a few sentences each.
* A conclusion section
# Conclusion section is missing.
* References
# The current reference list is not correctly formatted. References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Portfolio optimization|Portfolio Optimization]] ==

* Author list
# Remove cornell id
* An introduction of the topic
# The introductory sentence should be rephrased. The action of minimizing the risks does not inherently maximize the gains, rather PO aims to maximize gains whilst minimizing risks.
# Amount of whitespace can be reduced by changing the orientation of Figure 1 and the sentences in this section.
# Define terms such as risk, return, portfolio, etc., when you introduce them. Assume that the reader may not know much about finance. This goes for all other sections as well.
* Theory, methodology, and/or algorithmic discussions
# A brief mention of modern portfolio theory (i.e.. Markowitz) would be appropriate in this section.
# Several grammatical errors here involving sentence structure and clarity. Some questionable semantics (e.g., “The portfolio optimization mainly assumes two directions.”) and syntax (phrases such as “.. is as follows” should be followed by a colon). Misuse of commas and missing commas in this section. Two sentences introducing E(rp) and w should be combined into one.
# Use LaTex to distinguish variables written within a sentence, such as m and n.
# Rephrase “Cut the relevant information and conditions in the portfolio optimization, as well as the final requirements into the relevant variables, constraints and linear functions of the linear programming problem.”
# An explanation of a few common constraints would be helpful, rather than just including a table.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Solving the numerical example by GAMS is inappropriate. Please provide detailed step-by-step calculation results.
# All tables need to be labeled.
# Include figure number in label for consistency.
# Fix misspelling “dolling decision variables”.
# Use LaTex for all variables, equations, and constraints here.
# Example 2 table is hard to read, so making it bigger would help.
# Remove the “Using excel as the solver” part from the sentence before the solution discussion.
# Some grammatical errors here (phrases such as “.. is as follows” should be followed by a colon).
* A section to discuss and/or illustrate the applications
# Rephrase “Portfolio optimization can be used to screen investment projects that meet investors, rationally allocate investment amounts, etc.”
# Not sure “relevant” is the correct word choice here.
# You need more specific examples with the utility of portfolio optimization, this section is quite general as is. Some more detail and focus on real-world applications in the financial industry that relate to retirement planning, financial security, economic stability, etc., would be helpful.
* A conclusion section
# Need some commas here.
# The sentence “Linear programming has been around since the 1940’s and has such a wide base of applications” is not necessary.
* References
# Please consider linking the references as demonstrated in the Wiki tutorial on Canvas and in this template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove white space between end of sentences and reference numbers.

== [[Chance-constraint method|Chance constraint method]] ==

* Author list:
* An introduction of the topic
# Please consider correcting a few grammatical errors: “pre-planned for”, “god”, “certain levels of feasibility is guaranteed in what are”, and “Performance of a system”
# In “Chance-constraint”, it is capitalized randomly throughout the introduction. Please correct.
# Please use technical language to briefly introduce chance-constrained programming. Words like “acts of god”, “cost of doing business” are not appropriate for a technical Wiki.
* Theory, methodology, and/or algorithmic discussions
# Please add a citation to the first sentence.
# Xi is an uncertainty/randomness variable. It is better to use clear language.
# Please use the mathematical editor for adding explanations in the text. Using “ x is a decision variable” is hard to read. Same for f(x) and others.
# Theory is insufficient. Please expand and explain different approaches.
# Please add pros and cons explicitly as a list.
# Explain the physical meaning for examples of chance constraints along with all the notations used.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please remove this example as it is directly from this book. The example should be purely numerical without any background.
# Please use the equation editor for min, st., etc.
# Please use the mathematical editor for adding explanations in the text. Using “ x is a decision variable” is hard to read. Same for f(x) and others.
# Please change the table format so as not to confuse the reader.
# Multiple instances of [Chart to be added] are missing.
# Example is incomplete.
# Avoid pronouns such as “we”.
* A section to discuss and/or illustrate the applications
# Please connect several grammatical and spelling errors: “real life application”, Energy creation, particularly in renewable sources, have high variabilities”, and others
# “Zhao, Xue, Cao, and Zhang”. No need to list all authors within the article. Provide a reference is sufficient. If authors must be mentioned, (Zhao et al.) should be ok.
* A conclusion section
# Uniqueness and universality earlier are not clear to me. If they are not discussed earlier in the application, it would be better not to introduce new discussions in the conclusion.
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
* References
# References seem to vary in format. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Bayesian Optimization]] ==
* Section titles should not be "bold". Please double check using source editor on the section titles.
* Contents: The section titles should NOT be in bold to avoid strange format in TOC. Any formatting issue will incur a penalty in the grading.
* Author list: Remove cornell ID, Please check names
* Introduction
# The introduction is too general and not substantial enough. For example, simply saying BayesOpt is useful when the objective function is unknown obscures exactly HOW it is useful (namely, computational efficiency in applications where ground truth sampling is expensive). Discussion on applications should be moved to a separate section.
# Machine learning rarely includes black-box functions to be optimized. Bayesian optimization is almost never used for optimizing ML loss functions but can instead be used for hyperparameter optimization. Please update such claims in this section.
* Theory, methodology, and/or algorithmic discussions
# Captions need reformatting.
# Consider italicizing keywords rather than bolding.
# Please add a citation to the first sentence.
# Discussion on acquisition functions should include comparisons, tradeoffs, and reasons to use one over the other. Should also note that expected improvement is the most widely used in practice, and explain.
# Avoid pronouns such as “we”.
# Please write equations in the Wiki instead of attaching images for equations.
# Acquisition function figure could be made larger and clearer to improve readability.
* At least one numerical example
# Any references to functions or methods in code ‘e.g. fmin’ should be properly formatted as code-stylized text.
# Please use the equation editor for min, st., etc.
# Avoid including a figure of the code for this example and explicitly describe the steps to the modeling and solution process instead.
# Avoid pronouns such as “our” and “we”.
* A section to discuss and/or illustrate the applications
* A conclusion section
# Please do not use brackets to enclose lists.
# Some claims here should be supported by references. Please cite each source after its sentence.
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Try to avoid references to “pop” machine learning blogs where anyone can be an author. (e.g. towardsdatascience)
# All references are URLs. Please cite publications and literature.
# A simple Google Scholar search would give you many references.

Notes on grammar: Needs some work. Several instances where colons are inappropriately inserted mid sentence or in subheadings. Explanations are not terse. Several instances of switching between personal and impersonal style of writing, which is distracting.

== [[Conjugate gradient methods]] ==

* Author list: Remove cornell ID
* Introduction
# All inline notations (e.g., `x`, `A`) should be typed using LaTex.
* Theory, methodology, and/or algorithmic discussions
# All equations need to be better formatted.
# Is Gauss-Newton no longer referenced?
# Theorems listed in the first section should be accompanied with high level explanation, not just a list of the theorems themselves. The page should read like an article, with proper flow.
# Please indent equation blocks.
# Please properly format pseudocode.
* At least one numerical example
# Steps should be accompanied with explanation, or reference to the corresponding step in the pseudocode.
# Please properly format in a more organized manner, aligning equations appropriately and demarcating steps appropriately.
* A section to discuss and/or illustrate the applications
# Consider including 2 additional examples of applications
* A conclusion section
# Consider adding future research directions
* References
# Reference primary sources rather than Wikipedia
# Too few references.
# More references should be added. A simple Google Scholar search would give you many references.

== [[Geometric programming|Geometric Programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Examples of applications in this section use the same reference. Please cite their individual sources.
* Theory, methodology, and/or algorithmic discussions
# The symbol denoting the domain in the definition of a monomial is unclear. Please clarify it or fix this if it is incorrect.
# Definition of posynomial refers to section 2.1 which is missing from the Wiki (sections are not numbered in the main text).
# In the generalized posynomial subsection, bullet points do not tell us why h(x) is posynomial. Either provide reasons or simply state that h(x) is posynomial. Also explain why h3 is a generalized posynomial.
# Additional theory on the feasibility analysis could be provided in this section.
* At least one numerical example
# In the transformation example, the last two constraints could also be simplified by applying a natural logarithm on both sides. Please update them as well.
* A section to discuss and/or illustrate the applications
# The figure in this section needs to be labeled.
# The figure needs to be resized and perhaps aligned to the center.
* A conclusion section:
# Please avoid vague language such as: “This makes”.
# Please avoid opinionated statements: “one of the best ways”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# This Wiki has very few references. A quick Google Scholar search may provide relevant references.

== [[Adam]] ==

* Author list
* An introduction of the topic
# Some grammatical errors here, mostly related to the need for commas in certain places (e.g., “Before Adam..”).
# Some minor errors with parts of speech throughout the section, need to revisit phrases such as “which has broader scope in future for”, etc.
# Try splitting up some of the longer sentences in this section, a couple are hard to read.
# Avoid definitive statements about Adam being the best or always better solver, as this is simply not true (the choice of the “best” optimizer is setting-dependent). Use language such as “Research has shown that Adam has demonstrated superior experimental performance over..” and then cite academic references to back this claim.
# What does adam stand for? Introduction is insufficient. Please expand.
* Theory, methodology, and/or algorithmic discussions
# Revise grammar here, noticing some missing commas and uncapitalized word after period.
# Rephrase “second one is to update the old position with the updated position”.
# Use LaTex code or equation editor to display all equations and variables in this section, and actual subscripts instead of “m_t”, etc.
# Avoid inserting inline citations after words like “According to..” or “This article..” as it is a bit informal. This could be rephrased or changed to something like “According to author,^[2] …” with author name inserted.
# Remove white space before the period in RMSP discussion.
# Please provide a pseudocode.
# Please use list the two methods here “Adam is a combination of two gradient descent methods which are explained below”
# Please expand the theory section significantly. Theoretical convergence properties should be discussed, even if briefly.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
* A section to discuss and/or illustrate the applications
# Same comment as before, consider replacing inline citations after words like “According to..”.
* A conclusion section
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Try to avoid references to blogs and use peer-reviewed academic references instead.
# Too few references.
# More references should be added. A simple Google Scholar search would give you many references.

== [[A-star algorithm|a* algorithm]] ==

* Author list: Remove cornell ID
* Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.
* An introduction of the topic:
# Weird spacing between paragraphs. Please fix this issue.
# In the titles, please change the font from bold to normal to have consistent formatting in the site.
# Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.
# There are no citations in the introduction. Please cite every source.
* Theory, methodology, and/or algorithmic discussions
# Please add the mathematical description of the algorithm.
# Reference style varies in sentences. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please fix grammatical and spelling errors as (“from current position to the goal”, “There are a lot of discussions”, etc). Also, many hyphens are missing as “non playable”.
# In algorithms, it is a standard to add high-level description (i.e. pseudocode or flowchart). Please incorporate it.
# Use LaTex code or equation editor to display all equations and variables in this section (e.g., “f(n)...”, “h(n)..”, etc.). This goes for other sections as well.
* At least one numerical example
# The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.
# Instead of writing things like “The above image..”, label each figure and use the figure number to refer to it in text.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# No references in the applications. Please cite every source
# Preferably, add at least an additional application.
* A conclusion section
# Conclusion should summarize descriptions. Please modify it to provide a summary.
# Please pay attention to the length and structure of sentences here and in the full page. First sentence is hard to read.
* References
# References seem to vary in format and are not linked correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Incorrect reference style. Please follow the example and use the template.

== [[Job shop scheduling|Job-Shop Scheduling Problem]] ==

* An introduction of the topic
# The current introduction to the jobshop scheduling problem has only two sentences in addition to the parameter description. Introduction typically contains information about the problem, its importance in the real-world, and some information about the solution techniques and their types to solve the problem. Please add some information that covers the above.
* Theory, methodology, and/or algorithmic discussions
# It is unclear whether the assumptions stated in this section are required to apply the following solution techniques. Please clarify the same. Also use complete sentences to state them.
# The branch and bounds method described in this section only discusses the solution technique for problems with one machines. However, branch and bound is a general technique that can be applied to any MILP problems with varying scales. Please update the “methods” section to be as general as possible.
# Since this Wiki focuses on jobshop scheduling, at least two methods are expected. Branch and bound is a general MILP technique, so, it is recommended to add a tailored technique that can only solve specific jobshop scheduling problems. Solving the numerical example with this technique is not necessary.
# Reference to the branch and bound technique described in this section is a “youtube” video. Please add references in literature that describe this method in detail. The method used in this video is highly tailored for a single machine application. This is also an incorrect way to cite a reference. Please keep this section as general as possible.
# Use LaTex code or equation editor to display all equations and variables in this section and all other sections as well.
# Check grammar in this section. For example, phrases like “are as follows” need to be followed by a colon and not a period.
# Consider rewriting the assumptions as a list in this section.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# The example used in this section is exactly the same as the one in the youtube video. Please use a modification of this example or choose another example/method to demonstrate the solution technique. Your team should ideally create a numerical example independently. If you take a numerical example directly from a particular source, you will need to get explicit permission from the textbook author in writing and share that written permission with the instructors.
# The figure in this section is not numbered when all others are. Relabel this figure for consistency and its number to refer to it in-text.
# A numerical example should be simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments).
* A section to discuss and/or illustrate the applications
# This section should only focus on real-world applications of the jobshop scheduling problem. But currently, this section includes additional information on solution techniques/complexity that is appropriate for the Introduction section. Please discuss the applications of the problem in this section.
* A conclusion section
# The meaning of “Operations applications” is unclear. Please explain or update if necessary.
# The current conclusion section does not properly summarize the problem. Please refer to other Wiki examples for an idea to update the section accordingly.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please reference media sources like reference 5 appropriately.
# A simple Google Scholar search would give you many "formal" references.

== [[Optimization in game theory]] ==

* Author list: remove cornell IDs.
* An introduction of the topic
# References are not linked. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
* Theory, methodology, and/or algorithmic discussions
# Why only a subsection on "Nash Equilibrium" is included in "Theory" section? Please re-format.
# Please edit references.
# Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm.
# Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.
* At least one numerical example
# Please organize the last part in a more readable format. Questions may be in bold and numbered, answers are more direct, etc.
# Remember to cite all images and tables.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# Very good, link the reference and cite all sources.
* A conclusion section
# Please add more summarizing especially from theory sentences and avoid long sentences.
* References
# Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Reference primary sources rather than Wikipedia
# Incorrect reference style. Please correct.

== [[Trust-region methods]] ==

* Author list:
# Remove cornell IDs. Author is also spelled incorrectly.
# Add the course section.
* An introduction of the topic
# References are not linked. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Use LaTex code or equation editor to display all equations and variables (e.g., “xk”, “f`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “we”. This goes for all other sections as well.
* Theory, methodology, and/or algorithmic discussions
# Organization of ideas in this section needs work.
# You have not defined explicitly why the Cauchy point is important to compute beyond a vague allusion to performance improvements, which is also wrong (it is useful because of its guarantees for convergence, not performance) It is also misspelled.
# Each approach should have accompanying explanation and motivation for why it is being discussed. It is not enough to outline the algorithm.
# Please make sure symbols are properly subscripted and superscripted (e.g. “pk” should be “p_k”
# Please format the algorithm in proper algorithmic pseudocode format.
# Little to no discussion on global convergence guarantees
# Please include discussion about the advantages and disadvantages of the algorithm
# Fix typo “couchy point”.
* At least one numerical example
# Any code functions (uminfunc) should have proper text formatting.
# The graph needs a better caption explaining how the axes are labeled and what data points are being shown.
# Please increase the quality of the figure. It is hard to see the red line.
# Add citation to “The Rosenbrock function is a non-convex function, introduced by Howard H. Rosenbrock in 1960, which is often used as a performance test problem for optimization algorithms.”
* A section to discuss and/or illustrate the applications
# The content in this section as it is currently does NOT describe applications, but rather different approaches within the trust region methodology. Please provide specific applications (e.g. TRPO in reinforcement learning).
* A conclusion section
# Please add more summary, future research directions for example is a good start.
* References
# Incorrect reference style.
# Please consider having the references as this Wiki template, <nowiki>https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization</nowiki>
# More references should be added. A simple Google Scholar search would give you many references.

*There are numerous misspellings, grammatical errors, and incorrect claims. Please fix these.

== [[Momentum]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Apart from an explanation on momentum, it is necessary to briefly point out the limitations of SGD and why momentum could help with these limitations. Please update it accordingly.
# Remove bold on “Momentum”.
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
* Theory, methodology, and/or algorithmic discussions
# Equation formatting is very poor and should be formalized.
# It is important to use technical language for this Wiki. Although a layman’s explanation is appreciated, it would be better to skip using words like “zig zagging”. Try to explain all concepts in a technical language with few simplifications but NOT vice versa.
# The definition of the update rule for SGD with momentum looks incorrect, specifically the first expression. Please fix it and also explain all the parameters used.
# Use LaTex code or equation editor to display all equations and variables (e.g., “W”, “V`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “you”.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step". Since writing all iterations is not feasible, at least present a few iterations for both cases.
# Please try to label the plots that explains what each line color means.
# Starting point for SGD with momentum is different in explanation and the table. Please fix the same.
* A section to discuss and/or illustrate the applications
# Please use correct terminology like “optimizing non-convex functions” and not “training non-convex models”.
# Adam, Adadelta, and RMSprop are variants of SGD that already use momentum. Please double check the writing and update if necessary.
* A conclusion section
# Please refrain from using words like “zig zag” effects.
* References
# Almost all references used are URLs. Please try to add journal/conference articles or books for references, instead of directly citing the URLs. Please check the list below and run a quick Google (Scholar) search to identify relevant literature.

== [[Stochastic dynamic programming|Stochastic Dynamic programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Discussion on applications should be moved to a separate section.
* Theory, methodology, and/or algorithmic discussions
# Remove the grey box background of equations.
* At least one numerical example
* A section to discuss and/or illustrate the applications
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Outer-approximation (OA)|Outer-approximation]] ==

* An introduction of the topic
# See formatting guideline below
# Avoid opinionated statements such as “MINLP problems are usually the hardest to solve”.
# Rearrange the text such that the MINLP formulation is in the theory section and keep the introduction in words only.
* Theory, methodology, and/or algorithmic discussions
# Consider left aligning equations and optimization problem formulations by the “=”. See [[Stochastic programming|https://optimization.cbe.cornell.edu/index.php?title=Stochastic_programming]] for an example
# The sentence “The Outer-Approximation (OA) algorithm was first proposed by Duran and and Grossmann in 1986 to solve MINLP problems.” needs a reference.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# “Minimize” and “subject to” should be “min” and “s.t.” in MathType
* A section to discuss and/or illustrate the applications
# Does not explicitly point out why OA is applicable (and/or preferred) in these applications, rather than other MINLP approaches (show that the problem formulations are amenable to a solution approach through OA)
# The sentence “... an active research area and there exists a vast number of applications in fields such as engineering, computational chemistry, and finance.” needs references.
# Posting GAMS code on the page is generally inappropriate and discouraged. Please check with the TAs or me if you have a strong desire to post GAMS codes on the Wiki page. A typical textbook should not be limited to a specific software package. If the GAMS code must be posted, please also post ALL other software implementation versions, such as Pyomo and JuliaOPT, among others.
# Consider reformatting to make steps more readable. Inserting spaces and breaking down steps would help.
* A conclusion section
# Too short. Consider discussion on future research direction and discussion on uncertainty
# Please review abbreviations throughout the page. Why is MINLP redefined here? “Outer-Approximation is a well known efficient approach for solving convex mixed-integer nonlinear programs (MINLP)”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove "Template:Reflist"

== [[Unit commitment problem]] ==

* Author list
* An introduction of the topic
# Please expand the introduction and avoid discussions of examples or specific applications in this section.
# The sentence “Nonlinear, Non-convex programming optimization problem.” doesn’t make sense by itself and Non-convex shouldn’t be capitalized.
* Theory, methodology, and/or algorithmic discussions
# Figure/image format should be revised to better display the content.
# Uppercase characters are used randomly (e.g., “non-convex transmission Constraints”) . Please follow correct language conventions for sentence structure.
# Avoid inserting inline citations after words like “written in matrix form as equation [3]..” or “presented in [3]...” as it is a bit informal when you don’t explicitly name the subject. Also these two sentences are grammatically incorrect and appear to be missing an ending period and comma, respectively.
# Don’t say “written in matrix form as equation..” and just cite the reference, actually write out the equation.
# Properly label the figure in this section with a figure number and improve visibility by making it larger.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Label the figures in this section properly with figure numbers.
# Fix typo “while minimize” to “while minimizing”.
# Avoid pronouns such as “we”.
# Use the equation editor when typing equations.
# A numerical example is simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments). There is an Application section where you discuss the applications.
# The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).
* A section to discuss and/or illustrate the applications:
# I suggest changing the order of the subtitles here. For example, Single-Period Unit Commitment.
* A conclusion section
* References

== [[Frank-Wolfe]] ==

* Author list:
* An introduction of the topic
# I suggest highlighting disadvantages along with advantages.
* Theory, methodology, and/or algorithmic discussions
# “[n x 1] matrix” please use the equation editor to express mathematical descriptions and symbols (p,b, etc)
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please show at least a few iterations. Even for smaller examples if needed. Report the final solution.
# Please use the LaTex code or equation editor for min and include s.t., etc.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps. For your example, please explicitly state that the derivative is taken etc.
* A section to discuss and/or illustrate the applications:
* A conclusion section
# Same as the introduction. Pros and cons should be evaluated together!
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Line search methods|Line Search Method]] ==

* Author list
* An introduction of the topic
# Expand the introduction and avoid discussion on some of the specific steps in the solution process.
# Provide references here.
* Theory, methodology, and/or algorithmic discussions
# The phrase “are as follows” in the steepest descent method discussion needs to be followed by a colon.
# Rephrase “has a nice convergence theory” and cite a reference for this claim.
# Avoid pronouns such as “we”.
# Add citation after “.. proposed by Phillip Wolfe in 1969.”
# Figure 1 is between two sections. Please fix this issue.
* At least one numerical example:
# Add some space between iterations or subsection break
* A section to discuss and/or illustrate the applications:
# Too few references in this section.
# Last paragraph makes some claims without references.
* A conclusion section
* References
# References should be properly formatted. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Piecewise linear approximation|Piecewise Linear Approximation]]==

* Author list
* An introduction of the topic
# The content of this section is good, but there are some issues with sentence clarity and some other grammatical errors. Please revisit this section and make changes accordingly.
* Theory, methodology, and/or algorithmic discussions
# Fix typo “to force the x’ values become associated with”.
* At least one numerical example
* A section to discuss and/or illustrate the applications
# Please aim for a maximum average sentence length of ~25 words. Some of these longer sentences are hard to read.
* A conclusion section
# Expand the conclusion section to be longer than one sentence. The conclusion section to include a brief summary of what was discussed above, an emphasis on it’s significance, and a brief discussion of future extensions and research direction if applicable.
* References
# Include hyperlinks to sources when possible.

== [[Mathematical programming with equilibrium constraints|Mathematical Programming with Equilibrium constraints]] ==

* An introduction of the topic
# This section includes several terms like variational inequalities, constraint qualifications that were not discussed in the class. Please add a sentence to explain them before using them.
* Theory, methodology, and/or algorithmic discussions
# The meaning of parameter vector x is unclear. Please add more information or update if necessary.
# Equations and symbols in the PIPA subsection are not formatted correctly. Please use the same formatting for all equations, so they read as mathematical equations and not text. This goes for all other sections as well.
# Use equations instead of images to represent math programs and equations in the Implicit Descent and SQP subsection.
# Apart from the steps for each solution technique, please also add a few sentences that describe each method.
* At least one numerical example
# Please define the terms like NCP, MP before abbreviating them. Also try not to unnecessarily abbreviate simple terms.
# Equations should be typed by LaTex. Images for equations are unacceptable.
# GAMS code is strongly discouraged. Please solve the problem "step-by-step".
# The selected numerical example is fine but is directly solved with the MPEC solver in GAMS. Try to solve it manually like the homework/in-class problems step by step using the steps described in the previous section by choosing any of the methods.
# Avoid using figures in the equations (subject to etc)
* A section to discuss and/or illustrate the applications
# Add references to “power management, highway pricing, chemical process engineering, and traffic planning.”
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# This Wiki contains very few references. Please check the list below and run a quick Google (Scholar) search to identify relevant literature.

== [[Wing shape optimization|Wing shape Optimization]] ==

* Author list: Remove cornell ID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC. Any formatting issue will incur a penalty in the grading.
* An introduction of the topic
# The introduction is missing several references (e.g., “software packages like computational fluid dynamics..”, sentences containing things that aren’t common knowledge, performance claims, etc.)
# Avoid discussion involving finer details of subject methods in this section.
# In the titles, please change the font from bold to normal to have consistent formatting in the site. Same applies to box of content!
* Theory, methodology, and/or algorithmic discussions
# Properly cite the CFD package, don’t just include a link.
# Properly label the figure with a figure number.
# Consider removing white space between isolated sentences to improve readability.
* At least one numerical example
# If you’ve already defined an abbreviation (CFD), there is no need to define it again. Just use the abbreviation.
# Avoid pronouns such as “we” or “they”.
# Phrases like “under the following” need to be followed by a colon.
# Properly label the figure with a figure number and consider making them larger to improve visibility. Call the reader's attention to the figures in text by referencing the figure number.
# “As seen in the video below” is stated yet there are only images present and it may be initially unclear to the reader which figure is being referenced here.
# Avoid inserting inline citations like “[4] introduces an..” as it is a bit informal when you don’t explicitly name the subject.
# Don’t just cite the reference when discussing the problem formulation, explicitly write the model formulation and solution process using LaTex or equation visual editor.
# Your team should ideally create a numerical example independently. If you take a numerical example directly from a textbook, etc., you will need to get explicit permission from the author in writing and share that written permission with me.
# A numerical example is simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments). There is an Application section where you discuss the applications.
# The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).
* A section to discuss and/or illustrate the applications
# Some characters are randomly capitalized in this section.
* A conclusion section
# These variables should be defined before the conclusion section, they are out of place here. Also, please use normal text when explaining variables except for the variable symbol.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Interior-point method for NLP|Interior point method for NLP]] ==

* An introduction of the topic:
* Theory, methodology, and/or algorithmic discussions
# Primal-Dual formulation and comparison to the Barrier Method is not discussed.
# Include brief discussion about big O convergence rates.
# Need discussion about the concept of “central path” and the notion of self concordance
# Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
# Graphs and images are incorrectly formatted to the page. Consider proper alignment with respect to the text body.
# Use explicitly typed Latex equations instead of images to represent math programs and equations.
# Fix typo “optimisation”.
# Use LaTex code or equation editor to display all equations and variables (e.g., “xi ”, “μ”, etc.).
* At least one numerical example:
# There are formatting issues with figures 2,3. Please make sure to embed them within their respective sections.
* A section to discuss and/or illustrate the applications
* A conclusion section
# Minor character code typos in the conclusion.
# Also, please add more discussion in this section. Future research directions is a good start.
# There is a box "􏰐"
* References

== [[AdaGrad|Adagrad]] ==

* An introduction of the topic:
* Theory, methodology, and/or algorithmic discussions
# Include discussion on its variants (most important is AdaDelta).
# Include disadvantages of Adagrad, since this provides motivation for the discussion on the variants and improvements of Adagrad
# Include comparisons to other popular optimizers (particularly important is comparisons to regular SGD and Adam)
# Different convergence rates are possible depending on the setting where Adagrad is used, but this is not mentioned on the page currently. As such the regret bound section should be more thoroughly explained.
# Algorithm image is blurry. Either increase the fidelity or write the pseudocode directly in the wiki editor.
* At least one numerical example
# In the first sentence, “..take the following numerical example” should be followed by a colon.
# Fix typo “trayectory”.
* A section to discuss and/or illustrate the applications
# This section is too short; include specific applications in which input features are sparse and Adagrad excels.
# Add reference to the claim “Mainly, it is a good choice for deep learning models with sparse input features”.
* A conclusion section
* References

# Too few references overall, you should aggregate information from multiple sources (even if the base algorithm itself comes from a singular paper)

== [[McCormick envelopes|McCormick Envelopes]] ==

* Author list: OK but I suggest removing NetID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# First sentence is hard to read. Please consider keeping sentences below 25-30 words.
# No references provided. Please cite all sources.
# Figure 1 is provided in the middle between two sections. Please include in the introduction section.
* Theory, methodology, and/or algorithmic discussions
# References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# When using mathematical expressions and symbols, please use the equation editor. (e.g., x*y, exy + y, sin (x+y) - x2)
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# The solution technique should be clearly presented, and solved "step-by-step".
# GAMS code is unnecessary. Please provide detailed step-by-step calculation results.
* A section to discuss and/or illustrate the applications
# Having a list is not enough. Please explain at least three applications in a few sentences each.
# This section should be at least a paragraph to discuss relevant applications. Each application should be explicitly linked to the page topic. A few keywords do not meet the requirement at all.
* A conclusion section:
* References
# References are not expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please follow the standard reference style - the current format is incorrect.

== [[Branch and bound (BB) for MINLP|Branch and Bound for MINLP]] ==

* Author list:
** Remove NetIDS
** Please remove abbreviations from the title (i.e. BB).
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# Please cite sources appropriately: References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Introduction is very short for a well-recognized topic. Please expand significantly. You may refer to the Wiki examples to get an idea on writing the Introduction to a topic.
# An illustration might be useful here.
* Theory, methodology, and/or algorithmic discussions
# The algorithm described here considers only binary integer variables. However, MINLP problems may include non-binary integer variables too. Please update the method or provide a short description of the assumptions that the MINLP problem needs to satisfy in order for the presented technique to be applicable.
# Use linked citations please as the Wiki template above.
# Please provide steps in a more organized way. Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
# Step 2 is missing yet it is referenced in the text multiple times. Please address this in addition to the above comment.
# An illustration might be useful here as well.
# Please explain what a Gomory Cut is. If the topic is available on optimization.cb.cornell.edu, you can link it.
# The current equations seem to be simple text written in Italics. All mathematical symbols and equations should be formatted via LaTex.
# Please format the math programs with equations and notations using formulations in lecture notes as templates.
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# Please show a step-by-step solution in the example. The solution is incomplete. The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).
# Please use the equation editor for equations or mathematical symbols. - All mathematical symbols and equations should be formatted via LaTex - this is a learning objective of the Wiki assignment. You can find some useful links on converting your equations/symbols into LaTex code here: (<nowiki>https://optimization.cbe.cornell.edu/index.php?title=Help:Contents</nowiki>). Again, any formatting issue will incur a "compound" penalty in the grading.
# This example does not follow the MINLP structure discussed in the above section since binary variables are missing. Branch and bound may not be appropriate for such problems. Please provide an appropriate numerical example and solve it according to the above comments.
# Make sure your example is not taken from a book as that is strictly disallowed.
* A section to discuss and/or illustrate the applications
# This section is not well-formatted. Please provide 3 applications and explain each in a few sentences and how BB for MINLP could be used. Also, please eliminate having multiple sections (Application, Mathematical problem, industrial application). All these could be merged together.
# This section should be at least a paragraph to discuss relevant applications. Each application should be explicitly linked to the page topic. A few keywords do not meet the requirement at all.
* A conclusion section:
# The sentence is hard to understand "a scheme that grows exponentially because" please use a simple language. Is it also theoretically correct? It is also not mentioned and explained earlier. Thus, please avoid introducing new concepts or terms at the end.
# Please use summarizing sentences to describe earlier sections instead of introducing new concepts/discussion.
* References
# Too few references overall, you should aggregate information from multiple sources. A quick Google scholar search could provide relevant references.
# References are not expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please follow the standard reference style - the current format is incorrect.

2021 Cornell Optimization Open Textbook Feedback

2021-12-06T03:09:01Z

Asa273: /* McCormick Envelopes */

== [[Lagrangean duality|Lagrangian duality]] ==
* Author list, sections and TOC
# Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.
# Remove cornell ID from Author list
* An introduction of the topic
# This section includes sentences on constructing the dual problem and is referred to as Lagrangian relaxation (LR). This is incorrect, please fix the definition of LR.
# Definitions of LR and its relation to duality should be double checked and re-written.
# Only one reference is present in this section. Please add more relevant references by expanding this section.
# Consider merging the “introduction” and “history” sections.
# In the titles, please change the font from bold to normal to have consistent formatting in the site.
* Theory, methodology, and/or algorithmic discussions
# The Lagrangian variables associated with equality constraints h(x) are unbounded but the Lagrangian dual problem states them as non-negative. Please fix the same.
# Also to construct a dual, we do not change minimization to maximization directly. We observed such things in the examples in lecture notes due to simplification. The lagrangian dual problem would be minimize (,).
# Adding to the previous point, the Lagrangian is a lower bound on the original objective; the solution to the primal and dual or only equivalent if the duality gap is 0. You reference this in one section, but this is after your statement “Hence, solving the dual problem, which is a function of the Lagrangian multipliers (𝜆*) yields the same solution as the primal problem, which is a function of the original variables (x*). “. Please clarify the specific conditions that must hold for the solution of the dual to be equal to the primal’s.
# You refer to the “Complementary Slackness Theorem”, but don’t actually write the mathematical representation of complementary slackness. Please fix this. Also consider including the derivation of the complementary slackness condition, as it is both easy and short. Boyd is a good reference for this.
# Last step of the “process” subsection also needs updating according to the previous comments.
# The inline notations should also be typed using LaTex.
# Please use the LaTex code or equation editor for min, s.t., etc.
* At least one numerical example
# Only one dual variable is associated with each constraint. The numerical example uses two for the first and second constraint which is unnecessary. Please update it accordingly for both constraints. This particular example will only have two dual variables instead of the five dual variables used currently.
# All consecutive steps need to be updated since the dual variables would be updated.
# After substitution the nonlinear function should be further simplified. The current expression reads like a highly nonlinear function but can be easily simplified.
# Similar to the comments in the methodology section, inverting minimize to maximize is incorrect. Please update the dual objective function and domain of dual variables accordingly.
# Please use the LaTex code or equation editor for min, s.t., etc.
* A section to discuss and/or illustrate the applications
# Bullet points could be used to state the last four real-world examples that explain the physical meaning of the primal and dual problems.
# Add references for the last set of applications.
* A conclusion section
# This section contains a few typos. Please fix the same.
* References
# Some citations' hyperlinks are displaying.

== [[Disjunctive inequalities|Disjunctive Inequalities]] ==

* Author list
# Missing course section and semester
# Remove cornell ID
* An introduction of the topic
# No citations are present in this section.
# “mixed-integer programming (MIP)” should be used instead of “multiple integer programming (MIP)”. Please fix this error.
* Theory, methodology, and/or algorithmic discussions
# The abbreviation MILP is not previously defined. Please fix this issue.
# You consistently use the negative sign instead of the NOT operator for y (-y instead of ¬y).
# Some inconsistencies with the spacing of variables, constraints, etc., under the “General” section that need to be fixed.
# Typo in “This is shown below by M1, M2, y1, and y1:” where y1 needs to be changed to y2. Why use two different Big-M variables here? Elsewhere in the Wiki you only use one so this could lead to confusion with a general audience. Also if this was taken from the lecture notes then it needs to be cited.
* At least one numerical example
# Please reformulate and solve a complete numerical example rather than just reformulating a general example. Demonstrate the use of Big-M and Convex Hull formulation in an optimization problem that provides details such as individual steps in the problem solving process and final results. The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results.
# Add space between vee (V) operator and brackets in first line of Latex
# Please format variables correctly, for example, use <math>x_1</math> instead of x1.
* A section to discuss and/or illustrate the applications
# Please format the equations appropriately either by using latex code or the visual editor. These images are NOT acceptable!
* A conclusion section
# There is no conclusion presented in this section at all.
* References
# The included references have NOT been used anywhere in the Wiki. Add references for sentences that are not common knowledge and please link them appropriately with the text in Wiki. If the figures used here were not original works, you must also cite them.
# There are many papers on this topic. A simple Google (Scholar) search could provide you with sufficient references to cite.
# Many important references of this topic are missing.
# Please consider linking the references as demonstrated in the Wiki tutorial on Canvas and in this template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

==[[Stochastic programming|Stochastic Programming]] ==

* Author list: Remove cornell IDs
* An introduction of the topic
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
# This section only includes two sentences on Stochastic programming (SP), while the rest gives examples of uncertainty. Please discuss the need for SP in the presence of uncertainty. Also, discussion on robust optimization and its limitations should be removed since it is out of place.
* Theory, methodology, and/or algorithmic discussions
# Please avoid direct inline linkbacks to Wikipedia.
# The symbol “xi” in the methodology subsection should be explained.
* At least one numerical example
# Copying a numerical example "entirely" from a textbook is inappropriate. Your team should come up with a "numerical" case.
# No specific application context is needed for a numerical example.
# The inline notations (`x1`, `s1`) should also be typed using LaTex.
# Label all tables with a table number for better readability.
# Properly format the solution table with the label attached rather than the following sentence. The solution table looks different from the others, please fix this for consistency.
* A section to discuss and/or illustrate the applications;
# I suggest eliminating citing the last name of the first author (i.e. Zhou et al.)
* A conclusion section
* References
# URLs of some citations are not properly formatted (not showing the hyperlinks).

== [[Exponential transformation|Exponential Transformation]] ==

* Author list
# Missing course section
# Remove cornell ID
* An introduction of the topic
# Please expand the introduction.
# Please aim for a maximum average sentence length of ~25 words. Last sentence with 51 words is hard to read.
# Second Sentence: please change the word “they” as it could make the meaning ambiguous
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
# If you use abbreviations, please introduce them (e.g. NLP,MINLP)
* Theory, methodology, and/or algorithmic discussions
# Please explain the transformation in words along with equations
# Terms like posynomial should be described in detail.
# Please move the numerical example to the section below
# The “(eq 1)” is not needed here.
# Please expand this section.
* At least one numerical example
# In the third equation of the numerical example, it is confusing to have coefficients after numbers. Some readers may read it as an exponent.
# Last equation in this section after “further linearization” is incorrect. This equation cannot be further linearized, please fix this.
# Please explain the steps in the numerical examples in detail. The step-by-step solution should be provided.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# Missing part of text: “Proof of convexity of with positive definite test of Hessian…”
# Applications are not numerical examples. Please refer to this link for example of applications: [[Duality|https://optimization.cbe.cornell.edu/index.php?title=Duality]]
# Citation 7 is missing in current applications
# The section current applications is redundant
# Please use the LaTex code or equation editor for min, s.t., etc.
# Under current applications, do not just use a hyperlink to describe an application. Actually describe it. And properly inline citation style should be used instead of the hyperlink.
# The convexification application of MINLP can be further simplified for binary variables. Please refer to the lecture slides for more information.
* A conclusion section
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
* References
# Please consider linking the references by using this as Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Citation 7 is missing in current applications

== [[Sparse Reconstruction with Compressed Sensing|Sparse reconstruction with Compressed Sensing]] ==
This Wiki needs a significant rewrite. Please go through the comments for details.

* An introduction of the topic
# The introduction section should include information about the problem and its implications presented briefly. Please use full sentences to write this Wiki. You may use tools like Grammarly to check sentence formation and grammar.
# This section includes several typos like “sub modual”. Please fix them throughout the wiki and delete them if not required.
# Many abbreviations are used before previously defining them. Please define these abbreviations before using them in the text.
# This section is incomprehensible in its current form. Please rewrite with proper comprehension.
# Equations and math symbols need proper reformatting. The current version reads like text (along with equations) copy-pasted from a specific source. All mathematical symbols and equations should be formatted via LaTex - this is a learning objective of the Wiki assignment. You can find some useful links on converting your equations/symbols into LaTex code here: (https://optimization.cbe.cornell.edu/index.php?title=Help:Contents).
# Try to place the figure at the top of the Wiki between the main text.
# Avoid pronouns such as “we”.
# I suggest the use of more formal abstract illustrations.
* Theory, methodology, and/or algorithmic discussions
# Equations and symbols need proper reformatting.
# Lemmas and theorems are not expected for this Wiki. Sparse reconstruction is a straightforward concept but is unnecessarily complicated here. Please refer to other Wiki examples to get an idea of what the Wiki should convey.
# All equations need to be better formatted.

* At least one numerical example
# Numerical example is missing.
# Every iteration should be clearly presented, and solved "step-by-step".
* A section to discuss and/or illustrate the applications
# Having a list is not enough. Please explain at least three applications in a few sentences each.
* A conclusion section
# Conclusion section is missing.
* References
# The current reference list is not correctly formatted. References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Portfolio optimization|Portfolio Optimization]] ==

* Author list
# Remove cornell id
* An introduction of the topic
# The introductory sentence should be rephrased. The action of minimizing the risks does not inherently maximize the gains, rather PO aims to maximize gains whilst minimizing risks.
# Amount of whitespace can be reduced by changing the orientation of Figure 1 and the sentences in this section.
# Define terms such as risk, return, portfolio, etc., when you introduce them. Assume that the reader may not know much about finance. This goes for all other sections as well.
* Theory, methodology, and/or algorithmic discussions
# A brief mention of modern portfolio theory (i.e.. Markowitz) would be appropriate in this section.
# Several grammatical errors here involving sentence structure and clarity. Some questionable semantics (e.g., “The portfolio optimization mainly assumes two directions.”) and syntax (phrases such as “.. is as follows” should be followed by a colon). Misuse of commas and missing commas in this section. Two sentences introducing E(rp) and w should be combined into one.
# Use LaTex to distinguish variables written within a sentence, such as m and n.
# Rephrase “Cut the relevant information and conditions in the portfolio optimization, as well as the final requirements into the relevant variables, constraints and linear functions of the linear programming problem.”
# An explanation of a few common constraints would be helpful, rather than just including a table.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Solving the numerical example by GAMS is inappropriate. Please provide detailed step-by-step calculation results.
# All tables need to be labeled.
# Include figure number in label for consistency.
# Fix misspelling “dolling decision variables”.
# Use LaTex for all variables, equations, and constraints here.
# Example 2 table is hard to read, so making it bigger would help.
# Remove the “Using excel as the solver” part from the sentence before the solution discussion.
# Some grammatical errors here (phrases such as “.. is as follows” should be followed by a colon).
* A section to discuss and/or illustrate the applications
# Rephrase “Portfolio optimization can be used to screen investment projects that meet investors, rationally allocate investment amounts, etc.”
# Not sure “relevant” is the correct word choice here.
# You need more specific examples with the utility of portfolio optimization, this section is quite general as is. Some more detail and focus on real-world applications in the financial industry that relate to retirement planning, financial security, economic stability, etc., would be helpful.
* A conclusion section
# Need some commas here.
# The sentence “Linear programming has been around since the 1940’s and has such a wide base of applications” is not necessary.
* References
# Please consider linking the references as demonstrated in the Wiki tutorial on Canvas and in this template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove white space between end of sentences and reference numbers.

== [[Chance-constraint method|Chance constraint method]] ==

* Author list:
* An introduction of the topic
# Please consider correcting a few grammatical errors: “pre-planned for”, “god”, “certain levels of feasibility is guaranteed in what are”, and “Performance of a system”
# In “Chance-constraint”, it is capitalized randomly throughout the introduction. Please correct.
# Please use technical language to briefly introduce chance-constrained programming. Words like “acts of god”, “cost of doing business” are not appropriate for a technical Wiki.
* Theory, methodology, and/or algorithmic discussions
# Please add a citation to the first sentence.
# Xi is an uncertainty/randomness variable. It is better to use clear language.
# Please use the mathematical editor for adding explanations in the text. Using “ x is a decision variable” is hard to read. Same for f(x) and others.
# Theory is insufficient. Please expand and explain different approaches.
# Please add pros and cons explicitly as a list.
# Explain the physical meaning for examples of chance constraints along with all the notations used.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please remove this example as it is directly from this book. The example should be purely numerical without any background.
# Please use the equation editor for min, st., etc.
# Please use the mathematical editor for adding explanations in the text. Using “ x is a decision variable” is hard to read. Same for f(x) and others.
# Please change the table format so as not to confuse the reader.
# Multiple instances of [Chart to be added] are missing.
# Example is incomplete.
# Avoid pronouns such as “we”.
* A section to discuss and/or illustrate the applications
# Please connect several grammatical and spelling errors: “real life application”, Energy creation, particularly in renewable sources, have high variabilities”, and others
# “Zhao, Xue, Cao, and Zhang”. No need to list all authors within the article. Provide a reference is sufficient. If authors must be mentioned, (Zhao et al.) should be ok.
* A conclusion section
# Uniqueness and universality earlier are not clear to me. If they are not discussed earlier in the application, it would be better not to introduce new discussions in the conclusion.
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
* References
# References seem to vary in format. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Bayesian Optimization]] ==
* Section titles should not be "bold". Please double check using source editor on the section titles.
* Contents: The section titles should NOT be in bold to avoid strange format in TOC. Any formatting issue will incur a penalty in the grading.
* Author list: Remove cornell ID, Please check names
* Introduction
# The introduction is too general and not substantial enough. For example, simply saying BayesOpt is useful when the objective function is unknown obscures exactly HOW it is useful (namely, computational efficiency in applications where ground truth sampling is expensive). Discussion on applications should be moved to a separate section.
# Machine learning rarely includes black-box functions to be optimized. Bayesian optimization is almost never used for optimizing ML loss functions but can instead be used for hyperparameter optimization. Please update such claims in this section.
* Theory, methodology, and/or algorithmic discussions
# Captions need reformatting.
# Consider italicizing keywords rather than bolding.
# Please add a citation to the first sentence.
# Discussion on acquisition functions should include comparisons, tradeoffs, and reasons to use one over the other. Should also note that expected improvement is the most widely used in practice, and explain.
# Avoid pronouns such as “we”.
# Please write equations in the Wiki instead of attaching images for equations.
# Acquisition function figure could be made larger and clearer to improve readability.
* At least one numerical example
# Any references to functions or methods in code ‘e.g. fmin’ should be properly formatted as code-stylized text.
# Please use the equation editor for min, st., etc.
# Avoid including a figure of the code for this example and explicitly describe the steps to the modeling and solution process instead.
# Avoid pronouns such as “our” and “we”.
* A section to discuss and/or illustrate the applications
* A conclusion section
# Please do not use brackets to enclose lists.
# Some claims here should be supported by references. Please cite each source after its sentence.
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Try to avoid references to “pop” machine learning blogs where anyone can be an author. (e.g. towardsdatascience)
# All references are URLs. Please cite publications and literature.
# A simple Google Scholar search would give you many references.

Notes on grammar: Needs some work. Several instances where colons are inappropriately inserted mid sentence or in subheadings. Explanations are not terse. Several instances of switching between personal and impersonal style of writing, which is distracting.

== [[Conjugate gradient methods]] ==

* Author list: Remove cornell ID
* Introduction
# All inline notations (e.g., `x`, `A`) should be typed using LaTex.
* Theory, methodology, and/or algorithmic discussions
# All equations need to be better formatted.
# Is Gauss-Newton no longer referenced?
# Theorems listed in the first section should be accompanied with high level explanation, not just a list of the theorems themselves. The page should read like an article, with proper flow.
# Please indent equation blocks.
# Please properly format pseudocode.
* At least one numerical example
# Steps should be accompanied with explanation, or reference to the corresponding step in the pseudocode.
# Please properly format in a more organized manner, aligning equations appropriately and demarcating steps appropriately.
* A section to discuss and/or illustrate the applications
# Consider including 2 additional examples of applications
* A conclusion section
# Consider adding future research directions
* References
# Reference primary sources rather than Wikipedia
# Too few references.
# More references should be added. A simple Google Scholar search would give you many references.

== [[Geometric programming|Geometric Programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Examples of applications in this section use the same reference. Please cite their individual sources.
* Theory, methodology, and/or algorithmic discussions
# The symbol denoting the domain in the definition of a monomial is unclear. Please clarify it or fix this if it is incorrect.
# Definition of posynomial refers to section 2.1 which is missing from the Wiki (sections are not numbered in the main text).
# In the generalized posynomial subsection, bullet points do not tell us why h(x) is posynomial. Either provide reasons or simply state that h(x) is posynomial. Also explain why h3 is a generalized posynomial.
# Additional theory on the feasibility analysis could be provided in this section.
* At least one numerical example
# In the transformation example, the last two constraints could also be simplified by applying a natural logarithm on both sides. Please update them as well.
* A section to discuss and/or illustrate the applications
# The figure in this section needs to be labeled.
# The figure needs to be resized and perhaps aligned to the center.
* A conclusion section:
# Please avoid vague language such as: “This makes”.
# Please avoid opinionated statements: “one of the best ways”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# This Wiki has very few references. A quick Google Scholar search may provide relevant references.

== [[Adam]] ==

* Author list
* An introduction of the topic
# Some grammatical errors here, mostly related to the need for commas in certain places (e.g., “Before Adam..”).
# Some minor errors with parts of speech throughout the section, need to revisit phrases such as “which has broader scope in future for”, etc.
# Try splitting up some of the longer sentences in this section, a couple are hard to read.
# Avoid definitive statements about Adam being the best or always better solver, as this is simply not true (the choice of the “best” optimizer is setting-dependent). Use language such as “Research has shown that Adam has demonstrated superior experimental performance over..” and then cite academic references to back this claim.
# What does adam stand for? Introduction is insufficient. Please expand.
* Theory, methodology, and/or algorithmic discussions
# Revise grammar here, noticing some missing commas and uncapitalized word after period.
# Rephrase “second one is to update the old position with the updated position”.
# Use LaTex code or equation editor to display all equations and variables in this section, and actual subscripts instead of “m_t”, etc.
# Avoid inserting inline citations after words like “According to..” or “This article..” as it is a bit informal. This could be rephrased or changed to something like “According to author,^[2] …” with author name inserted.
# Remove white space before the period in RMSP discussion.
# Please provide a pseudocode.
# Please use list the two methods here “Adam is a combination of two gradient descent methods which are explained below”
# Please expand the theory section significantly. Theoretical convergence properties should be discussed, even if briefly.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
* A section to discuss and/or illustrate the applications
# Same comment as before, consider replacing inline citations after words like “According to..”.
* A conclusion section
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Try to avoid references to blogs and use peer-reviewed academic references instead.
# Too few references.
# More references should be added. A simple Google Scholar search would give you many references.

== [[A-star algorithm|a* algorithm]] ==

* Author list: Remove cornell ID
* Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.
* An introduction of the topic:
# Weird spacing between paragraphs. Please fix this issue.
# In the titles, please change the font from bold to normal to have consistent formatting in the site.
# Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.
# There are no citations in the introduction. Please cite every source.
* Theory, methodology, and/or algorithmic discussions
# Please add the mathematical description of the algorithm.
# Reference style varies in sentences. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please fix grammatical and spelling errors as (“from current position to the goal”, “There are a lot of discussions”, etc). Also, many hyphens are missing as “non playable”.
# In algorithms, it is a standard to add high-level description (i.e. pseudocode or flowchart). Please incorporate it.
# Use LaTex code or equation editor to display all equations and variables in this section (e.g., “f(n)...”, “h(n)..”, etc.). This goes for other sections as well.
* At least one numerical example
# The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.
# Instead of writing things like “The above image..”, label each figure and use the figure number to refer to it in text.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# No references in the applications. Please cite every source
# Preferably, add at least an additional application.
* A conclusion section
# Conclusion should summarize descriptions. Please modify it to provide a summary.
# Please pay attention to the length and structure of sentences here and in the full page. First sentence is hard to read.
* References
# References seem to vary in format and are not linked correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Incorrect reference style. Please follow the example and use the template.

== [[Job shop scheduling|Job-Shop Scheduling Problem]] ==

* An introduction of the topic
# The current introduction to the jobshop scheduling problem has only two sentences in addition to the parameter description. Introduction typically contains information about the problem, its importance in the real-world, and some information about the solution techniques and their types to solve the problem. Please add some information that covers the above.
* Theory, methodology, and/or algorithmic discussions
# It is unclear whether the assumptions stated in this section are required to apply the following solution techniques. Please clarify the same. Also use complete sentences to state them.
# The branch and bounds method described in this section only discusses the solution technique for problems with one machines. However, branch and bound is a general technique that can be applied to any MILP problems with varying scales. Please update the “methods” section to be as general as possible.
# Since this Wiki focuses on jobshop scheduling, at least two methods are expected. Branch and bound is a general MILP technique, so, it is recommended to add a tailored technique that can only solve specific jobshop scheduling problems. Solving the numerical example with this technique is not necessary.
# Reference to the branch and bound technique described in this section is a “youtube” video. Please add references in literature that describe this method in detail. The method used in this video is highly tailored for a single machine application. This is also an incorrect way to cite a reference. Please keep this section as general as possible.
# Use LaTex code or equation editor to display all equations and variables in this section and all other sections as well.
# Check grammar in this section. For example, phrases like “are as follows” need to be followed by a colon and not a period.
# Consider rewriting the assumptions as a list in this section.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# The example used in this section is exactly the same as the one in the youtube video. Please use a modification of this example or choose another example/method to demonstrate the solution technique. Your team should ideally create a numerical example independently. If you take a numerical example directly from a particular source, you will need to get explicit permission from the textbook author in writing and share that written permission with the instructors.
# The figure in this section is not numbered when all others are. Relabel this figure for consistency and its number to refer to it in-text.
# A numerical example should be simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments).
* A section to discuss and/or illustrate the applications
# This section should only focus on real-world applications of the jobshop scheduling problem. But currently, this section includes additional information on solution techniques/complexity that is appropriate for the Introduction section. Please discuss the applications of the problem in this section.
* A conclusion section
# The meaning of “Operations applications” is unclear. Please explain or update if necessary.
# The current conclusion section does not properly summarize the problem. Please refer to other Wiki examples for an idea to update the section accordingly.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please reference media sources like reference 5 appropriately.
# A simple Google Scholar search would give you many "formal" references.

== [[Optimization in game theory]] ==

* Author list: remove cornell IDs.
* An introduction of the topic
# References are not linked. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
* Theory, methodology, and/or algorithmic discussions
# Why only a subsection on "Nash Equilibrium" is included in "Theory" section? Please re-format.
# Please edit references.
# Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm.
# Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.
* At least one numerical example
# Please organize the last part in a more readable format. Questions may be in bold and numbered, answers are more direct, etc.
# Remember to cite all images and tables.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# Very good, link the reference and cite all sources.
* A conclusion section
# Please add more summarizing especially from theory sentences and avoid long sentences.
* References
# Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Reference primary sources rather than Wikipedia
# Incorrect reference style. Please correct.

== [[Trust-region methods]] ==

* Author list:
# Remove cornell IDs. Author is also spelled incorrectly.
# Add the course section.
* An introduction of the topic
# References are not linked. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Use LaTex code or equation editor to display all equations and variables (e.g., “xk”, “f`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “we”. This goes for all other sections as well.
* Theory, methodology, and/or algorithmic discussions
# Organization of ideas in this section needs work.
# You have not defined explicitly why the Cauchy point is important to compute beyond a vague allusion to performance improvements, which is also wrong (it is useful because of its guarantees for convergence, not performance) It is also misspelled.
# Each approach should have accompanying explanation and motivation for why it is being discussed. It is not enough to outline the algorithm.
# Please make sure symbols are properly subscripted and superscripted (e.g. “pk” should be “p_k”
# Please format the algorithm in proper algorithmic pseudocode format.
# Little to no discussion on global convergence guarantees
# Please include discussion about the advantages and disadvantages of the algorithm
# Fix typo “couchy point”.
* At least one numerical example
# Any code functions (uminfunc) should have proper text formatting.
# The graph needs a better caption explaining how the axes are labeled and what data points are being shown.
# Please increase the quality of the figure. It is hard to see the red line.
# Add citation to “The Rosenbrock function is a non-convex function, introduced by Howard H. Rosenbrock in 1960, which is often used as a performance test problem for optimization algorithms.”
* A section to discuss and/or illustrate the applications
# The content in this section as it is currently does NOT describe applications, but rather different approaches within the trust region methodology. Please provide specific applications (e.g. TRPO in reinforcement learning).
* A conclusion section
# Please add more summary, future research directions for example is a good start.
* References
# Incorrect reference style.
# Please consider having the references as this Wiki template, <nowiki>https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization</nowiki>
# More references should be added. A simple Google Scholar search would give you many references.

*There are numerous misspellings, grammatical errors, and incorrect claims. Please fix these.

== [[Momentum]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Apart from an explanation on momentum, it is necessary to briefly point out the limitations of SGD and why momentum could help with these limitations. Please update it accordingly.
# Remove bold on “Momentum”.
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
* Theory, methodology, and/or algorithmic discussions
# Equation formatting is very poor and should be formalized.
# It is important to use technical language for this Wiki. Although a layman’s explanation is appreciated, it would be better to skip using words like “zig zagging”. Try to explain all concepts in a technical language with few simplifications but NOT vice versa.
# The definition of the update rule for SGD with momentum looks incorrect, specifically the first expression. Please fix it and also explain all the parameters used.
# Use LaTex code or equation editor to display all equations and variables (e.g., “W”, “V`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “you”.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step". Since writing all iterations is not feasible, at least present a few iterations for both cases.
# Please try to label the plots that explains what each line color means.
# Starting point for SGD with momentum is different in explanation and the table. Please fix the same.
* A section to discuss and/or illustrate the applications
# Please use correct terminology like “optimizing non-convex functions” and not “training non-convex models”.
# Adam, Adadelta, and RMSprop are variants of SGD that already use momentum. Please double check the writing and update if necessary.
* A conclusion section
# Please refrain from using words like “zig zag” effects.
* References
# Almost all references used are URLs. Please try to add journal/conference articles or books for references, instead of directly citing the URLs. Please check the list below and run a quick Google (Scholar) search to identify relevant literature.

== [[Stochastic dynamic programming|Stochastic Dynamic programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Discussion on applications should be moved to a separate section.
* Theory, methodology, and/or algorithmic discussions
# Remove the grey box background of equations.
* At least one numerical example
* A section to discuss and/or illustrate the applications
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Outer-approximation (OA)|Outer-approximation]] ==

* An introduction of the topic
# See formatting guideline below
# Avoid opinionated statements such as “MINLP problems are usually the hardest to solve”.
# Rearrange the text such that the MINLP formulation is in the theory section and keep the introduction in words only.
* Theory, methodology, and/or algorithmic discussions
# Consider left aligning equations and optimization problem formulations by the “=”. See [[Stochastic programming|https://optimization.cbe.cornell.edu/index.php?title=Stochastic_programming]] for an example
# The sentence “The Outer-Approximation (OA) algorithm was first proposed by Duran and and Grossmann in 1986 to solve MINLP problems.” needs a reference.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# “Minimize” and “subject to” should be “min” and “s.t.” in MathType
* A section to discuss and/or illustrate the applications
# Does not explicitly point out why OA is applicable (and/or preferred) in these applications, rather than other MINLP approaches (show that the problem formulations are amenable to a solution approach through OA)
# The sentence “... an active research area and there exists a vast number of applications in fields such as engineering, computational chemistry, and finance.” needs references.
# Posting GAMS code on the page is generally inappropriate and discouraged. Please check with the TAs or me if you have a strong desire to post GAMS codes on the Wiki page. A typical textbook should not be limited to a specific software package. If the GAMS code must be posted, please also post ALL other software implementation versions, such as Pyomo and JuliaOPT, among others.
# Consider reformatting to make steps more readable. Inserting spaces and breaking down steps would help.
* A conclusion section
# Too short. Consider discussion on future research direction and discussion on uncertainty
# Please review abbreviations throughout the page. Why is MINLP redefined here? “Outer-Approximation is a well known efficient approach for solving convex mixed-integer nonlinear programs (MINLP)”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove "Template:Reflist"

== [[Unit commitment problem]] ==

* Author list
* An introduction of the topic
# Please expand the introduction and avoid discussions of examples or specific applications in this section.
# The sentence “Nonlinear, Non-convex programming optimization problem.” doesn’t make sense by itself and Non-convex shouldn’t be capitalized.
* Theory, methodology, and/or algorithmic discussions
# Figure/image format should be revised to better display the content.
# Uppercase characters are used randomly (e.g., “non-convex transmission Constraints”) . Please follow correct language conventions for sentence structure.
# Avoid inserting inline citations after words like “written in matrix form as equation [3]..” or “presented in [3]...” as it is a bit informal when you don’t explicitly name the subject. Also these two sentences are grammatically incorrect and appear to be missing an ending period and comma, respectively.
# Don’t say “written in matrix form as equation..” and just cite the reference, actually write out the equation.
# Properly label the figure in this section with a figure number and improve visibility by making it larger.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Label the figures in this section properly with figure numbers.
# Fix typo “while minimize” to “while minimizing”.
# Avoid pronouns such as “we”.
# Use the equation editor when typing equations.
# A numerical example is simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments). There is an Application section where you discuss the applications.
# The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).
* A section to discuss and/or illustrate the applications:
# I suggest changing the order of the subtitles here. For example, Single-Period Unit Commitment.
* A conclusion section
* References

== [[Frank-Wolfe]] ==

* Author list:
* An introduction of the topic
# I suggest highlighting disadvantages along with advantages.
* Theory, methodology, and/or algorithmic discussions
# “[n x 1] matrix” please use the equation editor to express mathematical descriptions and symbols (p,b, etc)
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please show at least a few iterations. Even for smaller examples if needed. Report the final solution.
# Please use the LaTex code or equation editor for min and include s.t., etc.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps. For your example, please explicitly state that the derivative is taken etc.
* A section to discuss and/or illustrate the applications:
* A conclusion section
# Same as the introduction. Pros and cons should be evaluated together!
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Line search methods|Line Search Method]] ==

* Author list
* An introduction of the topic
# Expand the introduction and avoid discussion on some of the specific steps in the solution process.
# Provide references here.
* Theory, methodology, and/or algorithmic discussions
# The phrase “are as follows” in the steepest descent method discussion needs to be followed by a colon.
# Rephrase “has a nice convergence theory” and cite a reference for this claim.
# Avoid pronouns such as “we”.
# Add citation after “.. proposed by Phillip Wolfe in 1969.”
# Figure 1 is between two sections. Please fix this issue.
* At least one numerical example:
# Add some space between iterations or subsection break
* A section to discuss and/or illustrate the applications:
# Too few references in this section.
# Last paragraph makes some claims without references.
* A conclusion section
* References
# References should be properly formatted. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Piecewise linear approximation|Piecewise Linear Approximation]]==

* Author list
* An introduction of the topic
# The content of this section is good, but there are some issues with sentence clarity and some other grammatical errors. Please revisit this section and make changes accordingly.
* Theory, methodology, and/or algorithmic discussions
# Fix typo “to force the x’ values become associated with”.
* At least one numerical example
* A section to discuss and/or illustrate the applications
# Please aim for a maximum average sentence length of ~25 words. Some of these longer sentences are hard to read.
* A conclusion section
# Expand the conclusion section to be longer than one sentence. The conclusion section to include a brief summary of what was discussed above, an emphasis on it’s significance, and a brief discussion of future extensions and research direction if applicable.
* References
# Include hyperlinks to sources when possible.

== [[Mathematical programming with equilibrium constraints|Mathematical Programming with Equilibrium constraints]] ==

* An introduction of the topic
# This section includes several terms like variational inequalities, constraint qualifications that were not discussed in the class. Please add a sentence to explain them before using them.
* Theory, methodology, and/or algorithmic discussions
# The meaning of parameter vector x is unclear. Please add more information or update if necessary.
# Equations and symbols in the PIPA subsection are not formatted correctly. Please use the same formatting for all equations, so they read as mathematical equations and not text. This goes for all other sections as well.
# Use equations instead of images to represent math programs and equations in the Implicit Descent and SQP subsection.
# Apart from the steps for each solution technique, please also add a few sentences that describe each method.
* At least one numerical example
# Please define the terms like NCP, MP before abbreviating them. Also try not to unnecessarily abbreviate simple terms.
# Equations should be typed by LaTex. Images for equations are unacceptable.
# GAMS code is strongly discouraged. Please solve the problem "step-by-step".
# The selected numerical example is fine but is directly solved with the MPEC solver in GAMS. Try to solve it manually like the homework/in-class problems step by step using the steps described in the previous section by choosing any of the methods.
# Avoid using figures in the equations (subject to etc)
* A section to discuss and/or illustrate the applications
# Add references to “power management, highway pricing, chemical process engineering, and traffic planning.”
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# This Wiki contains very few references. Please check the list below and run a quick Google (Scholar) search to identify relevant literature.

== [[Wing shape optimization|Wing shape Optimization]] ==

* Author list: Remove cornell ID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC. Any formatting issue will incur a penalty in the grading.
* An introduction of the topic
# The introduction is missing several references (e.g., “software packages like computational fluid dynamics..”, sentences containing things that aren’t common knowledge, performance claims, etc.)
# Avoid discussion involving finer details of subject methods in this section.
# In the titles, please change the font from bold to normal to have consistent formatting in the site. Same applies to box of content!
* Theory, methodology, and/or algorithmic discussions
# Properly cite the CFD package, don’t just include a link.
# Properly label the figure with a figure number.
# Consider removing white space between isolated sentences to improve readability.
* At least one numerical example
# If you’ve already defined an abbreviation (CFD), there is no need to define it again. Just use the abbreviation.
# Avoid pronouns such as “we” or “they”.
# Phrases like “under the following” need to be followed by a colon.
# Properly label the figure with a figure number and consider making them larger to improve visibility. Call the reader's attention to the figures in text by referencing the figure number.
# “As seen in the video below” is stated yet there are only images present and it may be initially unclear to the reader which figure is being referenced here.
# Avoid inserting inline citations like “[4] introduces an..” as it is a bit informal when you don’t explicitly name the subject.
# Don’t just cite the reference when discussing the problem formulation, explicitly write the model formulation and solution process using LaTex or equation visual editor.
# Your team should ideally create a numerical example independently. If you take a numerical example directly from a textbook, etc., you will need to get explicit permission from the author in writing and share that written permission with me.
# A numerical example is simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments). There is an Application section where you discuss the applications.
# The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).
* A section to discuss and/or illustrate the applications
# Some characters are randomly capitalized in this section.
* A conclusion section
# These variables should be defined before the conclusion section, they are out of place here. Also, please use normal text when explaining variables except for the variable symbol.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Interior-point method for NLP|Interior point method for NLP]] ==

* An introduction of the topic:
* Theory, methodology, and/or algorithmic discussions
# Primal-Dual formulation and comparison to the Barrier Method is not discussed.
# Include brief discussion about big O convergence rates.
# Need discussion about the concept of “central path” and the notion of self concordance
# Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
# Graphs and images are incorrectly formatted to the page. Consider proper alignment with respect to the text body.
# Use explicitly typed Latex equations instead of images to represent math programs and equations.
# Fix typo “optimisation”.
# Use LaTex code or equation editor to display all equations and variables (e.g., “xi ”, “μ”, etc.).
* At least one numerical example:
# There are formatting issues with figures 2,3. Please make sure to embed them within their respective sections.
* A section to discuss and/or illustrate the applications
* A conclusion section
# Minor character code typos in the conclusion.
# Also, please add more discussion in this section. Future research directions is a good start.
# There is a box "􏰐"
* References

== [[AdaGrad|Adagrad]] ==

* An introduction of the topic:
* Theory, methodology, and/or algorithmic discussions
# Include discussion on its variants (most important is AdaDelta).
# Include disadvantages of Adagrad, since this provides motivation for the discussion on the variants and improvements of Adagrad
# Include comparisons to other popular optimizers (particularly important is comparisons to regular SGD and Adam)
# Different convergence rates are possible depending on the setting where Adagrad is used, but this is not mentioned on the page currently. As such the regret bound section should be more thoroughly explained.
# Algorithm image is blurry. Either increase the fidelity or write the pseudocode directly in the wiki editor.
* At least one numerical example
# In the first sentence, “..take the following numerical example” should be followed by a colon.
# Fix typo “trayectory”.
* A section to discuss and/or illustrate the applications
# This section is too short; include specific applications in which input features are sparse and Adagrad excels.
# Add reference to the claim “Mainly, it is a good choice for deep learning models with sparse input features”.
* A conclusion section
* References

# Too few references overall, you should aggregate information from multiple sources (even if the base algorithm itself comes from a singular paper)

== [[McCormick envelopes|McCormick Envelopes]] ==

* Author list: OK but I suggest removing NetID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# First sentence is hard to read. Please consider keeping sentences below 25-30 words.
# No references provided. Please cite all sources.
# Figure 1 is provided in the middle between two sections. Please include in the introduction section.
* Theory, methodology, and/or algorithmic discussions
# References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# When using mathematical expressions and symbols, please use the equation editor. (e.g., x*y, exy + y, sin (x+y) - x2)
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# The solution technique should be clearly presented, and solved "step-by-step".
# Solving the numerical example by GAMS is inappropriate. Please provide detailed step-by-step calculation results.
* A section to discuss and/or illustrate the applications
# Having a list is not enough. Please explain at least three applications in a few sentences each.
# This section should be at least a paragraph to discuss relevant applications. Each application should be explicitly linked to the page topic. A few keywords do not meet the requirement at all.
* A conclusion section:
* References
# References are not expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please follow the standard reference style - the current format is incorrect.

== [[Branch and bound (BB) for MINLP|Branch and Bound for MINLP]] ==

* Author list:
** Remove NetIDS
** Please remove abbreviations from the title (i.e. BB).
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# Please cite sources appropriately: References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Introduction is very short for a well-recognized topic. Please expand significantly. You may refer to the Wiki examples to get an idea on writing the Introduction to a topic.
# An illustration might be useful here.
* Theory, methodology, and/or algorithmic discussions
# The algorithm described here considers only binary integer variables. However, MINLP problems may include non-binary integer variables too. Please update the method or provide a short description of the assumptions that the MINLP problem needs to satisfy in order for the presented technique to be applicable.
# Use linked citations please as the Wiki template above.
# Please provide steps in a more organized way. Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
# Step 2 is missing yet it is referenced in the text multiple times. Please address this in addition to the above comment.
# An illustration might be useful here as well.
# Please explain what a Gomory Cut is. If the topic is available on optimization.cb.cornell.edu, you can link it.
# The current equations seem to be simple text written in Italics. All mathematical symbols and equations should be formatted via LaTex.
# Please format the math programs with equations and notations using formulations in lecture notes as templates.
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# Please show a step-by-step solution in the example. The solution is incomplete. The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).
# Please use the equation editor for equations or mathematical symbols. - All mathematical symbols and equations should be formatted via LaTex - this is a learning objective of the Wiki assignment. You can find some useful links on converting your equations/symbols into LaTex code here: (<nowiki>https://optimization.cbe.cornell.edu/index.php?title=Help:Contents</nowiki>). Again, any formatting issue will incur a "compound" penalty in the grading.
# This example does not follow the MINLP structure discussed in the above section since binary variables are missing. Branch and bound may not be appropriate for such problems. Please provide an appropriate numerical example and solve it according to the above comments.
# Make sure your example is not taken from a book as that is strictly disallowed.
* A section to discuss and/or illustrate the applications
# This section is not well-formatted. Please provide 3 applications and explain each in a few sentences and how BB for MINLP could be used. Also, please eliminate having multiple sections (Application, Mathematical problem, industrial application). All these could be merged together.
# This section should be at least a paragraph to discuss relevant applications. Each application should be explicitly linked to the page topic. A few keywords do not meet the requirement at all.
* A conclusion section:
# The sentence is hard to understand "a scheme that grows exponentially because" please use a simple language. Is it also theoretically correct? It is also not mentioned and explained earlier. Thus, please avoid introducing new concepts or terms at the end.
# Please use summarizing sentences to describe earlier sections instead of introducing new concepts/discussion.
* References
# Too few references overall, you should aggregate information from multiple sources. A quick Google scholar search could provide relevant references.
# References are not expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please follow the standard reference style - the current format is incorrect.

2021 Cornell Optimization Open Textbook Feedback

2021-12-06T03:06:59Z

Asa273: /* Branch and Bound for MINLP */

== [[Lagrangean duality|Lagrangian duality]] ==
* Author list, sections and TOC
# Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.
# Remove cornell ID from Author list
* An introduction of the topic
# This section includes sentences on constructing the dual problem and is referred to as Lagrangian relaxation (LR). This is incorrect, please fix the definition of LR.
# Definitions of LR and its relation to duality should be double checked and re-written.
# Only one reference is present in this section. Please add more relevant references by expanding this section.
# Consider merging the “introduction” and “history” sections.
# In the titles, please change the font from bold to normal to have consistent formatting in the site.
* Theory, methodology, and/or algorithmic discussions
# The Lagrangian variables associated with equality constraints h(x) are unbounded but the Lagrangian dual problem states them as non-negative. Please fix the same.
# Also to construct a dual, we do not change minimization to maximization directly. We observed such things in the examples in lecture notes due to simplification. The lagrangian dual problem would be minimize (,).
# Adding to the previous point, the Lagrangian is a lower bound on the original objective; the solution to the primal and dual or only equivalent if the duality gap is 0. You reference this in one section, but this is after your statement “Hence, solving the dual problem, which is a function of the Lagrangian multipliers (𝜆*) yields the same solution as the primal problem, which is a function of the original variables (x*). “. Please clarify the specific conditions that must hold for the solution of the dual to be equal to the primal’s.
# You refer to the “Complementary Slackness Theorem”, but don’t actually write the mathematical representation of complementary slackness. Please fix this. Also consider including the derivation of the complementary slackness condition, as it is both easy and short. Boyd is a good reference for this.
# Last step of the “process” subsection also needs updating according to the previous comments.
# The inline notations should also be typed using LaTex.
# Please use the LaTex code or equation editor for min, s.t., etc.
* At least one numerical example
# Only one dual variable is associated with each constraint. The numerical example uses two for the first and second constraint which is unnecessary. Please update it accordingly for both constraints. This particular example will only have two dual variables instead of the five dual variables used currently.
# All consecutive steps need to be updated since the dual variables would be updated.
# After substitution the nonlinear function should be further simplified. The current expression reads like a highly nonlinear function but can be easily simplified.
# Similar to the comments in the methodology section, inverting minimize to maximize is incorrect. Please update the dual objective function and domain of dual variables accordingly.
# Please use the LaTex code or equation editor for min, s.t., etc.
* A section to discuss and/or illustrate the applications
# Bullet points could be used to state the last four real-world examples that explain the physical meaning of the primal and dual problems.
# Add references for the last set of applications.
* A conclusion section
# This section contains a few typos. Please fix the same.
* References
# Some citations' hyperlinks are displaying.

== [[Disjunctive inequalities|Disjunctive Inequalities]] ==

* Author list
# Missing course section and semester
# Remove cornell ID
* An introduction of the topic
# No citations are present in this section.
# “mixed-integer programming (MIP)” should be used instead of “multiple integer programming (MIP)”. Please fix this error.
* Theory, methodology, and/or algorithmic discussions
# The abbreviation MILP is not previously defined. Please fix this issue.
# You consistently use the negative sign instead of the NOT operator for y (-y instead of ¬y).
# Some inconsistencies with the spacing of variables, constraints, etc., under the “General” section that need to be fixed.
# Typo in “This is shown below by M1, M2, y1, and y1:” where y1 needs to be changed to y2. Why use two different Big-M variables here? Elsewhere in the Wiki you only use one so this could lead to confusion with a general audience. Also if this was taken from the lecture notes then it needs to be cited.
* At least one numerical example
# Please reformulate and solve a complete numerical example rather than just reformulating a general example. Demonstrate the use of Big-M and Convex Hull formulation in an optimization problem that provides details such as individual steps in the problem solving process and final results. The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results.
# Add space between vee (V) operator and brackets in first line of Latex
# Please format variables correctly, for example, use <math>x_1</math> instead of x1.
* A section to discuss and/or illustrate the applications
# Please format the equations appropriately either by using latex code or the visual editor. These images are NOT acceptable!
* A conclusion section
# There is no conclusion presented in this section at all.
* References
# The included references have NOT been used anywhere in the Wiki. Add references for sentences that are not common knowledge and please link them appropriately with the text in Wiki. If the figures used here were not original works, you must also cite them.
# There are many papers on this topic. A simple Google (Scholar) search could provide you with sufficient references to cite.
# Many important references of this topic are missing.
# Please consider linking the references as demonstrated in the Wiki tutorial on Canvas and in this template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

==[[Stochastic programming|Stochastic Programming]] ==

* Author list: Remove cornell IDs
* An introduction of the topic
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
# This section only includes two sentences on Stochastic programming (SP), while the rest gives examples of uncertainty. Please discuss the need for SP in the presence of uncertainty. Also, discussion on robust optimization and its limitations should be removed since it is out of place.
* Theory, methodology, and/or algorithmic discussions
# Please avoid direct inline linkbacks to Wikipedia.
# The symbol “xi” in the methodology subsection should be explained.
* At least one numerical example
# Copying a numerical example "entirely" from a textbook is inappropriate. Your team should come up with a "numerical" case.
# No specific application context is needed for a numerical example.
# The inline notations (`x1`, `s1`) should also be typed using LaTex.
# Label all tables with a table number for better readability.
# Properly format the solution table with the label attached rather than the following sentence. The solution table looks different from the others, please fix this for consistency.
* A section to discuss and/or illustrate the applications;
# I suggest eliminating citing the last name of the first author (i.e. Zhou et al.)
* A conclusion section
* References
# URLs of some citations are not properly formatted (not showing the hyperlinks).

== [[Exponential transformation|Exponential Transformation]] ==

* Author list
# Missing course section
# Remove cornell ID
* An introduction of the topic
# Please expand the introduction.
# Please aim for a maximum average sentence length of ~25 words. Last sentence with 51 words is hard to read.
# Second Sentence: please change the word “they” as it could make the meaning ambiguous
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
# If you use abbreviations, please introduce them (e.g. NLP,MINLP)
* Theory, methodology, and/or algorithmic discussions
# Please explain the transformation in words along with equations
# Terms like posynomial should be described in detail.
# Please move the numerical example to the section below
# The “(eq 1)” is not needed here.
# Please expand this section.
* At least one numerical example
# In the third equation of the numerical example, it is confusing to have coefficients after numbers. Some readers may read it as an exponent.
# Last equation in this section after “further linearization” is incorrect. This equation cannot be further linearized, please fix this.
# Please explain the steps in the numerical examples in detail. The step-by-step solution should be provided.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# Missing part of text: “Proof of convexity of with positive definite test of Hessian…”
# Applications are not numerical examples. Please refer to this link for example of applications: [[Duality|https://optimization.cbe.cornell.edu/index.php?title=Duality]]
# Citation 7 is missing in current applications
# The section current applications is redundant
# Please use the LaTex code or equation editor for min, s.t., etc.
# Under current applications, do not just use a hyperlink to describe an application. Actually describe it. And properly inline citation style should be used instead of the hyperlink.
# The convexification application of MINLP can be further simplified for binary variables. Please refer to the lecture slides for more information.
* A conclusion section
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
* References
# Please consider linking the references by using this as Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Citation 7 is missing in current applications

== [[Sparse Reconstruction with Compressed Sensing|Sparse reconstruction with Compressed Sensing]] ==
This Wiki needs a significant rewrite. Please go through the comments for details.

* An introduction of the topic
# The introduction section should include information about the problem and its implications presented briefly. Please use full sentences to write this Wiki. You may use tools like Grammarly to check sentence formation and grammar.
# This section includes several typos like “sub modual”. Please fix them throughout the wiki and delete them if not required.
# Many abbreviations are used before previously defining them. Please define these abbreviations before using them in the text.
# This section is incomprehensible in its current form. Please rewrite with proper comprehension.
# Equations and math symbols need proper reformatting. The current version reads like text (along with equations) copy-pasted from a specific source. All mathematical symbols and equations should be formatted via LaTex - this is a learning objective of the Wiki assignment. You can find some useful links on converting your equations/symbols into LaTex code here: (https://optimization.cbe.cornell.edu/index.php?title=Help:Contents).
# Try to place the figure at the top of the Wiki between the main text.
# Avoid pronouns such as “we”.
# I suggest the use of more formal abstract illustrations.
* Theory, methodology, and/or algorithmic discussions
# Equations and symbols need proper reformatting.
# Lemmas and theorems are not expected for this Wiki. Sparse reconstruction is a straightforward concept but is unnecessarily complicated here. Please refer to other Wiki examples to get an idea of what the Wiki should convey.
# All equations need to be better formatted.

* At least one numerical example
# Numerical example is missing.
# Every iteration should be clearly presented, and solved "step-by-step".
* A section to discuss and/or illustrate the applications
# Having a list is not enough. Please explain at least three applications in a few sentences each.
* A conclusion section
# Conclusion section is missing.
* References
# The current reference list is not correctly formatted. References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Portfolio optimization|Portfolio Optimization]] ==

* Author list
# Remove cornell id
* An introduction of the topic
# The introductory sentence should be rephrased. The action of minimizing the risks does not inherently maximize the gains, rather PO aims to maximize gains whilst minimizing risks.
# Amount of whitespace can be reduced by changing the orientation of Figure 1 and the sentences in this section.
# Define terms such as risk, return, portfolio, etc., when you introduce them. Assume that the reader may not know much about finance. This goes for all other sections as well.
* Theory, methodology, and/or algorithmic discussions
# A brief mention of modern portfolio theory (i.e.. Markowitz) would be appropriate in this section.
# Several grammatical errors here involving sentence structure and clarity. Some questionable semantics (e.g., “The portfolio optimization mainly assumes two directions.”) and syntax (phrases such as “.. is as follows” should be followed by a colon). Misuse of commas and missing commas in this section. Two sentences introducing E(rp) and w should be combined into one.
# Use LaTex to distinguish variables written within a sentence, such as m and n.
# Rephrase “Cut the relevant information and conditions in the portfolio optimization, as well as the final requirements into the relevant variables, constraints and linear functions of the linear programming problem.”
# An explanation of a few common constraints would be helpful, rather than just including a table.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Solving the numerical example by GAMS is inappropriate. Please provide detailed step-by-step calculation results.
# All tables need to be labeled.
# Include figure number in label for consistency.
# Fix misspelling “dolling decision variables”.
# Use LaTex for all variables, equations, and constraints here.
# Example 2 table is hard to read, so making it bigger would help.
# Remove the “Using excel as the solver” part from the sentence before the solution discussion.
# Some grammatical errors here (phrases such as “.. is as follows” should be followed by a colon).
* A section to discuss and/or illustrate the applications
# Rephrase “Portfolio optimization can be used to screen investment projects that meet investors, rationally allocate investment amounts, etc.”
# Not sure “relevant” is the correct word choice here.
# You need more specific examples with the utility of portfolio optimization, this section is quite general as is. Some more detail and focus on real-world applications in the financial industry that relate to retirement planning, financial security, economic stability, etc., would be helpful.
* A conclusion section
# Need some commas here.
# The sentence “Linear programming has been around since the 1940’s and has such a wide base of applications” is not necessary.
* References
# Please consider linking the references as demonstrated in the Wiki tutorial on Canvas and in this template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove white space between end of sentences and reference numbers.

== [[Chance-constraint method|Chance constraint method]] ==

* Author list:
* An introduction of the topic
# Please consider correcting a few grammatical errors: “pre-planned for”, “god”, “certain levels of feasibility is guaranteed in what are”, and “Performance of a system”
# In “Chance-constraint”, it is capitalized randomly throughout the introduction. Please correct.
# Please use technical language to briefly introduce chance-constrained programming. Words like “acts of god”, “cost of doing business” are not appropriate for a technical Wiki.
* Theory, methodology, and/or algorithmic discussions
# Please add a citation to the first sentence.
# Xi is an uncertainty/randomness variable. It is better to use clear language.
# Please use the mathematical editor for adding explanations in the text. Using “ x is a decision variable” is hard to read. Same for f(x) and others.
# Theory is insufficient. Please expand and explain different approaches.
# Please add pros and cons explicitly as a list.
# Explain the physical meaning for examples of chance constraints along with all the notations used.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please remove this example as it is directly from this book. The example should be purely numerical without any background.
# Please use the equation editor for min, st., etc.
# Please use the mathematical editor for adding explanations in the text. Using “ x is a decision variable” is hard to read. Same for f(x) and others.
# Please change the table format so as not to confuse the reader.
# Multiple instances of [Chart to be added] are missing.
# Example is incomplete.
# Avoid pronouns such as “we”.
* A section to discuss and/or illustrate the applications
# Please connect several grammatical and spelling errors: “real life application”, Energy creation, particularly in renewable sources, have high variabilities”, and others
# “Zhao, Xue, Cao, and Zhang”. No need to list all authors within the article. Provide a reference is sufficient. If authors must be mentioned, (Zhao et al.) should be ok.
* A conclusion section
# Uniqueness and universality earlier are not clear to me. If they are not discussed earlier in the application, it would be better not to introduce new discussions in the conclusion.
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
* References
# References seem to vary in format. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Bayesian Optimization]] ==
* Section titles should not be "bold". Please double check using source editor on the section titles.
* Contents: The section titles should NOT be in bold to avoid strange format in TOC. Any formatting issue will incur a penalty in the grading.
* Author list: Remove cornell ID, Please check names
* Introduction
# The introduction is too general and not substantial enough. For example, simply saying BayesOpt is useful when the objective function is unknown obscures exactly HOW it is useful (namely, computational efficiency in applications where ground truth sampling is expensive). Discussion on applications should be moved to a separate section.
# Machine learning rarely includes black-box functions to be optimized. Bayesian optimization is almost never used for optimizing ML loss functions but can instead be used for hyperparameter optimization. Please update such claims in this section.
* Theory, methodology, and/or algorithmic discussions
# Captions need reformatting.
# Consider italicizing keywords rather than bolding.
# Please add a citation to the first sentence.
# Discussion on acquisition functions should include comparisons, tradeoffs, and reasons to use one over the other. Should also note that expected improvement is the most widely used in practice, and explain.
# Avoid pronouns such as “we”.
# Please write equations in the Wiki instead of attaching images for equations.
# Acquisition function figure could be made larger and clearer to improve readability.
* At least one numerical example
# Any references to functions or methods in code ‘e.g. fmin’ should be properly formatted as code-stylized text.
# Please use the equation editor for min, st., etc.
# Avoid including a figure of the code for this example and explicitly describe the steps to the modeling and solution process instead.
# Avoid pronouns such as “our” and “we”.
* A section to discuss and/or illustrate the applications
* A conclusion section
# Please do not use brackets to enclose lists.
# Some claims here should be supported by references. Please cite each source after its sentence.
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Try to avoid references to “pop” machine learning blogs where anyone can be an author. (e.g. towardsdatascience)
# All references are URLs. Please cite publications and literature.
# A simple Google Scholar search would give you many references.

Notes on grammar: Needs some work. Several instances where colons are inappropriately inserted mid sentence or in subheadings. Explanations are not terse. Several instances of switching between personal and impersonal style of writing, which is distracting.

== [[Conjugate gradient methods]] ==

* Author list: Remove cornell ID
* Introduction
# All inline notations (e.g., `x`, `A`) should be typed using LaTex.
* Theory, methodology, and/or algorithmic discussions
# All equations need to be better formatted.
# Is Gauss-Newton no longer referenced?
# Theorems listed in the first section should be accompanied with high level explanation, not just a list of the theorems themselves. The page should read like an article, with proper flow.
# Please indent equation blocks.
# Please properly format pseudocode.
* At least one numerical example
# Steps should be accompanied with explanation, or reference to the corresponding step in the pseudocode.
# Please properly format in a more organized manner, aligning equations appropriately and demarcating steps appropriately.
* A section to discuss and/or illustrate the applications
# Consider including 2 additional examples of applications
* A conclusion section
# Consider adding future research directions
* References
# Reference primary sources rather than Wikipedia
# Too few references.
# More references should be added. A simple Google Scholar search would give you many references.

== [[Geometric programming|Geometric Programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Examples of applications in this section use the same reference. Please cite their individual sources.
* Theory, methodology, and/or algorithmic discussions
# The symbol denoting the domain in the definition of a monomial is unclear. Please clarify it or fix this if it is incorrect.
# Definition of posynomial refers to section 2.1 which is missing from the Wiki (sections are not numbered in the main text).
# In the generalized posynomial subsection, bullet points do not tell us why h(x) is posynomial. Either provide reasons or simply state that h(x) is posynomial. Also explain why h3 is a generalized posynomial.
# Additional theory on the feasibility analysis could be provided in this section.
* At least one numerical example
# In the transformation example, the last two constraints could also be simplified by applying a natural logarithm on both sides. Please update them as well.
* A section to discuss and/or illustrate the applications
# The figure in this section needs to be labeled.
# The figure needs to be resized and perhaps aligned to the center.
* A conclusion section:
# Please avoid vague language such as: “This makes”.
# Please avoid opinionated statements: “one of the best ways”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# This Wiki has very few references. A quick Google Scholar search may provide relevant references.

== [[Adam]] ==

* Author list
* An introduction of the topic
# Some grammatical errors here, mostly related to the need for commas in certain places (e.g., “Before Adam..”).
# Some minor errors with parts of speech throughout the section, need to revisit phrases such as “which has broader scope in future for”, etc.
# Try splitting up some of the longer sentences in this section, a couple are hard to read.
# Avoid definitive statements about Adam being the best or always better solver, as this is simply not true (the choice of the “best” optimizer is setting-dependent). Use language such as “Research has shown that Adam has demonstrated superior experimental performance over..” and then cite academic references to back this claim.
# What does adam stand for? Introduction is insufficient. Please expand.
* Theory, methodology, and/or algorithmic discussions
# Revise grammar here, noticing some missing commas and uncapitalized word after period.
# Rephrase “second one is to update the old position with the updated position”.
# Use LaTex code or equation editor to display all equations and variables in this section, and actual subscripts instead of “m_t”, etc.
# Avoid inserting inline citations after words like “According to..” or “This article..” as it is a bit informal. This could be rephrased or changed to something like “According to author,^[2] …” with author name inserted.
# Remove white space before the period in RMSP discussion.
# Please provide a pseudocode.
# Please use list the two methods here “Adam is a combination of two gradient descent methods which are explained below”
# Please expand the theory section significantly. Theoretical convergence properties should be discussed, even if briefly.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
* A section to discuss and/or illustrate the applications
# Same comment as before, consider replacing inline citations after words like “According to..”.
* A conclusion section
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Try to avoid references to blogs and use peer-reviewed academic references instead.
# Too few references.
# More references should be added. A simple Google Scholar search would give you many references.

== [[A-star algorithm|a* algorithm]] ==

* Author list: Remove cornell ID
* Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.
* An introduction of the topic:
# Weird spacing between paragraphs. Please fix this issue.
# In the titles, please change the font from bold to normal to have consistent formatting in the site.
# Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.
# There are no citations in the introduction. Please cite every source.
* Theory, methodology, and/or algorithmic discussions
# Please add the mathematical description of the algorithm.
# Reference style varies in sentences. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please fix grammatical and spelling errors as (“from current position to the goal”, “There are a lot of discussions”, etc). Also, many hyphens are missing as “non playable”.
# In algorithms, it is a standard to add high-level description (i.e. pseudocode or flowchart). Please incorporate it.
# Use LaTex code or equation editor to display all equations and variables in this section (e.g., “f(n)...”, “h(n)..”, etc.). This goes for other sections as well.
* At least one numerical example
# The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.
# Instead of writing things like “The above image..”, label each figure and use the figure number to refer to it in text.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# No references in the applications. Please cite every source
# Preferably, add at least an additional application.
* A conclusion section
# Conclusion should summarize descriptions. Please modify it to provide a summary.
# Please pay attention to the length and structure of sentences here and in the full page. First sentence is hard to read.
* References
# References seem to vary in format and are not linked correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Incorrect reference style. Please follow the example and use the template.

== [[Job shop scheduling|Job-Shop Scheduling Problem]] ==

* An introduction of the topic
# The current introduction to the jobshop scheduling problem has only two sentences in addition to the parameter description. Introduction typically contains information about the problem, its importance in the real-world, and some information about the solution techniques and their types to solve the problem. Please add some information that covers the above.
* Theory, methodology, and/or algorithmic discussions
# It is unclear whether the assumptions stated in this section are required to apply the following solution techniques. Please clarify the same. Also use complete sentences to state them.
# The branch and bounds method described in this section only discusses the solution technique for problems with one machines. However, branch and bound is a general technique that can be applied to any MILP problems with varying scales. Please update the “methods” section to be as general as possible.
# Since this Wiki focuses on jobshop scheduling, at least two methods are expected. Branch and bound is a general MILP technique, so, it is recommended to add a tailored technique that can only solve specific jobshop scheduling problems. Solving the numerical example with this technique is not necessary.
# Reference to the branch and bound technique described in this section is a “youtube” video. Please add references in literature that describe this method in detail. The method used in this video is highly tailored for a single machine application. This is also an incorrect way to cite a reference. Please keep this section as general as possible.
# Use LaTex code or equation editor to display all equations and variables in this section and all other sections as well.
# Check grammar in this section. For example, phrases like “are as follows” need to be followed by a colon and not a period.
# Consider rewriting the assumptions as a list in this section.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# The example used in this section is exactly the same as the one in the youtube video. Please use a modification of this example or choose another example/method to demonstrate the solution technique. Your team should ideally create a numerical example independently. If you take a numerical example directly from a particular source, you will need to get explicit permission from the textbook author in writing and share that written permission with the instructors.
# The figure in this section is not numbered when all others are. Relabel this figure for consistency and its number to refer to it in-text.
# A numerical example should be simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments).
* A section to discuss and/or illustrate the applications
# This section should only focus on real-world applications of the jobshop scheduling problem. But currently, this section includes additional information on solution techniques/complexity that is appropriate for the Introduction section. Please discuss the applications of the problem in this section.
* A conclusion section
# The meaning of “Operations applications” is unclear. Please explain or update if necessary.
# The current conclusion section does not properly summarize the problem. Please refer to other Wiki examples for an idea to update the section accordingly.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please reference media sources like reference 5 appropriately.
# A simple Google Scholar search would give you many "formal" references.

== [[Optimization in game theory]] ==

* Author list: remove cornell IDs.
* An introduction of the topic
# References are not linked. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
* Theory, methodology, and/or algorithmic discussions
# Why only a subsection on "Nash Equilibrium" is included in "Theory" section? Please re-format.
# Please edit references.
# Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm.
# Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.
* At least one numerical example
# Please organize the last part in a more readable format. Questions may be in bold and numbered, answers are more direct, etc.
# Remember to cite all images and tables.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# Very good, link the reference and cite all sources.
* A conclusion section
# Please add more summarizing especially from theory sentences and avoid long sentences.
* References
# Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Reference primary sources rather than Wikipedia
# Incorrect reference style. Please correct.

== [[Trust-region methods]] ==

* Author list:
# Remove cornell IDs. Author is also spelled incorrectly.
# Add the course section.
* An introduction of the topic
# References are not linked. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Use LaTex code or equation editor to display all equations and variables (e.g., “xk”, “f`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “we”. This goes for all other sections as well.
* Theory, methodology, and/or algorithmic discussions
# Organization of ideas in this section needs work.
# You have not defined explicitly why the Cauchy point is important to compute beyond a vague allusion to performance improvements, which is also wrong (it is useful because of its guarantees for convergence, not performance) It is also misspelled.
# Each approach should have accompanying explanation and motivation for why it is being discussed. It is not enough to outline the algorithm.
# Please make sure symbols are properly subscripted and superscripted (e.g. “pk” should be “p_k”
# Please format the algorithm in proper algorithmic pseudocode format.
# Little to no discussion on global convergence guarantees
# Please include discussion about the advantages and disadvantages of the algorithm
# Fix typo “couchy point”.
* At least one numerical example
# Any code functions (uminfunc) should have proper text formatting.
# The graph needs a better caption explaining how the axes are labeled and what data points are being shown.
# Please increase the quality of the figure. It is hard to see the red line.
# Add citation to “The Rosenbrock function is a non-convex function, introduced by Howard H. Rosenbrock in 1960, which is often used as a performance test problem for optimization algorithms.”
* A section to discuss and/or illustrate the applications
# The content in this section as it is currently does NOT describe applications, but rather different approaches within the trust region methodology. Please provide specific applications (e.g. TRPO in reinforcement learning).
* A conclusion section
# Please add more summary, future research directions for example is a good start.
* References
# Incorrect reference style.
# Please consider having the references as this Wiki template, <nowiki>https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization</nowiki>
# More references should be added. A simple Google Scholar search would give you many references.

*There are numerous misspellings, grammatical errors, and incorrect claims. Please fix these.

== [[Momentum]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Apart from an explanation on momentum, it is necessary to briefly point out the limitations of SGD and why momentum could help with these limitations. Please update it accordingly.
# Remove bold on “Momentum”.
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
* Theory, methodology, and/or algorithmic discussions
# Equation formatting is very poor and should be formalized.
# It is important to use technical language for this Wiki. Although a layman’s explanation is appreciated, it would be better to skip using words like “zig zagging”. Try to explain all concepts in a technical language with few simplifications but NOT vice versa.
# The definition of the update rule for SGD with momentum looks incorrect, specifically the first expression. Please fix it and also explain all the parameters used.
# Use LaTex code or equation editor to display all equations and variables (e.g., “W”, “V`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “you”.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step". Since writing all iterations is not feasible, at least present a few iterations for both cases.
# Please try to label the plots that explains what each line color means.
# Starting point for SGD with momentum is different in explanation and the table. Please fix the same.
* A section to discuss and/or illustrate the applications
# Please use correct terminology like “optimizing non-convex functions” and not “training non-convex models”.
# Adam, Adadelta, and RMSprop are variants of SGD that already use momentum. Please double check the writing and update if necessary.
* A conclusion section
# Please refrain from using words like “zig zag” effects.
* References
# Almost all references used are URLs. Please try to add journal/conference articles or books for references, instead of directly citing the URLs. Please check the list below and run a quick Google (Scholar) search to identify relevant literature.

== [[Stochastic dynamic programming|Stochastic Dynamic programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Discussion on applications should be moved to a separate section.
* Theory, methodology, and/or algorithmic discussions
# Remove the grey box background of equations.
* At least one numerical example
* A section to discuss and/or illustrate the applications
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Outer-approximation (OA)|Outer-approximation]] ==

* An introduction of the topic
# See formatting guideline below
# Avoid opinionated statements such as “MINLP problems are usually the hardest to solve”.
# Rearrange the text such that the MINLP formulation is in the theory section and keep the introduction in words only.
* Theory, methodology, and/or algorithmic discussions
# Consider left aligning equations and optimization problem formulations by the “=”. See [[Stochastic programming|https://optimization.cbe.cornell.edu/index.php?title=Stochastic_programming]] for an example
# The sentence “The Outer-Approximation (OA) algorithm was first proposed by Duran and and Grossmann in 1986 to solve MINLP problems.” needs a reference.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# “Minimize” and “subject to” should be “min” and “s.t.” in MathType
* A section to discuss and/or illustrate the applications
# Does not explicitly point out why OA is applicable (and/or preferred) in these applications, rather than other MINLP approaches (show that the problem formulations are amenable to a solution approach through OA)
# The sentence “... an active research area and there exists a vast number of applications in fields such as engineering, computational chemistry, and finance.” needs references.
# Posting GAMS code on the page is generally inappropriate and discouraged. Please check with the TAs or me if you have a strong desire to post GAMS codes on the Wiki page. A typical textbook should not be limited to a specific software package. If the GAMS code must be posted, please also post ALL other software implementation versions, such as Pyomo and JuliaOPT, among others.
# Consider reformatting to make steps more readable. Inserting spaces and breaking down steps would help.
* A conclusion section
# Too short. Consider discussion on future research direction and discussion on uncertainty
# Please review abbreviations throughout the page. Why is MINLP redefined here? “Outer-Approximation is a well known efficient approach for solving convex mixed-integer nonlinear programs (MINLP)”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove "Template:Reflist"

== [[Unit commitment problem]] ==

* Author list
* An introduction of the topic
# Please expand the introduction and avoid discussions of examples or specific applications in this section.
# The sentence “Nonlinear, Non-convex programming optimization problem.” doesn’t make sense by itself and Non-convex shouldn’t be capitalized.
* Theory, methodology, and/or algorithmic discussions
# Figure/image format should be revised to better display the content.
# Uppercase characters are used randomly (e.g., “non-convex transmission Constraints”) . Please follow correct language conventions for sentence structure.
# Avoid inserting inline citations after words like “written in matrix form as equation [3]..” or “presented in [3]...” as it is a bit informal when you don’t explicitly name the subject. Also these two sentences are grammatically incorrect and appear to be missing an ending period and comma, respectively.
# Don’t say “written in matrix form as equation..” and just cite the reference, actually write out the equation.
# Properly label the figure in this section with a figure number and improve visibility by making it larger.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Label the figures in this section properly with figure numbers.
# Fix typo “while minimize” to “while minimizing”.
# Avoid pronouns such as “we”.
# Use the equation editor when typing equations.
# A numerical example is simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments). There is an Application section where you discuss the applications.
# The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).
* A section to discuss and/or illustrate the applications:
# I suggest changing the order of the subtitles here. For example, Single-Period Unit Commitment.
* A conclusion section
* References

== [[Frank-Wolfe]] ==

* Author list:
* An introduction of the topic
# I suggest highlighting disadvantages along with advantages.
* Theory, methodology, and/or algorithmic discussions
# “[n x 1] matrix” please use the equation editor to express mathematical descriptions and symbols (p,b, etc)
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please show at least a few iterations. Even for smaller examples if needed. Report the final solution.
# Please use the LaTex code or equation editor for min and include s.t., etc.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps. For your example, please explicitly state that the derivative is taken etc.
* A section to discuss and/or illustrate the applications:
* A conclusion section
# Same as the introduction. Pros and cons should be evaluated together!
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Line search methods|Line Search Method]] ==

* Author list
* An introduction of the topic
# Expand the introduction and avoid discussion on some of the specific steps in the solution process.
# Provide references here.
* Theory, methodology, and/or algorithmic discussions
# The phrase “are as follows” in the steepest descent method discussion needs to be followed by a colon.
# Rephrase “has a nice convergence theory” and cite a reference for this claim.
# Avoid pronouns such as “we”.
# Add citation after “.. proposed by Phillip Wolfe in 1969.”
# Figure 1 is between two sections. Please fix this issue.
* At least one numerical example:
# Add some space between iterations or subsection break
* A section to discuss and/or illustrate the applications:
# Too few references in this section.
# Last paragraph makes some claims without references.
* A conclusion section
* References
# References should be properly formatted. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Piecewise linear approximation|Piecewise Linear Approximation]]==

* Author list
* An introduction of the topic
# The content of this section is good, but there are some issues with sentence clarity and some other grammatical errors. Please revisit this section and make changes accordingly.
* Theory, methodology, and/or algorithmic discussions
# Fix typo “to force the x’ values become associated with”.
* At least one numerical example
* A section to discuss and/or illustrate the applications
# Please aim for a maximum average sentence length of ~25 words. Some of these longer sentences are hard to read.
* A conclusion section
# Expand the conclusion section to be longer than one sentence. The conclusion section to include a brief summary of what was discussed above, an emphasis on it’s significance, and a brief discussion of future extensions and research direction if applicable.
* References
# Include hyperlinks to sources when possible.

== [[Mathematical programming with equilibrium constraints|Mathematical Programming with Equilibrium constraints]] ==

* An introduction of the topic
# This section includes several terms like variational inequalities, constraint qualifications that were not discussed in the class. Please add a sentence to explain them before using them.
* Theory, methodology, and/or algorithmic discussions
# The meaning of parameter vector x is unclear. Please add more information or update if necessary.
# Equations and symbols in the PIPA subsection are not formatted correctly. Please use the same formatting for all equations, so they read as mathematical equations and not text. This goes for all other sections as well.
# Use equations instead of images to represent math programs and equations in the Implicit Descent and SQP subsection.
# Apart from the steps for each solution technique, please also add a few sentences that describe each method.
* At least one numerical example
# Please define the terms like NCP, MP before abbreviating them. Also try not to unnecessarily abbreviate simple terms.
# Equations should be typed by LaTex. Images for equations are unacceptable.
# GAMS code is strongly discouraged. Please solve the problem "step-by-step".
# The selected numerical example is fine but is directly solved with the MPEC solver in GAMS. Try to solve it manually like the homework/in-class problems step by step using the steps described in the previous section by choosing any of the methods.
# Avoid using figures in the equations (subject to etc)
* A section to discuss and/or illustrate the applications
# Add references to “power management, highway pricing, chemical process engineering, and traffic planning.”
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# This Wiki contains very few references. Please check the list below and run a quick Google (Scholar) search to identify relevant literature.

== [[Wing shape optimization|Wing shape Optimization]] ==

* Author list: Remove cornell ID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC. Any formatting issue will incur a penalty in the grading.
* An introduction of the topic
# The introduction is missing several references (e.g., “software packages like computational fluid dynamics..”, sentences containing things that aren’t common knowledge, performance claims, etc.)
# Avoid discussion involving finer details of subject methods in this section.
# In the titles, please change the font from bold to normal to have consistent formatting in the site. Same applies to box of content!
* Theory, methodology, and/or algorithmic discussions
# Properly cite the CFD package, don’t just include a link.
# Properly label the figure with a figure number.
# Consider removing white space between isolated sentences to improve readability.
* At least one numerical example
# If you’ve already defined an abbreviation (CFD), there is no need to define it again. Just use the abbreviation.
# Avoid pronouns such as “we” or “they”.
# Phrases like “under the following” need to be followed by a colon.
# Properly label the figure with a figure number and consider making them larger to improve visibility. Call the reader's attention to the figures in text by referencing the figure number.
# “As seen in the video below” is stated yet there are only images present and it may be initially unclear to the reader which figure is being referenced here.
# Avoid inserting inline citations like “[4] introduces an..” as it is a bit informal when you don’t explicitly name the subject.
# Don’t just cite the reference when discussing the problem formulation, explicitly write the model formulation and solution process using LaTex or equation visual editor.
# Your team should ideally create a numerical example independently. If you take a numerical example directly from a textbook, etc., you will need to get explicit permission from the author in writing and share that written permission with me.
# A numerical example is simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments). There is an Application section where you discuss the applications.
# The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).
* A section to discuss and/or illustrate the applications
# Some characters are randomly capitalized in this section.
* A conclusion section
# These variables should be defined before the conclusion section, they are out of place here. Also, please use normal text when explaining variables except for the variable symbol.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Interior-point method for NLP|Interior point method for NLP]] ==

* An introduction of the topic:
* Theory, methodology, and/or algorithmic discussions
# Primal-Dual formulation and comparison to the Barrier Method is not discussed.
# Include brief discussion about big O convergence rates.
# Need discussion about the concept of “central path” and the notion of self concordance
# Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
# Graphs and images are incorrectly formatted to the page. Consider proper alignment with respect to the text body.
# Use explicitly typed Latex equations instead of images to represent math programs and equations.
# Fix typo “optimisation”.
# Use LaTex code or equation editor to display all equations and variables (e.g., “xi ”, “μ”, etc.).
* At least one numerical example:
# There are formatting issues with figures 2,3. Please make sure to embed them within their respective sections.
* A section to discuss and/or illustrate the applications
* A conclusion section
# Minor character code typos in the conclusion.
# Also, please add more discussion in this section. Future research directions is a good start.
# There is a box "􏰐"
* References

== [[AdaGrad|Adagrad]] ==

* An introduction of the topic:
* Theory, methodology, and/or algorithmic discussions
# Include discussion on its variants (most important is AdaDelta).
# Include disadvantages of Adagrad, since this provides motivation for the discussion on the variants and improvements of Adagrad
# Include comparisons to other popular optimizers (particularly important is comparisons to regular SGD and Adam)
# Different convergence rates are possible depending on the setting where Adagrad is used, but this is not mentioned on the page currently. As such the regret bound section should be more thoroughly explained.
# Algorithm image is blurry. Either increase the fidelity or write the pseudocode directly in the wiki editor.
* At least one numerical example
# In the first sentence, “..take the following numerical example” should be followed by a colon.
# Fix typo “trayectory”.
* A section to discuss and/or illustrate the applications
# This section is too short; include specific applications in which input features are sparse and Adagrad excels.
# Add reference to the claim “Mainly, it is a good choice for deep learning models with sparse input features”.
* A conclusion section
* References

# Too few references overall, you should aggregate information from multiple sources (even if the base algorithm itself comes from a singular paper)

== [[McCormick envelopes|McCormick Envelopes]] ==

* Author list: OK but I suggest removing NetID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# First sentence is hard to read. Please consider keeping sentences below 25-30 words.
# No references provided. Please cite all sources.
# Figure 1 is provided in the middle between two sections. Please include in the introduction section.
* Theory, methodology, and/or algorithmic discussions
# References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# When using mathematical expressions and symbols, please use the equation editor. (e.g., x*y, exy + y, sin (x+y) - x2)
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# For the sample GAMS code, please place it in a code box
* A section to discuss and/or illustrate the applications
# Having a list is not enough. Please explain at least three applications in a few sentences each.
# This section should be at least a paragraph to discuss relevant applications. Each application should be explicitly linked to the page topic. A few keywords do not meet the requirement at all.
* A conclusion section:
* References
# References are not expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please follow the standard reference style - the current format is incorrect.
== [[Branch and bound (BB) for MINLP|Branch and Bound for MINLP]] ==

* Author list:
** Remove NetIDS
** Please remove abbreviations from the title (i.e. BB).
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# Please cite sources appropriately: References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Introduction is very short for a well-recognized topic. Please expand significantly. You may refer to the Wiki examples to get an idea on writing the Introduction to a topic.
# An illustration might be useful here.
* Theory, methodology, and/or algorithmic discussions
# The algorithm described here considers only binary integer variables. However, MINLP problems may include non-binary integer variables too. Please update the method or provide a short description of the assumptions that the MINLP problem needs to satisfy in order for the presented technique to be applicable.
# Use linked citations please as the Wiki template above.
# Please provide steps in a more organized way. Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
# Step 2 is missing yet it is referenced in the text multiple times. Please address this in addition to the above comment.
# An illustration might be useful here as well.
# Please explain what a Gomory Cut is. If the topic is available on optimization.cb.cornell.edu, you can link it.
# The current equations seem to be simple text written in Italics. All mathematical symbols and equations should be formatted via LaTex.
# Please format the math programs with equations and notations using formulations in lecture notes as templates.
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# Please show a step-by-step solution in the example. The solution is incomplete. The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).
# Please use the equation editor for equations or mathematical symbols. - All mathematical symbols and equations should be formatted via LaTex - this is a learning objective of the Wiki assignment. You can find some useful links on converting your equations/symbols into LaTex code here: (<nowiki>https://optimization.cbe.cornell.edu/index.php?title=Help:Contents</nowiki>). Again, any formatting issue will incur a "compound" penalty in the grading.
# This example does not follow the MINLP structure discussed in the above section since binary variables are missing. Branch and bound may not be appropriate for such problems. Please provide an appropriate numerical example and solve it according to the above comments.
# Make sure your example is not taken from a book as that is strictly disallowed.
* A section to discuss and/or illustrate the applications
# This section is not well-formatted. Please provide 3 applications and explain each in a few sentences and how BB for MINLP could be used. Also, please eliminate having multiple sections (Application, Mathematical problem, industrial application). All these could be merged together.
# This section should be at least a paragraph to discuss relevant applications. Each application should be explicitly linked to the page topic. A few keywords do not meet the requirement at all.
* A conclusion section:
# The sentence is hard to understand "a scheme that grows exponentially because" please use a simple language. Is it also theoretically correct? It is also not mentioned and explained earlier. Thus, please avoid introducing new concepts or terms at the end.
# Please use summarizing sentences to describe earlier sections instead of introducing new concepts/discussion.
* References
# Too few references overall, you should aggregate information from multiple sources. A quick Google scholar search could provide relevant references.
# References are not expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please follow the standard reference style - the current format is incorrect.

2021 Cornell Optimization Open Textbook Feedback

2021-12-06T03:06:23Z

Asa273: /* Branch and Bound for MINLP */

== [[Lagrangean duality|Lagrangian duality]] ==
* Author list, sections and TOC
# Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.
# Remove cornell ID from Author list
* An introduction of the topic
# This section includes sentences on constructing the dual problem and is referred to as Lagrangian relaxation (LR). This is incorrect, please fix the definition of LR.
# Definitions of LR and its relation to duality should be double checked and re-written.
# Only one reference is present in this section. Please add more relevant references by expanding this section.
# Consider merging the “introduction” and “history” sections.
# In the titles, please change the font from bold to normal to have consistent formatting in the site.
* Theory, methodology, and/or algorithmic discussions
# The Lagrangian variables associated with equality constraints h(x) are unbounded but the Lagrangian dual problem states them as non-negative. Please fix the same.
# Also to construct a dual, we do not change minimization to maximization directly. We observed such things in the examples in lecture notes due to simplification. The lagrangian dual problem would be minimize (,).
# Adding to the previous point, the Lagrangian is a lower bound on the original objective; the solution to the primal and dual or only equivalent if the duality gap is 0. You reference this in one section, but this is after your statement “Hence, solving the dual problem, which is a function of the Lagrangian multipliers (𝜆*) yields the same solution as the primal problem, which is a function of the original variables (x*). “. Please clarify the specific conditions that must hold for the solution of the dual to be equal to the primal’s.
# You refer to the “Complementary Slackness Theorem”, but don’t actually write the mathematical representation of complementary slackness. Please fix this. Also consider including the derivation of the complementary slackness condition, as it is both easy and short. Boyd is a good reference for this.
# Last step of the “process” subsection also needs updating according to the previous comments.
# The inline notations should also be typed using LaTex.
# Please use the LaTex code or equation editor for min, s.t., etc.
* At least one numerical example
# Only one dual variable is associated with each constraint. The numerical example uses two for the first and second constraint which is unnecessary. Please update it accordingly for both constraints. This particular example will only have two dual variables instead of the five dual variables used currently.
# All consecutive steps need to be updated since the dual variables would be updated.
# After substitution the nonlinear function should be further simplified. The current expression reads like a highly nonlinear function but can be easily simplified.
# Similar to the comments in the methodology section, inverting minimize to maximize is incorrect. Please update the dual objective function and domain of dual variables accordingly.
# Please use the LaTex code or equation editor for min, s.t., etc.
* A section to discuss and/or illustrate the applications
# Bullet points could be used to state the last four real-world examples that explain the physical meaning of the primal and dual problems.
# Add references for the last set of applications.
* A conclusion section
# This section contains a few typos. Please fix the same.
* References
# Some citations' hyperlinks are displaying.

== [[Disjunctive inequalities|Disjunctive Inequalities]] ==

* Author list
# Missing course section and semester
# Remove cornell ID
* An introduction of the topic
# No citations are present in this section.
# “mixed-integer programming (MIP)” should be used instead of “multiple integer programming (MIP)”. Please fix this error.
* Theory, methodology, and/or algorithmic discussions
# The abbreviation MILP is not previously defined. Please fix this issue.
# You consistently use the negative sign instead of the NOT operator for y (-y instead of ¬y).
# Some inconsistencies with the spacing of variables, constraints, etc., under the “General” section that need to be fixed.
# Typo in “This is shown below by M1, M2, y1, and y1:” where y1 needs to be changed to y2. Why use two different Big-M variables here? Elsewhere in the Wiki you only use one so this could lead to confusion with a general audience. Also if this was taken from the lecture notes then it needs to be cited.
* At least one numerical example
# Please reformulate and solve a complete numerical example rather than just reformulating a general example. Demonstrate the use of Big-M and Convex Hull formulation in an optimization problem that provides details such as individual steps in the problem solving process and final results. The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results.
# Add space between vee (V) operator and brackets in first line of Latex
# Please format variables correctly, for example, use <math>x_1</math> instead of x1.
* A section to discuss and/or illustrate the applications
# Please format the equations appropriately either by using latex code or the visual editor. These images are NOT acceptable!
* A conclusion section
# There is no conclusion presented in this section at all.
* References
# The included references have NOT been used anywhere in the Wiki. Add references for sentences that are not common knowledge and please link them appropriately with the text in Wiki. If the figures used here were not original works, you must also cite them.
# There are many papers on this topic. A simple Google (Scholar) search could provide you with sufficient references to cite.
# Many important references of this topic are missing.
# Please consider linking the references as demonstrated in the Wiki tutorial on Canvas and in this template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

==[[Stochastic programming|Stochastic Programming]] ==

* Author list: Remove cornell IDs
* An introduction of the topic
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
# This section only includes two sentences on Stochastic programming (SP), while the rest gives examples of uncertainty. Please discuss the need for SP in the presence of uncertainty. Also, discussion on robust optimization and its limitations should be removed since it is out of place.
* Theory, methodology, and/or algorithmic discussions
# Please avoid direct inline linkbacks to Wikipedia.
# The symbol “xi” in the methodology subsection should be explained.
* At least one numerical example
# Copying a numerical example "entirely" from a textbook is inappropriate. Your team should come up with a "numerical" case.
# No specific application context is needed for a numerical example.
# The inline notations (`x1`, `s1`) should also be typed using LaTex.
# Label all tables with a table number for better readability.
# Properly format the solution table with the label attached rather than the following sentence. The solution table looks different from the others, please fix this for consistency.
* A section to discuss and/or illustrate the applications;
# I suggest eliminating citing the last name of the first author (i.e. Zhou et al.)
* A conclusion section
* References
# URLs of some citations are not properly formatted (not showing the hyperlinks).

== [[Exponential transformation|Exponential Transformation]] ==

* Author list
# Missing course section
# Remove cornell ID
* An introduction of the topic
# Please expand the introduction.
# Please aim for a maximum average sentence length of ~25 words. Last sentence with 51 words is hard to read.
# Second Sentence: please change the word “they” as it could make the meaning ambiguous
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
# If you use abbreviations, please introduce them (e.g. NLP,MINLP)
* Theory, methodology, and/or algorithmic discussions
# Please explain the transformation in words along with equations
# Terms like posynomial should be described in detail.
# Please move the numerical example to the section below
# The “(eq 1)” is not needed here.
# Please expand this section.
* At least one numerical example
# In the third equation of the numerical example, it is confusing to have coefficients after numbers. Some readers may read it as an exponent.
# Last equation in this section after “further linearization” is incorrect. This equation cannot be further linearized, please fix this.
# Please explain the steps in the numerical examples in detail. The step-by-step solution should be provided.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# Missing part of text: “Proof of convexity of with positive definite test of Hessian…”
# Applications are not numerical examples. Please refer to this link for example of applications: [[Duality|https://optimization.cbe.cornell.edu/index.php?title=Duality]]
# Citation 7 is missing in current applications
# The section current applications is redundant
# Please use the LaTex code or equation editor for min, s.t., etc.
# Under current applications, do not just use a hyperlink to describe an application. Actually describe it. And properly inline citation style should be used instead of the hyperlink.
# The convexification application of MINLP can be further simplified for binary variables. Please refer to the lecture slides for more information.
* A conclusion section
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
* References
# Please consider linking the references by using this as Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Citation 7 is missing in current applications

== [[Sparse Reconstruction with Compressed Sensing|Sparse reconstruction with Compressed Sensing]] ==
This Wiki needs a significant rewrite. Please go through the comments for details.

* An introduction of the topic
# The introduction section should include information about the problem and its implications presented briefly. Please use full sentences to write this Wiki. You may use tools like Grammarly to check sentence formation and grammar.
# This section includes several typos like “sub modual”. Please fix them throughout the wiki and delete them if not required.
# Many abbreviations are used before previously defining them. Please define these abbreviations before using them in the text.
# This section is incomprehensible in its current form. Please rewrite with proper comprehension.
# Equations and math symbols need proper reformatting. The current version reads like text (along with equations) copy-pasted from a specific source. All mathematical symbols and equations should be formatted via LaTex - this is a learning objective of the Wiki assignment. You can find some useful links on converting your equations/symbols into LaTex code here: (https://optimization.cbe.cornell.edu/index.php?title=Help:Contents).
# Try to place the figure at the top of the Wiki between the main text.
# Avoid pronouns such as “we”.
# I suggest the use of more formal abstract illustrations.
* Theory, methodology, and/or algorithmic discussions
# Equations and symbols need proper reformatting.
# Lemmas and theorems are not expected for this Wiki. Sparse reconstruction is a straightforward concept but is unnecessarily complicated here. Please refer to other Wiki examples to get an idea of what the Wiki should convey.
# All equations need to be better formatted.

* At least one numerical example
# Numerical example is missing.
# Every iteration should be clearly presented, and solved "step-by-step".
* A section to discuss and/or illustrate the applications
# Having a list is not enough. Please explain at least three applications in a few sentences each.
* A conclusion section
# Conclusion section is missing.
* References
# The current reference list is not correctly formatted. References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Portfolio optimization|Portfolio Optimization]] ==

* Author list
# Remove cornell id
* An introduction of the topic
# The introductory sentence should be rephrased. The action of minimizing the risks does not inherently maximize the gains, rather PO aims to maximize gains whilst minimizing risks.
# Amount of whitespace can be reduced by changing the orientation of Figure 1 and the sentences in this section.
# Define terms such as risk, return, portfolio, etc., when you introduce them. Assume that the reader may not know much about finance. This goes for all other sections as well.
* Theory, methodology, and/or algorithmic discussions
# A brief mention of modern portfolio theory (i.e.. Markowitz) would be appropriate in this section.
# Several grammatical errors here involving sentence structure and clarity. Some questionable semantics (e.g., “The portfolio optimization mainly assumes two directions.”) and syntax (phrases such as “.. is as follows” should be followed by a colon). Misuse of commas and missing commas in this section. Two sentences introducing E(rp) and w should be combined into one.
# Use LaTex to distinguish variables written within a sentence, such as m and n.
# Rephrase “Cut the relevant information and conditions in the portfolio optimization, as well as the final requirements into the relevant variables, constraints and linear functions of the linear programming problem.”
# An explanation of a few common constraints would be helpful, rather than just including a table.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Solving the numerical example by GAMS is inappropriate. Please provide detailed step-by-step calculation results.
# All tables need to be labeled.
# Include figure number in label for consistency.
# Fix misspelling “dolling decision variables”.
# Use LaTex for all variables, equations, and constraints here.
# Example 2 table is hard to read, so making it bigger would help.
# Remove the “Using excel as the solver” part from the sentence before the solution discussion.
# Some grammatical errors here (phrases such as “.. is as follows” should be followed by a colon).
* A section to discuss and/or illustrate the applications
# Rephrase “Portfolio optimization can be used to screen investment projects that meet investors, rationally allocate investment amounts, etc.”
# Not sure “relevant” is the correct word choice here.
# You need more specific examples with the utility of portfolio optimization, this section is quite general as is. Some more detail and focus on real-world applications in the financial industry that relate to retirement planning, financial security, economic stability, etc., would be helpful.
* A conclusion section
# Need some commas here.
# The sentence “Linear programming has been around since the 1940’s and has such a wide base of applications” is not necessary.
* References
# Please consider linking the references as demonstrated in the Wiki tutorial on Canvas and in this template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove white space between end of sentences and reference numbers.

== [[Chance-constraint method|Chance constraint method]] ==

* Author list:
* An introduction of the topic
# Please consider correcting a few grammatical errors: “pre-planned for”, “god”, “certain levels of feasibility is guaranteed in what are”, and “Performance of a system”
# In “Chance-constraint”, it is capitalized randomly throughout the introduction. Please correct.
# Please use technical language to briefly introduce chance-constrained programming. Words like “acts of god”, “cost of doing business” are not appropriate for a technical Wiki.
* Theory, methodology, and/or algorithmic discussions
# Please add a citation to the first sentence.
# Xi is an uncertainty/randomness variable. It is better to use clear language.
# Please use the mathematical editor for adding explanations in the text. Using “ x is a decision variable” is hard to read. Same for f(x) and others.
# Theory is insufficient. Please expand and explain different approaches.
# Please add pros and cons explicitly as a list.
# Explain the physical meaning for examples of chance constraints along with all the notations used.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please remove this example as it is directly from this book. The example should be purely numerical without any background.
# Please use the equation editor for min, st., etc.
# Please use the mathematical editor for adding explanations in the text. Using “ x is a decision variable” is hard to read. Same for f(x) and others.
# Please change the table format so as not to confuse the reader.
# Multiple instances of [Chart to be added] are missing.
# Example is incomplete.
# Avoid pronouns such as “we”.
* A section to discuss and/or illustrate the applications
# Please connect several grammatical and spelling errors: “real life application”, Energy creation, particularly in renewable sources, have high variabilities”, and others
# “Zhao, Xue, Cao, and Zhang”. No need to list all authors within the article. Provide a reference is sufficient. If authors must be mentioned, (Zhao et al.) should be ok.
* A conclusion section
# Uniqueness and universality earlier are not clear to me. If they are not discussed earlier in the application, it would be better not to introduce new discussions in the conclusion.
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
* References
# References seem to vary in format. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Bayesian Optimization]] ==
* Section titles should not be "bold". Please double check using source editor on the section titles.
* Contents: The section titles should NOT be in bold to avoid strange format in TOC. Any formatting issue will incur a penalty in the grading.
* Author list: Remove cornell ID, Please check names
* Introduction
# The introduction is too general and not substantial enough. For example, simply saying BayesOpt is useful when the objective function is unknown obscures exactly HOW it is useful (namely, computational efficiency in applications where ground truth sampling is expensive). Discussion on applications should be moved to a separate section.
# Machine learning rarely includes black-box functions to be optimized. Bayesian optimization is almost never used for optimizing ML loss functions but can instead be used for hyperparameter optimization. Please update such claims in this section.
* Theory, methodology, and/or algorithmic discussions
# Captions need reformatting.
# Consider italicizing keywords rather than bolding.
# Please add a citation to the first sentence.
# Discussion on acquisition functions should include comparisons, tradeoffs, and reasons to use one over the other. Should also note that expected improvement is the most widely used in practice, and explain.
# Avoid pronouns such as “we”.
# Please write equations in the Wiki instead of attaching images for equations.
# Acquisition function figure could be made larger and clearer to improve readability.
* At least one numerical example
# Any references to functions or methods in code ‘e.g. fmin’ should be properly formatted as code-stylized text.
# Please use the equation editor for min, st., etc.
# Avoid including a figure of the code for this example and explicitly describe the steps to the modeling and solution process instead.
# Avoid pronouns such as “our” and “we”.
* A section to discuss and/or illustrate the applications
* A conclusion section
# Please do not use brackets to enclose lists.
# Some claims here should be supported by references. Please cite each source after its sentence.
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Try to avoid references to “pop” machine learning blogs where anyone can be an author. (e.g. towardsdatascience)
# All references are URLs. Please cite publications and literature.
# A simple Google Scholar search would give you many references.

Notes on grammar: Needs some work. Several instances where colons are inappropriately inserted mid sentence or in subheadings. Explanations are not terse. Several instances of switching between personal and impersonal style of writing, which is distracting.

== [[Conjugate gradient methods]] ==

* Author list: Remove cornell ID
* Introduction
# All inline notations (e.g., `x`, `A`) should be typed using LaTex.
* Theory, methodology, and/or algorithmic discussions
# All equations need to be better formatted.
# Is Gauss-Newton no longer referenced?
# Theorems listed in the first section should be accompanied with high level explanation, not just a list of the theorems themselves. The page should read like an article, with proper flow.
# Please indent equation blocks.
# Please properly format pseudocode.
* At least one numerical example
# Steps should be accompanied with explanation, or reference to the corresponding step in the pseudocode.
# Please properly format in a more organized manner, aligning equations appropriately and demarcating steps appropriately.
* A section to discuss and/or illustrate the applications
# Consider including 2 additional examples of applications
* A conclusion section
# Consider adding future research directions
* References
# Reference primary sources rather than Wikipedia
# Too few references.
# More references should be added. A simple Google Scholar search would give you many references.

== [[Geometric programming|Geometric Programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Examples of applications in this section use the same reference. Please cite their individual sources.
* Theory, methodology, and/or algorithmic discussions
# The symbol denoting the domain in the definition of a monomial is unclear. Please clarify it or fix this if it is incorrect.
# Definition of posynomial refers to section 2.1 which is missing from the Wiki (sections are not numbered in the main text).
# In the generalized posynomial subsection, bullet points do not tell us why h(x) is posynomial. Either provide reasons or simply state that h(x) is posynomial. Also explain why h3 is a generalized posynomial.
# Additional theory on the feasibility analysis could be provided in this section.
* At least one numerical example
# In the transformation example, the last two constraints could also be simplified by applying a natural logarithm on both sides. Please update them as well.
* A section to discuss and/or illustrate the applications
# The figure in this section needs to be labeled.
# The figure needs to be resized and perhaps aligned to the center.
* A conclusion section:
# Please avoid vague language such as: “This makes”.
# Please avoid opinionated statements: “one of the best ways”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# This Wiki has very few references. A quick Google Scholar search may provide relevant references.

== [[Adam]] ==

* Author list
* An introduction of the topic
# Some grammatical errors here, mostly related to the need for commas in certain places (e.g., “Before Adam..”).
# Some minor errors with parts of speech throughout the section, need to revisit phrases such as “which has broader scope in future for”, etc.
# Try splitting up some of the longer sentences in this section, a couple are hard to read.
# Avoid definitive statements about Adam being the best or always better solver, as this is simply not true (the choice of the “best” optimizer is setting-dependent). Use language such as “Research has shown that Adam has demonstrated superior experimental performance over..” and then cite academic references to back this claim.
# What does adam stand for? Introduction is insufficient. Please expand.
* Theory, methodology, and/or algorithmic discussions
# Revise grammar here, noticing some missing commas and uncapitalized word after period.
# Rephrase “second one is to update the old position with the updated position”.
# Use LaTex code or equation editor to display all equations and variables in this section, and actual subscripts instead of “m_t”, etc.
# Avoid inserting inline citations after words like “According to..” or “This article..” as it is a bit informal. This could be rephrased or changed to something like “According to author,^[2] …” with author name inserted.
# Remove white space before the period in RMSP discussion.
# Please provide a pseudocode.
# Please use list the two methods here “Adam is a combination of two gradient descent methods which are explained below”
# Please expand the theory section significantly. Theoretical convergence properties should be discussed, even if briefly.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
* A section to discuss and/or illustrate the applications
# Same comment as before, consider replacing inline citations after words like “According to..”.
* A conclusion section
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Try to avoid references to blogs and use peer-reviewed academic references instead.
# Too few references.
# More references should be added. A simple Google Scholar search would give you many references.

== [[A-star algorithm|a* algorithm]] ==

* Author list: Remove cornell ID
* Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.
* An introduction of the topic:
# Weird spacing between paragraphs. Please fix this issue.
# In the titles, please change the font from bold to normal to have consistent formatting in the site.
# Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.
# There are no citations in the introduction. Please cite every source.
* Theory, methodology, and/or algorithmic discussions
# Please add the mathematical description of the algorithm.
# Reference style varies in sentences. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please fix grammatical and spelling errors as (“from current position to the goal”, “There are a lot of discussions”, etc). Also, many hyphens are missing as “non playable”.
# In algorithms, it is a standard to add high-level description (i.e. pseudocode or flowchart). Please incorporate it.
# Use LaTex code or equation editor to display all equations and variables in this section (e.g., “f(n)...”, “h(n)..”, etc.). This goes for other sections as well.
* At least one numerical example
# The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.
# Instead of writing things like “The above image..”, label each figure and use the figure number to refer to it in text.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# No references in the applications. Please cite every source
# Preferably, add at least an additional application.
* A conclusion section
# Conclusion should summarize descriptions. Please modify it to provide a summary.
# Please pay attention to the length and structure of sentences here and in the full page. First sentence is hard to read.
* References
# References seem to vary in format and are not linked correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Incorrect reference style. Please follow the example and use the template.

== [[Job shop scheduling|Job-Shop Scheduling Problem]] ==

* An introduction of the topic
# The current introduction to the jobshop scheduling problem has only two sentences in addition to the parameter description. Introduction typically contains information about the problem, its importance in the real-world, and some information about the solution techniques and their types to solve the problem. Please add some information that covers the above.
* Theory, methodology, and/or algorithmic discussions
# It is unclear whether the assumptions stated in this section are required to apply the following solution techniques. Please clarify the same. Also use complete sentences to state them.
# The branch and bounds method described in this section only discusses the solution technique for problems with one machines. However, branch and bound is a general technique that can be applied to any MILP problems with varying scales. Please update the “methods” section to be as general as possible.
# Since this Wiki focuses on jobshop scheduling, at least two methods are expected. Branch and bound is a general MILP technique, so, it is recommended to add a tailored technique that can only solve specific jobshop scheduling problems. Solving the numerical example with this technique is not necessary.
# Reference to the branch and bound technique described in this section is a “youtube” video. Please add references in literature that describe this method in detail. The method used in this video is highly tailored for a single machine application. This is also an incorrect way to cite a reference. Please keep this section as general as possible.
# Use LaTex code or equation editor to display all equations and variables in this section and all other sections as well.
# Check grammar in this section. For example, phrases like “are as follows” need to be followed by a colon and not a period.
# Consider rewriting the assumptions as a list in this section.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# The example used in this section is exactly the same as the one in the youtube video. Please use a modification of this example or choose another example/method to demonstrate the solution technique. Your team should ideally create a numerical example independently. If you take a numerical example directly from a particular source, you will need to get explicit permission from the textbook author in writing and share that written permission with the instructors.
# The figure in this section is not numbered when all others are. Relabel this figure for consistency and its number to refer to it in-text.
# A numerical example should be simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments).
* A section to discuss and/or illustrate the applications
# This section should only focus on real-world applications of the jobshop scheduling problem. But currently, this section includes additional information on solution techniques/complexity that is appropriate for the Introduction section. Please discuss the applications of the problem in this section.
* A conclusion section
# The meaning of “Operations applications” is unclear. Please explain or update if necessary.
# The current conclusion section does not properly summarize the problem. Please refer to other Wiki examples for an idea to update the section accordingly.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please reference media sources like reference 5 appropriately.
# A simple Google Scholar search would give you many "formal" references.

== [[Optimization in game theory]] ==

* Author list: remove cornell IDs.
* An introduction of the topic
# References are not linked. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
* Theory, methodology, and/or algorithmic discussions
# Why only a subsection on "Nash Equilibrium" is included in "Theory" section? Please re-format.
# Please edit references.
# Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm.
# Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.
* At least one numerical example
# Please organize the last part in a more readable format. Questions may be in bold and numbered, answers are more direct, etc.
# Remember to cite all images and tables.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# Very good, link the reference and cite all sources.
* A conclusion section
# Please add more summarizing especially from theory sentences and avoid long sentences.
* References
# Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Reference primary sources rather than Wikipedia
# Incorrect reference style. Please correct.

== [[Trust-region methods]] ==

* Author list:
# Remove cornell IDs. Author is also spelled incorrectly.
# Add the course section.
* An introduction of the topic
# References are not linked. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Use LaTex code or equation editor to display all equations and variables (e.g., “xk”, “f`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “we”. This goes for all other sections as well.
* Theory, methodology, and/or algorithmic discussions
# Organization of ideas in this section needs work.
# You have not defined explicitly why the Cauchy point is important to compute beyond a vague allusion to performance improvements, which is also wrong (it is useful because of its guarantees for convergence, not performance) It is also misspelled.
# Each approach should have accompanying explanation and motivation for why it is being discussed. It is not enough to outline the algorithm.
# Please make sure symbols are properly subscripted and superscripted (e.g. “pk” should be “p_k”
# Please format the algorithm in proper algorithmic pseudocode format.
# Little to no discussion on global convergence guarantees
# Please include discussion about the advantages and disadvantages of the algorithm
# Fix typo “couchy point”.
* At least one numerical example
# Any code functions (uminfunc) should have proper text formatting.
# The graph needs a better caption explaining how the axes are labeled and what data points are being shown.
# Please increase the quality of the figure. It is hard to see the red line.
# Add citation to “The Rosenbrock function is a non-convex function, introduced by Howard H. Rosenbrock in 1960, which is often used as a performance test problem for optimization algorithms.”
* A section to discuss and/or illustrate the applications
# The content in this section as it is currently does NOT describe applications, but rather different approaches within the trust region methodology. Please provide specific applications (e.g. TRPO in reinforcement learning).
* A conclusion section
# Please add more summary, future research directions for example is a good start.
* References
# Incorrect reference style.
# Please consider having the references as this Wiki template, <nowiki>https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization</nowiki>
# More references should be added. A simple Google Scholar search would give you many references.

*There are numerous misspellings, grammatical errors, and incorrect claims. Please fix these.

== [[Momentum]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Apart from an explanation on momentum, it is necessary to briefly point out the limitations of SGD and why momentum could help with these limitations. Please update it accordingly.
# Remove bold on “Momentum”.
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
* Theory, methodology, and/or algorithmic discussions
# Equation formatting is very poor and should be formalized.
# It is important to use technical language for this Wiki. Although a layman’s explanation is appreciated, it would be better to skip using words like “zig zagging”. Try to explain all concepts in a technical language with few simplifications but NOT vice versa.
# The definition of the update rule for SGD with momentum looks incorrect, specifically the first expression. Please fix it and also explain all the parameters used.
# Use LaTex code or equation editor to display all equations and variables (e.g., “W”, “V`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “you”.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step". Since writing all iterations is not feasible, at least present a few iterations for both cases.
# Please try to label the plots that explains what each line color means.
# Starting point for SGD with momentum is different in explanation and the table. Please fix the same.
* A section to discuss and/or illustrate the applications
# Please use correct terminology like “optimizing non-convex functions” and not “training non-convex models”.
# Adam, Adadelta, and RMSprop are variants of SGD that already use momentum. Please double check the writing and update if necessary.
* A conclusion section
# Please refrain from using words like “zig zag” effects.
* References
# Almost all references used are URLs. Please try to add journal/conference articles or books for references, instead of directly citing the URLs. Please check the list below and run a quick Google (Scholar) search to identify relevant literature.

== [[Stochastic dynamic programming|Stochastic Dynamic programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Discussion on applications should be moved to a separate section.
* Theory, methodology, and/or algorithmic discussions
# Remove the grey box background of equations.
* At least one numerical example
* A section to discuss and/or illustrate the applications
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Outer-approximation (OA)|Outer-approximation]] ==

* An introduction of the topic
# See formatting guideline below
# Avoid opinionated statements such as “MINLP problems are usually the hardest to solve”.
# Rearrange the text such that the MINLP formulation is in the theory section and keep the introduction in words only.
* Theory, methodology, and/or algorithmic discussions
# Consider left aligning equations and optimization problem formulations by the “=”. See [[Stochastic programming|https://optimization.cbe.cornell.edu/index.php?title=Stochastic_programming]] for an example
# The sentence “The Outer-Approximation (OA) algorithm was first proposed by Duran and and Grossmann in 1986 to solve MINLP problems.” needs a reference.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# “Minimize” and “subject to” should be “min” and “s.t.” in MathType
* A section to discuss and/or illustrate the applications
# Does not explicitly point out why OA is applicable (and/or preferred) in these applications, rather than other MINLP approaches (show that the problem formulations are amenable to a solution approach through OA)
# The sentence “... an active research area and there exists a vast number of applications in fields such as engineering, computational chemistry, and finance.” needs references.
# Posting GAMS code on the page is generally inappropriate and discouraged. Please check with the TAs or me if you have a strong desire to post GAMS codes on the Wiki page. A typical textbook should not be limited to a specific software package. If the GAMS code must be posted, please also post ALL other software implementation versions, such as Pyomo and JuliaOPT, among others.
# Consider reformatting to make steps more readable. Inserting spaces and breaking down steps would help.
* A conclusion section
# Too short. Consider discussion on future research direction and discussion on uncertainty
# Please review abbreviations throughout the page. Why is MINLP redefined here? “Outer-Approximation is a well known efficient approach for solving convex mixed-integer nonlinear programs (MINLP)”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove "Template:Reflist"

== [[Unit commitment problem]] ==

* Author list
* An introduction of the topic
# Please expand the introduction and avoid discussions of examples or specific applications in this section.
# The sentence “Nonlinear, Non-convex programming optimization problem.” doesn’t make sense by itself and Non-convex shouldn’t be capitalized.
* Theory, methodology, and/or algorithmic discussions
# Figure/image format should be revised to better display the content.
# Uppercase characters are used randomly (e.g., “non-convex transmission Constraints”) . Please follow correct language conventions for sentence structure.
# Avoid inserting inline citations after words like “written in matrix form as equation [3]..” or “presented in [3]...” as it is a bit informal when you don’t explicitly name the subject. Also these two sentences are grammatically incorrect and appear to be missing an ending period and comma, respectively.
# Don’t say “written in matrix form as equation..” and just cite the reference, actually write out the equation.
# Properly label the figure in this section with a figure number and improve visibility by making it larger.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Label the figures in this section properly with figure numbers.
# Fix typo “while minimize” to “while minimizing”.
# Avoid pronouns such as “we”.
# Use the equation editor when typing equations.
# A numerical example is simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments). There is an Application section where you discuss the applications.
# The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).
* A section to discuss and/or illustrate the applications:
# I suggest changing the order of the subtitles here. For example, Single-Period Unit Commitment.
* A conclusion section
* References

== [[Frank-Wolfe]] ==

* Author list:
* An introduction of the topic
# I suggest highlighting disadvantages along with advantages.
* Theory, methodology, and/or algorithmic discussions
# “[n x 1] matrix” please use the equation editor to express mathematical descriptions and symbols (p,b, etc)
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please show at least a few iterations. Even for smaller examples if needed. Report the final solution.
# Please use the LaTex code or equation editor for min and include s.t., etc.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps. For your example, please explicitly state that the derivative is taken etc.
* A section to discuss and/or illustrate the applications:
* A conclusion section
# Same as the introduction. Pros and cons should be evaluated together!
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Line search methods|Line Search Method]] ==

* Author list
* An introduction of the topic
# Expand the introduction and avoid discussion on some of the specific steps in the solution process.
# Provide references here.
* Theory, methodology, and/or algorithmic discussions
# The phrase “are as follows” in the steepest descent method discussion needs to be followed by a colon.
# Rephrase “has a nice convergence theory” and cite a reference for this claim.
# Avoid pronouns such as “we”.
# Add citation after “.. proposed by Phillip Wolfe in 1969.”
# Figure 1 is between two sections. Please fix this issue.
* At least one numerical example:
# Add some space between iterations or subsection break
* A section to discuss and/or illustrate the applications:
# Too few references in this section.
# Last paragraph makes some claims without references.
* A conclusion section
* References
# References should be properly formatted. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Piecewise linear approximation|Piecewise Linear Approximation]]==

* Author list
* An introduction of the topic
# The content of this section is good, but there are some issues with sentence clarity and some other grammatical errors. Please revisit this section and make changes accordingly.
* Theory, methodology, and/or algorithmic discussions
# Fix typo “to force the x’ values become associated with”.
* At least one numerical example
* A section to discuss and/or illustrate the applications
# Please aim for a maximum average sentence length of ~25 words. Some of these longer sentences are hard to read.
* A conclusion section
# Expand the conclusion section to be longer than one sentence. The conclusion section to include a brief summary of what was discussed above, an emphasis on it’s significance, and a brief discussion of future extensions and research direction if applicable.
* References
# Include hyperlinks to sources when possible.

== [[Mathematical programming with equilibrium constraints|Mathematical Programming with Equilibrium constraints]] ==

* An introduction of the topic
# This section includes several terms like variational inequalities, constraint qualifications that were not discussed in the class. Please add a sentence to explain them before using them.
* Theory, methodology, and/or algorithmic discussions
# The meaning of parameter vector x is unclear. Please add more information or update if necessary.
# Equations and symbols in the PIPA subsection are not formatted correctly. Please use the same formatting for all equations, so they read as mathematical equations and not text. This goes for all other sections as well.
# Use equations instead of images to represent math programs and equations in the Implicit Descent and SQP subsection.
# Apart from the steps for each solution technique, please also add a few sentences that describe each method.
* At least one numerical example
# Please define the terms like NCP, MP before abbreviating them. Also try not to unnecessarily abbreviate simple terms.
# Equations should be typed by LaTex. Images for equations are unacceptable.
# GAMS code is strongly discouraged. Please solve the problem "step-by-step".
# The selected numerical example is fine but is directly solved with the MPEC solver in GAMS. Try to solve it manually like the homework/in-class problems step by step using the steps described in the previous section by choosing any of the methods.
# Avoid using figures in the equations (subject to etc)
* A section to discuss and/or illustrate the applications
# Add references to “power management, highway pricing, chemical process engineering, and traffic planning.”
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# This Wiki contains very few references. Please check the list below and run a quick Google (Scholar) search to identify relevant literature.

== [[Wing shape optimization|Wing shape Optimization]] ==

* Author list: Remove cornell ID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC. Any formatting issue will incur a penalty in the grading.
* An introduction of the topic
# The introduction is missing several references (e.g., “software packages like computational fluid dynamics..”, sentences containing things that aren’t common knowledge, performance claims, etc.)
# Avoid discussion involving finer details of subject methods in this section.
# In the titles, please change the font from bold to normal to have consistent formatting in the site. Same applies to box of content!
* Theory, methodology, and/or algorithmic discussions
# Properly cite the CFD package, don’t just include a link.
# Properly label the figure with a figure number.
# Consider removing white space between isolated sentences to improve readability.
* At least one numerical example
# If you’ve already defined an abbreviation (CFD), there is no need to define it again. Just use the abbreviation.
# Avoid pronouns such as “we” or “they”.
# Phrases like “under the following” need to be followed by a colon.
# Properly label the figure with a figure number and consider making them larger to improve visibility. Call the reader's attention to the figures in text by referencing the figure number.
# “As seen in the video below” is stated yet there are only images present and it may be initially unclear to the reader which figure is being referenced here.
# Avoid inserting inline citations like “[4] introduces an..” as it is a bit informal when you don’t explicitly name the subject.
# Don’t just cite the reference when discussing the problem formulation, explicitly write the model formulation and solution process using LaTex or equation visual editor.
# Your team should ideally create a numerical example independently. If you take a numerical example directly from a textbook, etc., you will need to get explicit permission from the author in writing and share that written permission with me.
# A numerical example is simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments). There is an Application section where you discuss the applications.
# The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).
* A section to discuss and/or illustrate the applications
# Some characters are randomly capitalized in this section.
* A conclusion section
# These variables should be defined before the conclusion section, they are out of place here. Also, please use normal text when explaining variables except for the variable symbol.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Interior-point method for NLP|Interior point method for NLP]] ==

* An introduction of the topic:
* Theory, methodology, and/or algorithmic discussions
# Primal-Dual formulation and comparison to the Barrier Method is not discussed.
# Include brief discussion about big O convergence rates.
# Need discussion about the concept of “central path” and the notion of self concordance
# Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
# Graphs and images are incorrectly formatted to the page. Consider proper alignment with respect to the text body.
# Use explicitly typed Latex equations instead of images to represent math programs and equations.
# Fix typo “optimisation”.
# Use LaTex code or equation editor to display all equations and variables (e.g., “xi ”, “μ”, etc.).
* At least one numerical example:
# There are formatting issues with figures 2,3. Please make sure to embed them within their respective sections.
* A section to discuss and/or illustrate the applications
* A conclusion section
# Minor character code typos in the conclusion.
# Also, please add more discussion in this section. Future research directions is a good start.
# There is a box "􏰐"
* References

== [[AdaGrad|Adagrad]] ==

* An introduction of the topic:
* Theory, methodology, and/or algorithmic discussions
# Include discussion on its variants (most important is AdaDelta).
# Include disadvantages of Adagrad, since this provides motivation for the discussion on the variants and improvements of Adagrad
# Include comparisons to other popular optimizers (particularly important is comparisons to regular SGD and Adam)
# Different convergence rates are possible depending on the setting where Adagrad is used, but this is not mentioned on the page currently. As such the regret bound section should be more thoroughly explained.
# Algorithm image is blurry. Either increase the fidelity or write the pseudocode directly in the wiki editor.
* At least one numerical example
# In the first sentence, “..take the following numerical example” should be followed by a colon.
# Fix typo “trayectory”.
* A section to discuss and/or illustrate the applications
# This section is too short; include specific applications in which input features are sparse and Adagrad excels.
# Add reference to the claim “Mainly, it is a good choice for deep learning models with sparse input features”.
* A conclusion section
* References

# Too few references overall, you should aggregate information from multiple sources (even if the base algorithm itself comes from a singular paper)

== [[McCormick envelopes|McCormick Envelopes]] ==

* Author list: OK but I suggest removing NetID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# First sentence is hard to read. Please consider keeping sentences below 25-30 words.
# No references provided. Please cite all sources.
# Figure 1 is provided in the middle between two sections. Please include in the introduction section.
* Theory, methodology, and/or algorithmic discussions
# References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# When using mathematical expressions and symbols, please use the equation editor. (e.g., x*y, exy + y, sin (x+y) - x2)
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# For the sample GAMS code, please place it in a code box
* A section to discuss and/or illustrate the applications
# Having a list is not enough. Please explain at least three applications in a few sentences each.
# This section should be at least a paragraph to discuss relevant applications. Each application should be explicitly linked to the page topic. A few keywords do not meet the requirement at all.
* A conclusion section:
* References
# References are not expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please follow the standard reference style - the current format is incorrect.
== [[Branch and bound (BB) for MINLP|Branch and Bound for MINLP]] ==

* Author list:
** Remove NetIDS
** Please remove abbreviations from the title (i.e. BB).
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# Please cite sources appropriately: References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Introduction is very short for a well-recognized topic. Please expand significantly. You may refer to the Wiki examples to get an idea on writing the Introduction to a topic.
# An illustration might be useful here.
* Theory, methodology, and/or algorithmic discussions
# The algorithm described here considers only binary integer variables. However, MINLP problems may include non-binary integer variables too. Please update the method or provide a short description of the assumptions that the MINLP problem needs to satisfy in order for the presented technique to be applicable.
# Use linked citations please as the Wiki template above.
# Please provide steps in a more organized way. Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
# Step 2 is missing yet it is referenced in the text multiple times. Please address this in addition to the above comment.
# An illustration might be useful here as well.
# Please explain what a Gomory Cut is. If the topic is available on optimization.cb.cornell.edu, you can link it.
# The current equations seem to be simple text written in Italics. All mathematical symbols and equations should be formatted via LaTex.
# Please format the math programs with equations and notations using formulations in lecture notes as templates.
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# Please show a step-by-step solution in the example. The solution is incomplete. The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).
# Please use the equation editor for equations or mathematical symbols. - All mathematical symbols and equations should be formatted via LaTex - this is a learning objective of the Wiki assignment. You can find some useful links on converting your equations/symbols into LaTex code here: (<nowiki>https://optimization.cbe.cornell.edu/index.php?title=Help:Contents</nowiki>). Again, any formatting issue will incur a "compound" penalty in the grading.
# This example does not follow the MINLP structure discussed in the above section since binary variables are missing. Branch and bound may not be appropriate for such problems. Please provide an appropriate numerical example and solve it according to the above comments.
# Make sure your example is not taken from a book as that is strictly disallowed.
* A section to discuss and/or illustrate the applications
# This section is not well formatted. Please provide 3 applications and explain each in a few sentences and how BB for MINLP. Also, please eliminate having multiple sections (Application, Mathematical problem, industrial application). All these could be merged together.
# This section should be at least a paragraph to discuss relevant applications. Each application should be explicitly linked to the page topic. A few keywords do not meet the requirement at all.
* A conclusion section:
# The sentence is hard to understand "a scheme that grows exponentially because" please use a simple language. Is it also theoretically correct? It is also not mentioned and explained earlier. Thus, please avoid introducing new concepts or terms at the end.
# Please use summarizing sentences to describe earlier sections instead of introducing new concepts/discussion.
* References
# Too few references overall, you should aggregate information from multiple sources. A quick Google scholar search could provide relevant references.
# References are not expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please follow the standard reference style - the current format is incorrect.

2021 Cornell Optimization Open Textbook Feedback

2021-12-06T03:05:21Z

Asa273: /* Branch and Bound for MINLP */

== [[Lagrangean duality|Lagrangian duality]] ==
* Author list, sections and TOC
# Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.
# Remove cornell ID from Author list
* An introduction of the topic
# This section includes sentences on constructing the dual problem and is referred to as Lagrangian relaxation (LR). This is incorrect, please fix the definition of LR.
# Definitions of LR and its relation to duality should be double checked and re-written.
# Only one reference is present in this section. Please add more relevant references by expanding this section.
# Consider merging the “introduction” and “history” sections.
# In the titles, please change the font from bold to normal to have consistent formatting in the site.
* Theory, methodology, and/or algorithmic discussions
# The Lagrangian variables associated with equality constraints h(x) are unbounded but the Lagrangian dual problem states them as non-negative. Please fix the same.
# Also to construct a dual, we do not change minimization to maximization directly. We observed such things in the examples in lecture notes due to simplification. The lagrangian dual problem would be minimize (,).
# Adding to the previous point, the Lagrangian is a lower bound on the original objective; the solution to the primal and dual or only equivalent if the duality gap is 0. You reference this in one section, but this is after your statement “Hence, solving the dual problem, which is a function of the Lagrangian multipliers (𝜆*) yields the same solution as the primal problem, which is a function of the original variables (x*). “. Please clarify the specific conditions that must hold for the solution of the dual to be equal to the primal’s.
# You refer to the “Complementary Slackness Theorem”, but don’t actually write the mathematical representation of complementary slackness. Please fix this. Also consider including the derivation of the complementary slackness condition, as it is both easy and short. Boyd is a good reference for this.
# Last step of the “process” subsection also needs updating according to the previous comments.
# The inline notations should also be typed using LaTex.
# Please use the LaTex code or equation editor for min, s.t., etc.
* At least one numerical example
# Only one dual variable is associated with each constraint. The numerical example uses two for the first and second constraint which is unnecessary. Please update it accordingly for both constraints. This particular example will only have two dual variables instead of the five dual variables used currently.
# All consecutive steps need to be updated since the dual variables would be updated.
# After substitution the nonlinear function should be further simplified. The current expression reads like a highly nonlinear function but can be easily simplified.
# Similar to the comments in the methodology section, inverting minimize to maximize is incorrect. Please update the dual objective function and domain of dual variables accordingly.
# Please use the LaTex code or equation editor for min, s.t., etc.
* A section to discuss and/or illustrate the applications
# Bullet points could be used to state the last four real-world examples that explain the physical meaning of the primal and dual problems.
# Add references for the last set of applications.
* A conclusion section
# This section contains a few typos. Please fix the same.
* References
# Some citations' hyperlinks are displaying.

== [[Disjunctive inequalities|Disjunctive Inequalities]] ==

* Author list
# Missing course section and semester
# Remove cornell ID
* An introduction of the topic
# No citations are present in this section.
# “mixed-integer programming (MIP)” should be used instead of “multiple integer programming (MIP)”. Please fix this error.
* Theory, methodology, and/or algorithmic discussions
# The abbreviation MILP is not previously defined. Please fix this issue.
# You consistently use the negative sign instead of the NOT operator for y (-y instead of ¬y).
# Some inconsistencies with the spacing of variables, constraints, etc., under the “General” section that need to be fixed.
# Typo in “This is shown below by M1, M2, y1, and y1:” where y1 needs to be changed to y2. Why use two different Big-M variables here? Elsewhere in the Wiki you only use one so this could lead to confusion with a general audience. Also if this was taken from the lecture notes then it needs to be cited.
* At least one numerical example
# Please reformulate and solve a complete numerical example rather than just reformulating a general example. Demonstrate the use of Big-M and Convex Hull formulation in an optimization problem that provides details such as individual steps in the problem solving process and final results. The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results.
# Add space between vee (V) operator and brackets in first line of Latex
# Please format variables correctly, for example, use <math>x_1</math> instead of x1.
* A section to discuss and/or illustrate the applications
# Please format the equations appropriately either by using latex code or the visual editor. These images are NOT acceptable!
* A conclusion section
# There is no conclusion presented in this section at all.
* References
# The included references have NOT been used anywhere in the Wiki. Add references for sentences that are not common knowledge and please link them appropriately with the text in Wiki. If the figures used here were not original works, you must also cite them.
# There are many papers on this topic. A simple Google (Scholar) search could provide you with sufficient references to cite.
# Many important references of this topic are missing.
# Please consider linking the references as demonstrated in the Wiki tutorial on Canvas and in this template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

==[[Stochastic programming|Stochastic Programming]] ==

* Author list: Remove cornell IDs
* An introduction of the topic
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
# This section only includes two sentences on Stochastic programming (SP), while the rest gives examples of uncertainty. Please discuss the need for SP in the presence of uncertainty. Also, discussion on robust optimization and its limitations should be removed since it is out of place.
* Theory, methodology, and/or algorithmic discussions
# Please avoid direct inline linkbacks to Wikipedia.
# The symbol “xi” in the methodology subsection should be explained.
* At least one numerical example
# Copying a numerical example "entirely" from a textbook is inappropriate. Your team should come up with a "numerical" case.
# No specific application context is needed for a numerical example.
# The inline notations (`x1`, `s1`) should also be typed using LaTex.
# Label all tables with a table number for better readability.
# Properly format the solution table with the label attached rather than the following sentence. The solution table looks different from the others, please fix this for consistency.
* A section to discuss and/or illustrate the applications;
# I suggest eliminating citing the last name of the first author (i.e. Zhou et al.)
* A conclusion section
* References
# URLs of some citations are not properly formatted (not showing the hyperlinks).

== [[Exponential transformation|Exponential Transformation]] ==

* Author list
# Missing course section
# Remove cornell ID
* An introduction of the topic
# Please expand the introduction.
# Please aim for a maximum average sentence length of ~25 words. Last sentence with 51 words is hard to read.
# Second Sentence: please change the word “they” as it could make the meaning ambiguous
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
# If you use abbreviations, please introduce them (e.g. NLP,MINLP)
* Theory, methodology, and/or algorithmic discussions
# Please explain the transformation in words along with equations
# Terms like posynomial should be described in detail.
# Please move the numerical example to the section below
# The “(eq 1)” is not needed here.
# Please expand this section.
* At least one numerical example
# In the third equation of the numerical example, it is confusing to have coefficients after numbers. Some readers may read it as an exponent.
# Last equation in this section after “further linearization” is incorrect. This equation cannot be further linearized, please fix this.
# Please explain the steps in the numerical examples in detail. The step-by-step solution should be provided.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# Missing part of text: “Proof of convexity of with positive definite test of Hessian…”
# Applications are not numerical examples. Please refer to this link for example of applications: [[Duality|https://optimization.cbe.cornell.edu/index.php?title=Duality]]
# Citation 7 is missing in current applications
# The section current applications is redundant
# Please use the LaTex code or equation editor for min, s.t., etc.
# Under current applications, do not just use a hyperlink to describe an application. Actually describe it. And properly inline citation style should be used instead of the hyperlink.
# The convexification application of MINLP can be further simplified for binary variables. Please refer to the lecture slides for more information.
* A conclusion section
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
* References
# Please consider linking the references by using this as Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Citation 7 is missing in current applications

== [[Sparse Reconstruction with Compressed Sensing|Sparse reconstruction with Compressed Sensing]] ==
This Wiki needs a significant rewrite. Please go through the comments for details.

* An introduction of the topic
# The introduction section should include information about the problem and its implications presented briefly. Please use full sentences to write this Wiki. You may use tools like Grammarly to check sentence formation and grammar.
# This section includes several typos like “sub modual”. Please fix them throughout the wiki and delete them if not required.
# Many abbreviations are used before previously defining them. Please define these abbreviations before using them in the text.
# This section is incomprehensible in its current form. Please rewrite with proper comprehension.
# Equations and math symbols need proper reformatting. The current version reads like text (along with equations) copy-pasted from a specific source. All mathematical symbols and equations should be formatted via LaTex - this is a learning objective of the Wiki assignment. You can find some useful links on converting your equations/symbols into LaTex code here: (https://optimization.cbe.cornell.edu/index.php?title=Help:Contents).
# Try to place the figure at the top of the Wiki between the main text.
# Avoid pronouns such as “we”.
# I suggest the use of more formal abstract illustrations.
* Theory, methodology, and/or algorithmic discussions
# Equations and symbols need proper reformatting.
# Lemmas and theorems are not expected for this Wiki. Sparse reconstruction is a straightforward concept but is unnecessarily complicated here. Please refer to other Wiki examples to get an idea of what the Wiki should convey.
# All equations need to be better formatted.

* At least one numerical example
# Numerical example is missing.
# Every iteration should be clearly presented, and solved "step-by-step".
* A section to discuss and/or illustrate the applications
# Having a list is not enough. Please explain at least three applications in a few sentences each.
* A conclusion section
# Conclusion section is missing.
* References
# The current reference list is not correctly formatted. References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Portfolio optimization|Portfolio Optimization]] ==

* Author list
# Remove cornell id
* An introduction of the topic
# The introductory sentence should be rephrased. The action of minimizing the risks does not inherently maximize the gains, rather PO aims to maximize gains whilst minimizing risks.
# Amount of whitespace can be reduced by changing the orientation of Figure 1 and the sentences in this section.
# Define terms such as risk, return, portfolio, etc., when you introduce them. Assume that the reader may not know much about finance. This goes for all other sections as well.
* Theory, methodology, and/or algorithmic discussions
# A brief mention of modern portfolio theory (i.e.. Markowitz) would be appropriate in this section.
# Several grammatical errors here involving sentence structure and clarity. Some questionable semantics (e.g., “The portfolio optimization mainly assumes two directions.”) and syntax (phrases such as “.. is as follows” should be followed by a colon). Misuse of commas and missing commas in this section. Two sentences introducing E(rp) and w should be combined into one.
# Use LaTex to distinguish variables written within a sentence, such as m and n.
# Rephrase “Cut the relevant information and conditions in the portfolio optimization, as well as the final requirements into the relevant variables, constraints and linear functions of the linear programming problem.”
# An explanation of a few common constraints would be helpful, rather than just including a table.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Solving the numerical example by GAMS is inappropriate. Please provide detailed step-by-step calculation results.
# All tables need to be labeled.
# Include figure number in label for consistency.
# Fix misspelling “dolling decision variables”.
# Use LaTex for all variables, equations, and constraints here.
# Example 2 table is hard to read, so making it bigger would help.
# Remove the “Using excel as the solver” part from the sentence before the solution discussion.
# Some grammatical errors here (phrases such as “.. is as follows” should be followed by a colon).
* A section to discuss and/or illustrate the applications
# Rephrase “Portfolio optimization can be used to screen investment projects that meet investors, rationally allocate investment amounts, etc.”
# Not sure “relevant” is the correct word choice here.
# You need more specific examples with the utility of portfolio optimization, this section is quite general as is. Some more detail and focus on real-world applications in the financial industry that relate to retirement planning, financial security, economic stability, etc., would be helpful.
* A conclusion section
# Need some commas here.
# The sentence “Linear programming has been around since the 1940’s and has such a wide base of applications” is not necessary.
* References
# Please consider linking the references as demonstrated in the Wiki tutorial on Canvas and in this template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove white space between end of sentences and reference numbers.

== [[Chance-constraint method|Chance constraint method]] ==

* Author list:
* An introduction of the topic
# Please consider correcting a few grammatical errors: “pre-planned for”, “god”, “certain levels of feasibility is guaranteed in what are”, and “Performance of a system”
# In “Chance-constraint”, it is capitalized randomly throughout the introduction. Please correct.
# Please use technical language to briefly introduce chance-constrained programming. Words like “acts of god”, “cost of doing business” are not appropriate for a technical Wiki.
* Theory, methodology, and/or algorithmic discussions
# Please add a citation to the first sentence.
# Xi is an uncertainty/randomness variable. It is better to use clear language.
# Please use the mathematical editor for adding explanations in the text. Using “ x is a decision variable” is hard to read. Same for f(x) and others.
# Theory is insufficient. Please expand and explain different approaches.
# Please add pros and cons explicitly as a list.
# Explain the physical meaning for examples of chance constraints along with all the notations used.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please remove this example as it is directly from this book. The example should be purely numerical without any background.
# Please use the equation editor for min, st., etc.
# Please use the mathematical editor for adding explanations in the text. Using “ x is a decision variable” is hard to read. Same for f(x) and others.
# Please change the table format so as not to confuse the reader.
# Multiple instances of [Chart to be added] are missing.
# Example is incomplete.
# Avoid pronouns such as “we”.
* A section to discuss and/or illustrate the applications
# Please connect several grammatical and spelling errors: “real life application”, Energy creation, particularly in renewable sources, have high variabilities”, and others
# “Zhao, Xue, Cao, and Zhang”. No need to list all authors within the article. Provide a reference is sufficient. If authors must be mentioned, (Zhao et al.) should be ok.
* A conclusion section
# Uniqueness and universality earlier are not clear to me. If they are not discussed earlier in the application, it would be better not to introduce new discussions in the conclusion.
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
* References
# References seem to vary in format. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Bayesian Optimization]] ==
* Section titles should not be "bold". Please double check using source editor on the section titles.
* Contents: The section titles should NOT be in bold to avoid strange format in TOC. Any formatting issue will incur a penalty in the grading.
* Author list: Remove cornell ID, Please check names
* Introduction
# The introduction is too general and not substantial enough. For example, simply saying BayesOpt is useful when the objective function is unknown obscures exactly HOW it is useful (namely, computational efficiency in applications where ground truth sampling is expensive). Discussion on applications should be moved to a separate section.
# Machine learning rarely includes black-box functions to be optimized. Bayesian optimization is almost never used for optimizing ML loss functions but can instead be used for hyperparameter optimization. Please update such claims in this section.
* Theory, methodology, and/or algorithmic discussions
# Captions need reformatting.
# Consider italicizing keywords rather than bolding.
# Please add a citation to the first sentence.
# Discussion on acquisition functions should include comparisons, tradeoffs, and reasons to use one over the other. Should also note that expected improvement is the most widely used in practice, and explain.
# Avoid pronouns such as “we”.
# Please write equations in the Wiki instead of attaching images for equations.
# Acquisition function figure could be made larger and clearer to improve readability.
* At least one numerical example
# Any references to functions or methods in code ‘e.g. fmin’ should be properly formatted as code-stylized text.
# Please use the equation editor for min, st., etc.
# Avoid including a figure of the code for this example and explicitly describe the steps to the modeling and solution process instead.
# Avoid pronouns such as “our” and “we”.
* A section to discuss and/or illustrate the applications
* A conclusion section
# Please do not use brackets to enclose lists.
# Some claims here should be supported by references. Please cite each source after its sentence.
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Try to avoid references to “pop” machine learning blogs where anyone can be an author. (e.g. towardsdatascience)
# All references are URLs. Please cite publications and literature.
# A simple Google Scholar search would give you many references.

Notes on grammar: Needs some work. Several instances where colons are inappropriately inserted mid sentence or in subheadings. Explanations are not terse. Several instances of switching between personal and impersonal style of writing, which is distracting.

== [[Conjugate gradient methods]] ==

* Author list: Remove cornell ID
* Introduction
# All inline notations (e.g., `x`, `A`) should be typed using LaTex.
* Theory, methodology, and/or algorithmic discussions
# All equations need to be better formatted.
# Is Gauss-Newton no longer referenced?
# Theorems listed in the first section should be accompanied with high level explanation, not just a list of the theorems themselves. The page should read like an article, with proper flow.
# Please indent equation blocks.
# Please properly format pseudocode.
* At least one numerical example
# Steps should be accompanied with explanation, or reference to the corresponding step in the pseudocode.
# Please properly format in a more organized manner, aligning equations appropriately and demarcating steps appropriately.
* A section to discuss and/or illustrate the applications
# Consider including 2 additional examples of applications
* A conclusion section
# Consider adding future research directions
* References
# Reference primary sources rather than Wikipedia
# Too few references.
# More references should be added. A simple Google Scholar search would give you many references.

== [[Geometric programming|Geometric Programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Examples of applications in this section use the same reference. Please cite their individual sources.
* Theory, methodology, and/or algorithmic discussions
# The symbol denoting the domain in the definition of a monomial is unclear. Please clarify it or fix this if it is incorrect.
# Definition of posynomial refers to section 2.1 which is missing from the Wiki (sections are not numbered in the main text).
# In the generalized posynomial subsection, bullet points do not tell us why h(x) is posynomial. Either provide reasons or simply state that h(x) is posynomial. Also explain why h3 is a generalized posynomial.
# Additional theory on the feasibility analysis could be provided in this section.
* At least one numerical example
# In the transformation example, the last two constraints could also be simplified by applying a natural logarithm on both sides. Please update them as well.
* A section to discuss and/or illustrate the applications
# The figure in this section needs to be labeled.
# The figure needs to be resized and perhaps aligned to the center.
* A conclusion section:
# Please avoid vague language such as: “This makes”.
# Please avoid opinionated statements: “one of the best ways”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# This Wiki has very few references. A quick Google Scholar search may provide relevant references.

== [[Adam]] ==

* Author list
* An introduction of the topic
# Some grammatical errors here, mostly related to the need for commas in certain places (e.g., “Before Adam..”).
# Some minor errors with parts of speech throughout the section, need to revisit phrases such as “which has broader scope in future for”, etc.
# Try splitting up some of the longer sentences in this section, a couple are hard to read.
# Avoid definitive statements about Adam being the best or always better solver, as this is simply not true (the choice of the “best” optimizer is setting-dependent). Use language such as “Research has shown that Adam has demonstrated superior experimental performance over..” and then cite academic references to back this claim.
# What does adam stand for? Introduction is insufficient. Please expand.
* Theory, methodology, and/or algorithmic discussions
# Revise grammar here, noticing some missing commas and uncapitalized word after period.
# Rephrase “second one is to update the old position with the updated position”.
# Use LaTex code or equation editor to display all equations and variables in this section, and actual subscripts instead of “m_t”, etc.
# Avoid inserting inline citations after words like “According to..” or “This article..” as it is a bit informal. This could be rephrased or changed to something like “According to author,^[2] …” with author name inserted.
# Remove white space before the period in RMSP discussion.
# Please provide a pseudocode.
# Please use list the two methods here “Adam is a combination of two gradient descent methods which are explained below”
# Please expand the theory section significantly. Theoretical convergence properties should be discussed, even if briefly.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
* A section to discuss and/or illustrate the applications
# Same comment as before, consider replacing inline citations after words like “According to..”.
* A conclusion section
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Try to avoid references to blogs and use peer-reviewed academic references instead.
# Too few references.
# More references should be added. A simple Google Scholar search would give you many references.

== [[A-star algorithm|a* algorithm]] ==

* Author list: Remove cornell ID
* Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.
* An introduction of the topic:
# Weird spacing between paragraphs. Please fix this issue.
# In the titles, please change the font from bold to normal to have consistent formatting in the site.
# Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.
# There are no citations in the introduction. Please cite every source.
* Theory, methodology, and/or algorithmic discussions
# Please add the mathematical description of the algorithm.
# Reference style varies in sentences. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please fix grammatical and spelling errors as (“from current position to the goal”, “There are a lot of discussions”, etc). Also, many hyphens are missing as “non playable”.
# In algorithms, it is a standard to add high-level description (i.e. pseudocode or flowchart). Please incorporate it.
# Use LaTex code or equation editor to display all equations and variables in this section (e.g., “f(n)...”, “h(n)..”, etc.). This goes for other sections as well.
* At least one numerical example
# The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.
# Instead of writing things like “The above image..”, label each figure and use the figure number to refer to it in text.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# No references in the applications. Please cite every source
# Preferably, add at least an additional application.
* A conclusion section
# Conclusion should summarize descriptions. Please modify it to provide a summary.
# Please pay attention to the length and structure of sentences here and in the full page. First sentence is hard to read.
* References
# References seem to vary in format and are not linked correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Incorrect reference style. Please follow the example and use the template.

== [[Job shop scheduling|Job-Shop Scheduling Problem]] ==

* An introduction of the topic
# The current introduction to the jobshop scheduling problem has only two sentences in addition to the parameter description. Introduction typically contains information about the problem, its importance in the real-world, and some information about the solution techniques and their types to solve the problem. Please add some information that covers the above.
* Theory, methodology, and/or algorithmic discussions
# It is unclear whether the assumptions stated in this section are required to apply the following solution techniques. Please clarify the same. Also use complete sentences to state them.
# The branch and bounds method described in this section only discusses the solution technique for problems with one machines. However, branch and bound is a general technique that can be applied to any MILP problems with varying scales. Please update the “methods” section to be as general as possible.
# Since this Wiki focuses on jobshop scheduling, at least two methods are expected. Branch and bound is a general MILP technique, so, it is recommended to add a tailored technique that can only solve specific jobshop scheduling problems. Solving the numerical example with this technique is not necessary.
# Reference to the branch and bound technique described in this section is a “youtube” video. Please add references in literature that describe this method in detail. The method used in this video is highly tailored for a single machine application. This is also an incorrect way to cite a reference. Please keep this section as general as possible.
# Use LaTex code or equation editor to display all equations and variables in this section and all other sections as well.
# Check grammar in this section. For example, phrases like “are as follows” need to be followed by a colon and not a period.
# Consider rewriting the assumptions as a list in this section.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# The example used in this section is exactly the same as the one in the youtube video. Please use a modification of this example or choose another example/method to demonstrate the solution technique. Your team should ideally create a numerical example independently. If you take a numerical example directly from a particular source, you will need to get explicit permission from the textbook author in writing and share that written permission with the instructors.
# The figure in this section is not numbered when all others are. Relabel this figure for consistency and its number to refer to it in-text.
# A numerical example should be simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments).
* A section to discuss and/or illustrate the applications
# This section should only focus on real-world applications of the jobshop scheduling problem. But currently, this section includes additional information on solution techniques/complexity that is appropriate for the Introduction section. Please discuss the applications of the problem in this section.
* A conclusion section
# The meaning of “Operations applications” is unclear. Please explain or update if necessary.
# The current conclusion section does not properly summarize the problem. Please refer to other Wiki examples for an idea to update the section accordingly.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please reference media sources like reference 5 appropriately.
# A simple Google Scholar search would give you many "formal" references.

== [[Optimization in game theory]] ==

* Author list: remove cornell IDs.
* An introduction of the topic
# References are not linked. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
* Theory, methodology, and/or algorithmic discussions
# Why only a subsection on "Nash Equilibrium" is included in "Theory" section? Please re-format.
# Please edit references.
# Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm.
# Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.
* At least one numerical example
# Please organize the last part in a more readable format. Questions may be in bold and numbered, answers are more direct, etc.
# Remember to cite all images and tables.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# Very good, link the reference and cite all sources.
* A conclusion section
# Please add more summarizing especially from theory sentences and avoid long sentences.
* References
# Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Reference primary sources rather than Wikipedia
# Incorrect reference style. Please correct.

== [[Trust-region methods]] ==

* Author list:
# Remove cornell IDs. Author is also spelled incorrectly.
# Add the course section.
* An introduction of the topic
# References are not linked. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Use LaTex code or equation editor to display all equations and variables (e.g., “xk”, “f`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “we”. This goes for all other sections as well.
* Theory, methodology, and/or algorithmic discussions
# Organization of ideas in this section needs work.
# You have not defined explicitly why the Cauchy point is important to compute beyond a vague allusion to performance improvements, which is also wrong (it is useful because of its guarantees for convergence, not performance) It is also misspelled.
# Each approach should have accompanying explanation and motivation for why it is being discussed. It is not enough to outline the algorithm.
# Please make sure symbols are properly subscripted and superscripted (e.g. “pk” should be “p_k”
# Please format the algorithm in proper algorithmic pseudocode format.
# Little to no discussion on global convergence guarantees
# Please include discussion about the advantages and disadvantages of the algorithm
# Fix typo “couchy point”.
* At least one numerical example
# Any code functions (uminfunc) should have proper text formatting.
# The graph needs a better caption explaining how the axes are labeled and what data points are being shown.
# Please increase the quality of the figure. It is hard to see the red line.
# Add citation to “The Rosenbrock function is a non-convex function, introduced by Howard H. Rosenbrock in 1960, which is often used as a performance test problem for optimization algorithms.”
* A section to discuss and/or illustrate the applications
# The content in this section as it is currently does NOT describe applications, but rather different approaches within the trust region methodology. Please provide specific applications (e.g. TRPO in reinforcement learning).
* A conclusion section
# Please add more summary, future research directions for example is a good start.
* References
# Incorrect reference style.
# Please consider having the references as this Wiki template, <nowiki>https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization</nowiki>
# More references should be added. A simple Google Scholar search would give you many references.

*There are numerous misspellings, grammatical errors, and incorrect claims. Please fix these.

== [[Momentum]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Apart from an explanation on momentum, it is necessary to briefly point out the limitations of SGD and why momentum could help with these limitations. Please update it accordingly.
# Remove bold on “Momentum”.
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
* Theory, methodology, and/or algorithmic discussions
# Equation formatting is very poor and should be formalized.
# It is important to use technical language for this Wiki. Although a layman’s explanation is appreciated, it would be better to skip using words like “zig zagging”. Try to explain all concepts in a technical language with few simplifications but NOT vice versa.
# The definition of the update rule for SGD with momentum looks incorrect, specifically the first expression. Please fix it and also explain all the parameters used.
# Use LaTex code or equation editor to display all equations and variables (e.g., “W”, “V`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “you”.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step". Since writing all iterations is not feasible, at least present a few iterations for both cases.
# Please try to label the plots that explains what each line color means.
# Starting point for SGD with momentum is different in explanation and the table. Please fix the same.
* A section to discuss and/or illustrate the applications
# Please use correct terminology like “optimizing non-convex functions” and not “training non-convex models”.
# Adam, Adadelta, and RMSprop are variants of SGD that already use momentum. Please double check the writing and update if necessary.
* A conclusion section
# Please refrain from using words like “zig zag” effects.
* References
# Almost all references used are URLs. Please try to add journal/conference articles or books for references, instead of directly citing the URLs. Please check the list below and run a quick Google (Scholar) search to identify relevant literature.

== [[Stochastic dynamic programming|Stochastic Dynamic programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Discussion on applications should be moved to a separate section.
* Theory, methodology, and/or algorithmic discussions
# Remove the grey box background of equations.
* At least one numerical example
* A section to discuss and/or illustrate the applications
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Outer-approximation (OA)|Outer-approximation]] ==

* An introduction of the topic
# See formatting guideline below
# Avoid opinionated statements such as “MINLP problems are usually the hardest to solve”.
# Rearrange the text such that the MINLP formulation is in the theory section and keep the introduction in words only.
* Theory, methodology, and/or algorithmic discussions
# Consider left aligning equations and optimization problem formulations by the “=”. See [[Stochastic programming|https://optimization.cbe.cornell.edu/index.php?title=Stochastic_programming]] for an example
# The sentence “The Outer-Approximation (OA) algorithm was first proposed by Duran and and Grossmann in 1986 to solve MINLP problems.” needs a reference.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# “Minimize” and “subject to” should be “min” and “s.t.” in MathType
* A section to discuss and/or illustrate the applications
# Does not explicitly point out why OA is applicable (and/or preferred) in these applications, rather than other MINLP approaches (show that the problem formulations are amenable to a solution approach through OA)
# The sentence “... an active research area and there exists a vast number of applications in fields such as engineering, computational chemistry, and finance.” needs references.
# Posting GAMS code on the page is generally inappropriate and discouraged. Please check with the TAs or me if you have a strong desire to post GAMS codes on the Wiki page. A typical textbook should not be limited to a specific software package. If the GAMS code must be posted, please also post ALL other software implementation versions, such as Pyomo and JuliaOPT, among others.
# Consider reformatting to make steps more readable. Inserting spaces and breaking down steps would help.
* A conclusion section
# Too short. Consider discussion on future research direction and discussion on uncertainty
# Please review abbreviations throughout the page. Why is MINLP redefined here? “Outer-Approximation is a well known efficient approach for solving convex mixed-integer nonlinear programs (MINLP)”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove "Template:Reflist"

== [[Unit commitment problem]] ==

* Author list
* An introduction of the topic
# Please expand the introduction and avoid discussions of examples or specific applications in this section.
# The sentence “Nonlinear, Non-convex programming optimization problem.” doesn’t make sense by itself and Non-convex shouldn’t be capitalized.
* Theory, methodology, and/or algorithmic discussions
# Figure/image format should be revised to better display the content.
# Uppercase characters are used randomly (e.g., “non-convex transmission Constraints”) . Please follow correct language conventions for sentence structure.
# Avoid inserting inline citations after words like “written in matrix form as equation [3]..” or “presented in [3]...” as it is a bit informal when you don’t explicitly name the subject. Also these two sentences are grammatically incorrect and appear to be missing an ending period and comma, respectively.
# Don’t say “written in matrix form as equation..” and just cite the reference, actually write out the equation.
# Properly label the figure in this section with a figure number and improve visibility by making it larger.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Label the figures in this section properly with figure numbers.
# Fix typo “while minimize” to “while minimizing”.
# Avoid pronouns such as “we”.
# Use the equation editor when typing equations.
# A numerical example is simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments). There is an Application section where you discuss the applications.
# The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).
* A section to discuss and/or illustrate the applications:
# I suggest changing the order of the subtitles here. For example, Single-Period Unit Commitment.
* A conclusion section
* References

== [[Frank-Wolfe]] ==

* Author list:
* An introduction of the topic
# I suggest highlighting disadvantages along with advantages.
* Theory, methodology, and/or algorithmic discussions
# “[n x 1] matrix” please use the equation editor to express mathematical descriptions and symbols (p,b, etc)
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please show at least a few iterations. Even for smaller examples if needed. Report the final solution.
# Please use the LaTex code or equation editor for min and include s.t., etc.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps. For your example, please explicitly state that the derivative is taken etc.
* A section to discuss and/or illustrate the applications:
* A conclusion section
# Same as the introduction. Pros and cons should be evaluated together!
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Line search methods|Line Search Method]] ==

* Author list
* An introduction of the topic
# Expand the introduction and avoid discussion on some of the specific steps in the solution process.
# Provide references here.
* Theory, methodology, and/or algorithmic discussions
# The phrase “are as follows” in the steepest descent method discussion needs to be followed by a colon.
# Rephrase “has a nice convergence theory” and cite a reference for this claim.
# Avoid pronouns such as “we”.
# Add citation after “.. proposed by Phillip Wolfe in 1969.”
# Figure 1 is between two sections. Please fix this issue.
* At least one numerical example:
# Add some space between iterations or subsection break
* A section to discuss and/or illustrate the applications:
# Too few references in this section.
# Last paragraph makes some claims without references.
* A conclusion section
* References
# References should be properly formatted. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Piecewise linear approximation|Piecewise Linear Approximation]]==

* Author list
* An introduction of the topic
# The content of this section is good, but there are some issues with sentence clarity and some other grammatical errors. Please revisit this section and make changes accordingly.
* Theory, methodology, and/or algorithmic discussions
# Fix typo “to force the x’ values become associated with”.
* At least one numerical example
* A section to discuss and/or illustrate the applications
# Please aim for a maximum average sentence length of ~25 words. Some of these longer sentences are hard to read.
* A conclusion section
# Expand the conclusion section to be longer than one sentence. The conclusion section to include a brief summary of what was discussed above, an emphasis on it’s significance, and a brief discussion of future extensions and research direction if applicable.
* References
# Include hyperlinks to sources when possible.

== [[Mathematical programming with equilibrium constraints|Mathematical Programming with Equilibrium constraints]] ==

* An introduction of the topic
# This section includes several terms like variational inequalities, constraint qualifications that were not discussed in the class. Please add a sentence to explain them before using them.
* Theory, methodology, and/or algorithmic discussions
# The meaning of parameter vector x is unclear. Please add more information or update if necessary.
# Equations and symbols in the PIPA subsection are not formatted correctly. Please use the same formatting for all equations, so they read as mathematical equations and not text. This goes for all other sections as well.
# Use equations instead of images to represent math programs and equations in the Implicit Descent and SQP subsection.
# Apart from the steps for each solution technique, please also add a few sentences that describe each method.
* At least one numerical example
# Please define the terms like NCP, MP before abbreviating them. Also try not to unnecessarily abbreviate simple terms.
# Equations should be typed by LaTex. Images for equations are unacceptable.
# GAMS code is strongly discouraged. Please solve the problem "step-by-step".
# The selected numerical example is fine but is directly solved with the MPEC solver in GAMS. Try to solve it manually like the homework/in-class problems step by step using the steps described in the previous section by choosing any of the methods.
# Avoid using figures in the equations (subject to etc)
* A section to discuss and/or illustrate the applications
# Add references to “power management, highway pricing, chemical process engineering, and traffic planning.”
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# This Wiki contains very few references. Please check the list below and run a quick Google (Scholar) search to identify relevant literature.

== [[Wing shape optimization|Wing shape Optimization]] ==

* Author list: Remove cornell ID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC. Any formatting issue will incur a penalty in the grading.
* An introduction of the topic
# The introduction is missing several references (e.g., “software packages like computational fluid dynamics..”, sentences containing things that aren’t common knowledge, performance claims, etc.)
# Avoid discussion involving finer details of subject methods in this section.
# In the titles, please change the font from bold to normal to have consistent formatting in the site. Same applies to box of content!
* Theory, methodology, and/or algorithmic discussions
# Properly cite the CFD package, don’t just include a link.
# Properly label the figure with a figure number.
# Consider removing white space between isolated sentences to improve readability.
* At least one numerical example
# If you’ve already defined an abbreviation (CFD), there is no need to define it again. Just use the abbreviation.
# Avoid pronouns such as “we” or “they”.
# Phrases like “under the following” need to be followed by a colon.
# Properly label the figure with a figure number and consider making them larger to improve visibility. Call the reader's attention to the figures in text by referencing the figure number.
# “As seen in the video below” is stated yet there are only images present and it may be initially unclear to the reader which figure is being referenced here.
# Avoid inserting inline citations like “[4] introduces an..” as it is a bit informal when you don’t explicitly name the subject.
# Don’t just cite the reference when discussing the problem formulation, explicitly write the model formulation and solution process using LaTex or equation visual editor.
# Your team should ideally create a numerical example independently. If you take a numerical example directly from a textbook, etc., you will need to get explicit permission from the author in writing and share that written permission with me.
# A numerical example is simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments). There is an Application section where you discuss the applications.
# The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).
* A section to discuss and/or illustrate the applications
# Some characters are randomly capitalized in this section.
* A conclusion section
# These variables should be defined before the conclusion section, they are out of place here. Also, please use normal text when explaining variables except for the variable symbol.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Interior-point method for NLP|Interior point method for NLP]] ==

* An introduction of the topic:
* Theory, methodology, and/or algorithmic discussions
# Primal-Dual formulation and comparison to the Barrier Method is not discussed.
# Include brief discussion about big O convergence rates.
# Need discussion about the concept of “central path” and the notion of self concordance
# Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
# Graphs and images are incorrectly formatted to the page. Consider proper alignment with respect to the text body.
# Use explicitly typed Latex equations instead of images to represent math programs and equations.
# Fix typo “optimisation”.
# Use LaTex code or equation editor to display all equations and variables (e.g., “xi ”, “μ”, etc.).
* At least one numerical example:
# There are formatting issues with figures 2,3. Please make sure to embed them within their respective sections.
* A section to discuss and/or illustrate the applications
* A conclusion section
# Minor character code typos in the conclusion.
# Also, please add more discussion in this section. Future research directions is a good start.
# There is a box "􏰐"
* References

== [[AdaGrad|Adagrad]] ==

* An introduction of the topic:
* Theory, methodology, and/or algorithmic discussions
# Include discussion on its variants (most important is AdaDelta).
# Include disadvantages of Adagrad, since this provides motivation for the discussion on the variants and improvements of Adagrad
# Include comparisons to other popular optimizers (particularly important is comparisons to regular SGD and Adam)
# Different convergence rates are possible depending on the setting where Adagrad is used, but this is not mentioned on the page currently. As such the regret bound section should be more thoroughly explained.
# Algorithm image is blurry. Either increase the fidelity or write the pseudocode directly in the wiki editor.
* At least one numerical example
# In the first sentence, “..take the following numerical example” should be followed by a colon.
# Fix typo “trayectory”.
* A section to discuss and/or illustrate the applications
# This section is too short; include specific applications in which input features are sparse and Adagrad excels.
# Add reference to the claim “Mainly, it is a good choice for deep learning models with sparse input features”.
* A conclusion section
* References

# Too few references overall, you should aggregate information from multiple sources (even if the base algorithm itself comes from a singular paper)

== [[McCormick envelopes|McCormick Envelopes]] ==

* Author list: OK but I suggest removing NetID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# First sentence is hard to read. Please consider keeping sentences below 25-30 words.
# No references provided. Please cite all sources.
# Figure 1 is provided in the middle between two sections. Please include in the introduction section.
* Theory, methodology, and/or algorithmic discussions
# References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# When using mathematical expressions and symbols, please use the equation editor. (e.g., x*y, exy + y, sin (x+y) - x2)
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# For the sample GAMS code, please place it in a code box
* A section to discuss and/or illustrate the applications
# Having a list is not enough. Please explain at least three applications in a few sentences each.
# This section should be at least a paragraph to discuss relevant applications. Each application should be explicitly linked to the page topic. A few keywords do not meet the requirement at all.
* A conclusion section:
* References
# References are not expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please follow the standard reference style - the current format is incorrect.
== [[Branch and bound (BB) for MINLP|Branch and Bound for MINLP]] ==

* Author list:
** Remove NetIDS
** Please remove abbreviations from the title (i.e. BB).
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# Please cite sources appropriately: References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Introduction is very short for a well-recognized topic. Please expand significantly. You may refer to the Wiki examples to get an idea on writing the Introduction to a topic.
# An illustration might be useful here.
* Theory, methodology, and/or algorithmic discussions
# The algorithm described here considers only binary integer variables. However, MINLP problems may include non-binary integer variables too. Please update the method or provide a short description of the assumptions that the MINLP problem needs to satisfy in order for the presented technique to be applicable.
# Use linked citations please as the Wiki template above.
# Please provide steps in a more organized way. Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
# Step 2 is missing yet it is referenced in the text multiple times. Please address this in addition to the above comment.
# An illustration might be useful here as well.
# Please explain what a Gomory Cut is. If the topic is available on optimization.cb.cornell.edu, you can link it.
# The current equations seem to be simple text written in Italics. All mathematical symbols and equations should be formatted via LaTex.
# Please format the math programs with equations and notations using formulations in lecture notes as templates.
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# Please show a step-by-step solution in the example. The solution is incomplete. The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).
# Please use the equation editor for equations or mathematical symbols. - All mathematical symbols and equations should be formatted via LaTex - this is a learning objective of the Wiki assignment. You can find some useful links on converting your equations/symbols into LaTex code here: (<nowiki>https://optimization.cbe.cornell.edu/index.php?title=Help:Contents</nowiki>). Again, any formatting issue will incur a "compound" penalty in the grading.
# This example does not follow the MINLP structure discussed in the above section since binary variables are missing. Branch and bounds may not be appropriate for such problems. Please provide an appropriate numerical example and solve it according to the above comments.
# Make sure your example is not taken from a book as that is strictly disallowed.
* A section to discuss and/or illustrate the applications
# This section is not well formatted. Please provide 3 applications and explain each in a few sentences and how BB for MINLP. Also, please eliminate having multiple sections (Application, Mathematical problem, industrial application). All these could be merged together.
# This section should be at least a paragraph to discuss relevant applications. Each application should be explicitly linked to the page topic. A few keywords do not meet the requirement at all.
* A conclusion section:
# The sentence is hard to understand "a scheme that grows exponentially because" please use a simple language. Is it also theoretically correct? It is also not mentioned and explained earlier. Thus, please avoid introducing new concepts or terms at the end.
# Please use summarizing sentences to describe earlier sections instead of introducing new concepts/discussion.
* References
# Too few references overall, you should aggregate information from multiple sources. A quick Google scholar search could provide relevant references.
# References are not expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please follow the standard reference style - the current format is incorrect.

2021 Cornell Optimization Open Textbook Feedback

2021-12-05T20:19:48Z

Asa273: /* Mathematical Programming with Equilibrium constraints */

== [[Lagrangean duality|Lagrangian duality]] ==
* Author list, sections and TOC
# Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.
# Remove cornell ID from Author list
* An introduction of the topic
# This section includes sentences on constructing the dual problem and is referred to as Lagrangian relaxation (LR). This is incorrect, please fix the definition of LR.
# Definitions of LR and its relation to duality should be double checked and re-written.
# Only one reference is present in this section. Please add more relevant references by expanding this section.
# Consider merging the “introduction” and “history” sections.
# In the titles, please change the font from bold to normal to have consistent formatting in the site.
* Theory, methodology, and/or algorithmic discussions
# The Lagrangian variables associated with equality constraints h(x) are unbounded but the Lagrangian dual problem states them as non-negative. Please fix the same.
# Also to construct a dual, we do not change minimization to maximization directly. We observed such things in the examples in lecture notes due to simplification. The lagrangian dual problem would be minimize (,).
# Adding to the previous point, the Lagrangian is a lower bound on the original objective; the solution to the primal and dual or only equivalent if the duality gap is 0. You reference this in one section, but this is after your statement “Hence, solving the dual problem, which is a function of the Lagrangian multipliers (𝜆*) yields the same solution as the primal problem, which is a function of the original variables (x*). “. Please clarify the specific conditions that must hold for the solution of the dual to be equal to the primal’s.
# You refer to the “Complementary Slackness Theorem”, but don’t actually write the mathematical representation of complementary slackness. Please fix this. Also consider including the derivation of the complementary slackness condition, as it is both easy and short. Boyd is a good reference for this.
# Last step of the “process” subsection also needs updating according to the previous comments.
# The inline notations should also be typed using LaTex.
# Please use the LaTex code or equation editor for min, s.t., etc.
* At least one numerical example
# Only one dual variable is associated with each constraint. The numerical example uses two for the first and second constraint which is unnecessary. Please update it accordingly for both constraints. This particular example will only have two dual variables instead of the five dual variables used currently.
# All consecutive steps need to be updated since the dual variables would be updated.
# After substitution the nonlinear function should be further simplified. The current expression reads like a highly nonlinear function but can be easily simplified.
# Similar to the comments in the methodology section, inverting minimize to maximize is incorrect. Please update the dual objective function and domain of dual variables accordingly.
# Please use the LaTex code or equation editor for min, s.t., etc.
* A section to discuss and/or illustrate the applications
# Bullet points could be used to state the last four real-world examples that explain the physical meaning of the primal and dual problems.
# Add references for the last set of applications.
* A conclusion section
# This section contains a few typos. Please fix the same.
* References
# Some citations' hyperlinks are displaying.

== [[Disjunctive inequalities|Disjunctive Inequalities]] ==

* Author list
# Missing course section and semester
# Remove cornell ID
* An introduction of the topic
# No citations are present in this section.
# “mixed-integer programming (MIP)” should be used instead of “multiple integer programming (MIP)”. Please fix this error.
* Theory, methodology, and/or algorithmic discussions
# The abbreviation MILP is not previously defined. Please fix this issue.
# You consistently use the negative sign instead of the NOT operator for y (-y instead of ¬y).
# Some inconsistencies with the spacing of variables, constraints, etc., under the “General” section that need to be fixed.
# Typo in “This is shown below by M1, M2, y1, and y1:” where y1 needs to be changed to y2. Why use two different Big-M variables here? Elsewhere in the Wiki you only use one so this could lead to confusion with a general audience. Also if this was taken from the lecture notes then it needs to be cited.
* At least one numerical example
# Please reformulate and solve a complete numerical example rather than just reformulating a general example. Demonstrate the use of Big-M and Convex Hull formulation in an optimization problem that provides details such as individual steps in the problem solving process and final results.
# Add space between vee (V) operator and brackets in first line of Latex
# Please format variables correctly, for example, use <math>x_1</math> instead of x1.
* A section to discuss and/or illustrate the applications
# Please format the equations appropriately either by using latex code or the visual editor. These images are NOT acceptable!
* A conclusion section
# There is no conclusion presented in this section at all.
* References
# The included references have NOT been used anywhere in the Wiki. Add references for sentences that are not common knowledge and please link them appropriately with the text in Wiki. If the figures used here were not original works, you must also cite them.
# There are many papers on this topic. A simple Google (Scholar) search could provide you with sufficient references to cite.
# Many important references of this topic are missing.
# Please consider linking the references as demonstrated in the Wiki tutorial on Canvas and in this template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

==[[Stochastic programming|Stochastic Programming]] ==

* Author list: Remove cornell IDs
* An introduction of the topic
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
# This section only includes two sentences on Stochastic programming (SP), while the rest gives examples of uncertainty. Please discuss the need for SP in the presence of uncertainty. Also, discussion on robust optimization and its limitations should be removed since it is out of place.
* Theory, methodology, and/or algorithmic discussions
# Please avoid direct inline linkbacks to Wikipedia.
# The symbol “xi” in the methodology subsection should be explained.
* At least one numerical example
# Copying a numerical example "entirely" from a textbook is inappropriate. Your team should come up with a "numerical" case.
# No specific application context is needed for a numerical example.
# The inline notations (`x1`, `s1`) should also be typed using LaTex.
# Label all tables with a table number for better readability.
# Properly format the solution table with the label attached rather than the following sentence. The solution table looks different from the others, please fix this for consistency.
* A section to discuss and/or illustrate the applications;
# I suggest eliminating citing the last name of the first author (i.e. Zhou et al.)
* A conclusion section
* References
# URLs of some citations are not properly formatted (not showing the hyperlinks).

== [[Exponential transformation|Exponential Transformation]] ==

* Author list
# Missing course section
# Remove cornell ID
* An introduction of the topic
# Please expand the introduction.
# Please aim for a maximum average sentence length of ~25 words. Last sentence with 51 words is hard to read.
# Second Sentence: please change the word “they” as it could make the meaning ambiguous
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
# If you use abbreviations, please introduce them (e.g. NLP,MINLP)
* Theory, methodology, and/or algorithmic discussions
# Please explain the transformation in words along with equations
# Terms like posynomial should be described in detail.
# Please move the numerical example to the section below
# The “(eq 1)” is not needed here.
# Please expand this section.
* At least one numerical example
# In the third equation of the numerical example, it is confusing to have coefficients after numbers. Some readers may read it as an exponent.
# Last equation in this section after “further linearization” is incorrect. This equation cannot be further linearized, please fix this.
# Please explain the steps in the numerical examples in detail. The step-by-step solution should be provided.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# Missing part of text: “Proof of convexity of with positive definite test of Hessian…”
# Applications are not numerical examples. Please refer to this link for example of applications: [[Duality|https://optimization.cbe.cornell.edu/index.php?title=Duality]]
# Citation 7 is missing in current applications
# The section current applications is redundant
# Please use the LaTex code or equation editor for min, s.t., etc.
# Under current applications, do not just use a hyperlink to describe an application. Actually describe it. And properly inline citation style should be used instead of the hyperlink.
# The convexification application of MINLP can be further simplified for binary variables. Please refer to the lecture slides for more information.
* A conclusion section
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
* References
# Please consider linking the references by using this as Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Citation 7 is missing in current applications

== [[Sparse Reconstruction with Compressed Sensing|Sparse reconstruction with Compressed Sensing]] ==
This Wiki needs a significant rewrite. Please go through the comments for details.

* An introduction of the topic
# The introduction section should include information about the problem and its implications presented briefly. Please use full sentences to write this Wiki. You may use tools like Grammarly to check sentence formation and grammar.
# This section includes several typos like “sub modual”. Please fix them throughout the wiki and delete them if not required.
# Many abbreviations are used before previously defining them. Please define these abbreviations before using them in the text.
# This section is incomprehensible in its current form. Please rewrite with proper comprehension.
# Equations and math symbols need proper reformatting. The current version reads like text (along with equations) copy-pasted from a specific source. All mathematical symbols and equations should be formatted via LaTex - this is a learning objective of the Wiki assignment. You can find some useful links on converting your equations/symbols into LaTex code here: (https://optimization.cbe.cornell.edu/index.php?title=Help:Contents).
# Try to place the figure at the top of the Wiki between the main text.
# Avoid pronouns such as “we”.
# I suggest the use of more formal abstract illustrations.
* Theory, methodology, and/or algorithmic discussions
# Equations and symbols need proper reformatting.
# Lemmas and theorems are not expected for this Wiki. Sparse reconstruction is a straightforward concept but is unnecessarily complicated here. Please refer to other Wiki examples to get an idea of what the Wiki should convey.
# All equations need to be better formatted.

* At least one numerical example
# Numerical example is missing.
# Every iteration should be clearly presented, and solved "step-by-step".
* A section to discuss and/or illustrate the applications
# Having a list is not enough. Please explain at least three applications in a few sentences each.
* A conclusion section
# Conclusion section is missing.
* References
# The current reference list is not correctly formatted. References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Portfolio optimization|Portfolio Optimization]] ==

* Author list
# Remove cornell id
* An introduction of the topic
# The introductory sentence should be rephrased. The action of minimizing the risks does not inherently maximize the gains, rather PO aims to maximize gains whilst minimizing risks.
# Amount of whitespace can be reduced by changing the orientation of Figure 1 and the sentences in this section.
# Define terms such as risk, return, portfolio, etc., when you introduce them. Assume that the reader may not know much about finance. This goes for all other sections as well.
* Theory, methodology, and/or algorithmic discussions
# A brief mention of modern portfolio theory (i.e.. Markowitz) would be appropriate in this section.
# Several grammatical errors here involving sentence structure and clarity. Some questionable semantics (e.g., “The portfolio optimization mainly assumes two directions.”) and syntax (phrases such as “.. is as follows” should be followed by a colon). Misuse of commas and missing commas in this section. Two sentences introducing E(rp) and w should be combined into one.
# Use LaTex to distinguish variables written within a sentence, such as m and n.
# Rephrase “Cut the relevant information and conditions in the portfolio optimization, as well as the final requirements into the relevant variables, constraints and linear functions of the linear programming problem.”
# An explanation of a few common constraints would be helpful, rather than just including a table.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Solving the numerical example by GAMS is inappropriate. Please provide detailed step-by-step calculation results.
# All tables need to be labeled.
# Include figure number in label for consistency.
# Fix misspelling “dolling decision variables”.
# Use LaTex for all variables, equations, and constraints here.
# Example 2 table is hard to read, so making it bigger would help.
# Remove the “Using excel as the solver” part from the sentence before the solution discussion.
# Some grammatical errors here (phrases such as “.. is as follows” should be followed by a colon).
* A section to discuss and/or illustrate the applications
# Rephrase “Portfolio optimization can be used to screen investment projects that meet investors, rationally allocate investment amounts, etc.”
# Not sure “relevant” is the correct word choice here.
# You need more specific examples with the utility of portfolio optimization, this section is quite general as is. Some more detail and focus on real-world applications in the financial industry that relate to retirement planning, financial security, economic stability, etc., would be helpful.
* A conclusion section
# Need some commas here.
# The sentence “Linear programming has been around since the 1940’s and has such a wide base of applications” is not necessary.
* References
# Please consider linking the references as demonstrated in the Wiki tutorial on Canvas and in this template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove white space between end of sentences and reference numbers.

== [[Chance-constraint method|Chance constraint method]] ==

* Author list:
* An introduction of the topic
# Please consider correcting a few grammatical errors: “pre-planned for”, “god”, “certain levels of feasibility is guaranteed in what are”, and “Performance of a system”
# In “Chance-constraint”, it is capitalized randomly throughout the introduction. Please correct.
# Please use technical language to briefly introduce chance-constrained programming. Words like “acts of god”, “cost of doing business” are not appropriate for a technical Wiki.
* Theory, methodology, and/or algorithmic discussions
# Please add a citation to the first sentence.
# Xi is an uncertainty/randomness variable. It is better to use clear language.
# Please use the mathematical editor for adding explanations in the text. Using “ x is a decision variable” is hard to read. Same for f(x) and others.
# Theory is insufficient. Please expand and explain different approaches.
# Please add pros and cons explicitly as a list.
# Explain the physical meaning for examples of chance constraints along with all the notations used.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please remove this example as it is directly from this book. The example should be purely numerical without any background.
# Please use the equation editor for min, st., etc.
# Please use the mathematical editor for adding explanations in the text. Using “ x is a decision variable” is hard to read. Same for f(x) and others.
# Please change the table format so as not to confuse the reader.
# Multiple instances of [Chart to be added] are missing.
# Example is incomplete.
# Avoid pronouns such as “we”.
* A section to discuss and/or illustrate the applications
# Please connect several grammatical and spelling errors: “real life application”, Energy creation, particularly in renewable sources, have high variabilities”, and others
# “Zhao, Xue, Cao, and Zhang”. No need to list all authors within the article. Provide a reference is sufficient. If authors must be mentioned, (Zhao et al.) should be ok.
* A conclusion section
# Uniqueness and universality earlier are not clear to me. If they are not discussed earlier in the application, it would be better not to introduce new discussions in the conclusion.
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
* References
# References seem to vary in format. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Bayesian Optimization]] ==
* Section titles should not be "bold". Please double check using source editor on the section titles.
* Contents: Subheadings for EI and the algorithm should not be bolded, Random words should not be capitalized.
* Author list: Remove cornell ID, Please check names
* Introduction
# The introduction is too general and not substantial enough. For example, simply saying BayesOpt is useful when the objective function is unknown obscures exactly HOW it is useful (namely, computational efficiency in applications where ground truth sampling is expensive). Discussion on applications should be moved to a separate section.
# Machine learning rarely includes black-box functions to be optimized. Bayesian optimization is almost never used for optimizing ML loss functions but can instead be used for hyperparameter optimization. Please update such claims in this section.
* Theory, methodology, and/or algorithmic discussions
# Captions need reformatting.
# Consider italicizing keywords rather than bolding.
# Please add a citation to the first sentence.
# Discussion on acquisition functions should include comparisons, tradeoffs, and reasons to use one over the other. Should also note that expected improvement is the most widely used in practice, and explain.
# Avoid pronouns such as “we”.
# Please write equations in the Wiki instead of attaching images for equations.
# Acquisition function figure could be made larger and clearer to improve readability.
* At least one numerical example
# Any references to functions or methods in code ‘e.g. fmin’ should be properly formatted as code-stylized text.
# Please use the equation editor for min, st., etc.
# Avoid including a figure of the code for this example and explicitly describe the steps to the modeling and solution process instead.
# Avoid pronouns such as “our” and “we”.
* A section to discuss and/or illustrate the applications
* A conclusion section
# Please do not use brackets to enclose lists.
# Some claims here should be supported by references. Please cite each source after its sentence.
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Try to avoid references to “pop” machine learning blogs where anyone can be an author. (e.g. towardsdatascience)
# All references are URLs. Please cite publications and literature.
# A simple Google Scholar search would give you many references.

Notes on grammar: Needs some work. Several instances where colons are inappropriately inserted mid sentence or in subheadings. Explanations are not terse. Several instances of switching between personal and impersonal style of writing, which is distracting.

== [[Conjugate gradient methods]] ==

* Author list: Remove cornell ID
* Introduction
# All inline notations (e.g., `x`, `A`) should be typed using LaTex.
* Theory, methodology, and/or algorithmic discussions
# All equations need to be better formatted.
# Is Gauss-Newton no longer referenced?
# Theorems listed in the first section should be accompanied with high level explanation, not just a list of the theorems themselves. The page should read like an article, with proper flow.
# Please indent equation blocks.
# Please properly format pseudocode.
* At least one numerical example
# Steps should be accompanied with explanation, or reference to the corresponding step in the pseudocode.
# Please properly format in a more organized manner, aligning equations appropriately and demarcating steps appropriately.
* A section to discuss and/or illustrate the applications
# Consider including 2 additional examples of applications
* A conclusion section
# Consider adding future research directions
* References
# Reference primary sources rather than Wikipedia
# Too few references.
# More references should be added. A simple Google Scholar search would give you many references.

== [[Geometric programming|Geometric Programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Examples of applications in this section use the same reference. Please cite their individual sources.
* Theory, methodology, and/or algorithmic discussions
# The symbol denoting the domain in the definition of a monomial is unclear. Please clarify it or fix this if it is incorrect.
# Definition of posynomial refers to section 2.1 which is missing from the Wiki (sections are not numbered in the main text).
# In the generalized posynomial subsection, bullet points do not tell us why h(x) is posynomial. Either provide reasons or simply state that h(x) is posynomial. Also explain why h3 is a generalized posynomial.
# Additional theory on the feasibility analysis could be provided in this section.
* At least one numerical example
# In the transformation example, the last two constraints could also be simplified by applying a natural logarithm on both sides. Please update them as well.
* A section to discuss and/or illustrate the applications
# The figure in this section needs to be labeled.
# The figure needs to be resized and perhaps aligned to the center.
* A conclusion section:
# Please avoid vague language such as: “This makes”.
# Please avoid opinionated statements: “one of the best ways”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# This Wiki has very few references. A quick Google Scholar search may provide relevant references.

== [[Adam]] ==

* Author list
* An introduction of the topic
# Some grammatical errors here, mostly related to the need for commas in certain places (e.g., “Before Adam..”).
# Some minor errors with parts of speech throughout the section, need to revisit phrases such as “which has broader scope in future for”, etc.
# Try splitting up some of the longer sentences in this section, a couple are hard to read.
# Avoid definitive statements about Adam being the best or always better solver, as this is simply not true (the choice of the “best” optimizer is setting-dependent). Use language such as “Research has shown that Adam has demonstrated superior experimental performance over..” and then cite academic references to back this claim.
# What does adam stand for? Introduction is insufficient. Please expand.
* Theory, methodology, and/or algorithmic discussions
# Revise grammar here, noticing some missing commas and uncapitalized word after period.
# Rephrase “second one is to update the old position with the updated position”.
# Use LaTex code or equation editor to display all equations and variables in this section, and actual subscripts instead of “m_t”, etc.
# Avoid inserting inline citations after words like “According to..” or “This article..” as it is a bit informal. This could be rephrased or changed to something like “According to author,^[2] …” with author name inserted.
# Remove white space before the period in RMSP discussion.
# Please provide a pseudocode.
# Please use list the two methods here “Adam is a combination of two gradient descent methods which are explained below”
# Please expand the theory section significantly. Theoretical convergence properties should be discussed, even if briefly.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
* A section to discuss and/or illustrate the applications
# Same comment as before, consider replacing inline citations after words like “According to..”.
* A conclusion section
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Try to avoid references to blogs and use peer-reviewed academic references instead.
# Too few references.
# More references should be added. A simple Google Scholar search would give you many references.

== [[A-star algorithm|a* algorithm]] ==

* Author list: Remove cornell ID
* Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.
* An introduction of the topic:
# Weird spacing between paragraphs. Please fix this issue.
# In the titles, please change the font from bold to normal to have consistent formatting in the site.
# Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.
# There are no citations in the introduction. Please cite every source.
* Theory, methodology, and/or algorithmic discussions
# Please add the mathematical description of the algorithm.
# Reference style varies in sentences. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please fix grammatical and spelling errors as (“from current position to the goal”, “There are a lot of discussions”, etc). Also, many hyphens are missing as “non playable”.
# In algorithms, it is a standard to add high-level description (i.e. pseudocode or flowchart). Please incorporate it.
# Use LaTex code or equation editor to display all equations and variables in this section (e.g., “f(n)...”, “h(n)..”, etc.). This goes for other sections as well.
* At least one numerical example
# The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.
# Instead of writing things like “The above image..”, label each figure and use the figure number to refer to it in text.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# No references in the applications. Please cite every source
# Preferably, add at least an additional application.
* A conclusion section
# Conclusion should summarize descriptions. Please modify it to provide a summary.
# Please pay attention to the length and structure of sentences here and in the full page. First sentence is hard to read.
* References
# References seem to vary in format and are not linked correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Incorrect reference style. Please follow the example and use the template.

== [[Job shop scheduling|Job-Shop Scheduling Problem]] ==

* An introduction of the topic
# The current introduction to the jobshop scheduling problem has only two sentences in addition to the parameter description. Introduction typically contains information about the problem, its importance in the real-world, and some information about the solution techniques and their types to solve the problem. Please add some information that covers the above.
* Theory, methodology, and/or algorithmic discussions
# It is unclear whether the assumptions stated in this section are required to apply the following solution techniques. Please clarify the same. Also use complete sentences to state them.
# The branch and bounds method described in this section only discusses the solution technique for problems with one machines. However, branch and bound is a general technique that can be applied to any MILP problems with varying scales. Please update the “methods” section to be as general as possible.
# Since this Wiki focuses on jobshop scheduling, at least two methods are expected. Branch and bound is a general MILP technique, so, it is recommended to add a tailored technique that can only solve specific jobshop scheduling problems. Solving the numerical example with this technique is not necessary.
# Reference to the branch and bound technique described in this section is a “youtube” video. Please add references in literature that describe this method in detail. The method used in this video is highly tailored for a single machine application. This is also an incorrect way to cite a reference. Please keep this section as general as possible.
# Use LaTex code or equation editor to display all equations and variables in this section and all other sections as well.
# Check grammar in this section. For example, phrases like “are as follows” need to be followed by a colon and not a period.
# Consider rewriting the assumptions as a list in this section.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# The example used in this section is exactly the same as the one in the youtube video. Please use a modification of this example or choose another example/method to demonstrate the solution technique. Your team should ideally create a numerical example independently. If you take a numerical example directly from a particular source, you will need to get explicit permission from the textbook author in writing and share that written permission with the instructors.
# The figure in this section is not numbered when all others are. Relabel this figure for consistency and its number to refer to it in-text.
# A numerical example should be simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments).
* A section to discuss and/or illustrate the applications
# This section should only focus on real-world applications of the jobshop scheduling problem. But currently, this section includes additional information on solution techniques/complexity that is appropriate for the Introduction section. Please discuss the applications of the problem in this section.
* A conclusion section
# The meaning of “Operations applications” is unclear. Please explain or update if necessary.
# The current conclusion section does not properly summarize the problem. Please refer to other Wiki examples for an idea to update the section accordingly.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please reference media sources like reference 5 appropriately.
# A simple Google Scholar search would give you many "formal" references.

== [[Optimization in game theory]] ==

* Author list: remove cornell IDs.
* An introduction of the topic
# References are not linked. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
* Theory, methodology, and/or algorithmic discussions
# Why only a subsection on "Nash Equilibrium" is included in "Theory" section? Please re-format.
# Please edit references.
# Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm.
# Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.
* At least one numerical example
# Please organize the last part in a more readable format. Questions may be in bold and numbered, answers are more direct, etc.
# Remember to cite all images and tables.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# Very good, link the reference and cite all sources.
* A conclusion section
# Please add more summarizing especially from theory sentences and avoid long sentences.
* References
# Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Reference primary sources rather than Wikipedia
# Incorrect reference style. Please correct.

== [[Trust-region methods]] ==

* Author list:
# Remove cornell IDs. Author is also spelled incorrectly.
# Add the course section.
* An introduction of the topic
# References are not linked. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Use LaTex code or equation editor to display all equations and variables (e.g., “xk”, “f`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “we”. This goes for all other sections as well.
* Theory, methodology, and/or algorithmic discussions
# Organization of ideas in this section needs work.
# You have not defined explicitly why the Cauchy point is important to compute beyond a vague allusion to performance improvements, which is also wrong (it is useful because of its guarantees for convergence, not performance) It is also misspelled.
# Each approach should have accompanying explanation and motivation for why it is being discussed. It is not enough to outline the algorithm.
# Please make sure symbols are properly subscripted and superscripted (e.g. “pk” should be “p_k”
# Please format the algorithm in proper algorithmic pseudocode format.
# Little to no discussion on global convergence guarantees
# Please include discussion about the advantages and disadvantages of the algorithm
# Fix typo “couchy point”.
* At least one numerical example
# Any code functions (uminfunc) should have proper text formatting.
# The graph needs a better caption explaining how the axes are labeled and what data points are being shown.
# Please increase the quality of the figure. It is hard to see the red line.
# Add citation to “The Rosenbrock function is a non-convex function, introduced by Howard H. Rosenbrock in 1960, which is often used as a performance test problem for optimization algorithms.”
* A section to discuss and/or illustrate the applications
# The content in this section as it is currently does NOT describe applications, but rather different approaches within the trust region methodology. Please provide specific applications (e.g. TRPO in reinforcement learning).
* A conclusion section
# Please add more summary, future research directions for example is a good start.
* References
# Incorrect reference style.
# Please consider having the references as this Wiki template, <nowiki>https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization</nowiki>
# More references should be added. A simple Google Scholar search would give you many references.

*There are numerous misspellings, grammatical errors, and incorrect claims. Please fix these.

== [[Momentum]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Apart from an explanation on momentum, it is necessary to briefly point out the limitations of SGD and why momentum could help with these limitations. Please update it accordingly.
# Remove bold on “Momentum”.
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
* Theory, methodology, and/or algorithmic discussions
# Equation formatting is very poor and should be formalized.
# It is important to use technical language for this Wiki. Although a layman’s explanation is appreciated, it would be better to skip using words like “zig zagging”. Try to explain all concepts in a technical language with few simplifications but NOT vice versa.
# The definition of the update rule for SGD with momentum looks incorrect, specifically the first expression. Please fix it and also explain all the parameters used.
# Use LaTex code or equation editor to display all equations and variables (e.g., “W”, “V`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “you”.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step". Since writing all iterations is not feasible, at least present a few iterations for both cases.
# Please try to label the plots that explains what each line color means.
# Starting point for SGD with momentum is different in explanation and the table. Please fix the same.
* A section to discuss and/or illustrate the applications
# Please use correct terminology like “optimizing non-convex functions” and not “training non-convex models”.
# Adam, Adadelta, and RMSprop are variants of SGD that already use momentum. Please double check the writing and update if necessary.
* A conclusion section
# Please refrain from using words like “zig zag” effects.
* References
# Almost all references used are URLs. Please try to add journal/conference articles or books for references, instead of directly citing the URLs. Please check the list below and run a quick Google (Scholar) search to identify relevant literature.

== [[Stochastic dynamic programming|Stochastic Dynamic programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Discussion on applications should be moved to a separate section.
* Theory, methodology, and/or algorithmic discussions
# Remove the grey box background of equations.
* At least one numerical example
* A section to discuss and/or illustrate the applications
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Outer-approximation (OA)|Outer-approximation]] ==

* An introduction of the topic
# See formatting guideline below
# Avoid opinionated statements such as “MINLP problems are usually the hardest to solve”.
# Rearrange the text such that the MINLP formulation is in the theory section and keep the introduction in words only.
* Theory, methodology, and/or algorithmic discussions
# Consider left aligning equations and optimization problem formulations by the “=”. See [[Stochastic programming|https://optimization.cbe.cornell.edu/index.php?title=Stochastic_programming]] for an example
# The sentence “The Outer-Approximation (OA) algorithm was first proposed by Duran and and Grossmann in 1986 to solve MINLP problems.” needs a reference.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# “Minimize” and “subject to” should be “min” and “s.t.” in MathType
* A section to discuss and/or illustrate the applications
# Does not explicitly point out why OA is applicable (and/or preferred) in these applications, rather than other MINLP approaches (show that the problem formulations are amenable to a solution approach through OA)
# The sentence “... an active research area and there exists a vast number of applications in fields such as engineering, computational chemistry, and finance.” needs references.
# Place GAMS code in a single code box or remove it.
# Consider reformatting to make steps more readable. Inserting spaces and breaking down steps would help.
* A conclusion section
# Too short. Consider discussion on future research direction and discussion on uncertainty
# Please review abbreviations throughout the page. Why is MINLP redefined here? “Outer-Approximation is a well known efficient approach for solving convex mixed-integer nonlinear programs (MINLP)”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove "Template:Reflist"

== [[Unit commitment problem]] ==

* Author list
* An introduction of the topic
# Please expand the introduction and avoid discussions of examples or specific applications in this section.
# The sentence “Nonlinear, Non-convex programming optimization problem.” doesn’t make sense by itself and Non-convex shouldn’t be capitalized.
* Theory, methodology, and/or algorithmic discussions
# Figure/image format should be revised to better display the content.
# Uppercase characters are used randomly (e.g., “non-convex transmission Constraints”) . Please follow correct language conventions for sentence structure.
# Avoid inserting inline citations after words like “written in matrix form as equation [3]..” or “presented in [3]...” as it is a bit informal when you don’t explicitly name the subject. Also these two sentences are grammatically incorrect and appear to be missing an ending period and comma, respectively.
# Don’t say “written in matrix form as equation..” and just cite the reference, actually write out the equation.
# Properly label the figure in this section with a figure number and improve visibility by making it larger.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Label the figures in this section properly with figure numbers.
# Fix typo “while minimize” to “while minimizing”.
# Avoid pronouns such as “we”.
# Use the equation editor when typing equations.
* A section to discuss and/or illustrate the applications:
# I suggest changing the order of the subtitles here. For example, Single-Period Unit Commitment.
* A conclusion section
* References

== [[Frank-Wolfe]] ==

* Author list:
* An introduction of the topic
# I suggest highlighting disadvantages along with advantages.
* Theory, methodology, and/or algorithmic discussions
# “[n x 1] matrix” please use the equation editor to express mathematical descriptions and symbols (p,b, etc)
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please show at least a few iterations. Even for smaller examples if needed. Report the final solution.
# Please use the LaTex code or equation editor for min and include s.t., etc.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps. For your example, please explicitly state that the derivative is taken etc.
* A section to discuss and/or illustrate the applications:
* A conclusion section
# Same as the introduction. Pros and cons should be evaluated together!
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Line search methods|Line Search Method]] ==

* Author list
* An introduction of the topic
# Expand the introduction and avoid discussion on some of the specific steps in the solution process.
# Provide references here.
* Theory, methodology, and/or algorithmic discussions
# The phrase “are as follows” in the steepest descent method discussion needs to be followed by a colon.
# Rephrase “has a nice convergence theory” and cite a reference for this claim.
# Avoid pronouns such as “we”.
# Add citation after “.. proposed by Phillip Wolfe in 1969.”
# Figure 1 is between two sections. Please fix this issue.
* At least one numerical example:
# Add some space between iterations or subsection break
* A section to discuss and/or illustrate the applications:
# Too few references in this section.
# Last paragraph makes some claims without references.
* A conclusion section
* References
# References should be properly formatted. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Piecewise linear approximation|Piecewise Linear Approximation]]==

* Author list
* An introduction of the topic
# The content of this section is good, but there are some issues with sentence clarity and some other grammatical errors. Please revisit this section and make changes accordingly.
* Theory, methodology, and/or algorithmic discussions
# Fix typo “to force the x’ values become associated with”.
* At least one numerical example
* A section to discuss and/or illustrate the applications
# Please aim for a maximum average sentence length of ~25 words. Some of these longer sentences are hard to read.
* A conclusion section
# Expand the conclusion section to be longer than one sentence. The conclusion section to include a brief summary of what was discussed above, an emphasis on it’s significance, and a brief discussion of future extensions and research direction if applicable.
* References
# Include hyperlinks to sources when possible.

== [[Mathematical programming with equilibrium constraints|Mathematical Programming with Equilibrium constraints]] ==

* An introduction of the topic
# This section includes several terms like variational inequalities, constraint qualifications that were not discussed in the class. Please add a sentence to explain them before using them.
* Theory, methodology, and/or algorithmic discussions
# The meaning of parameter vector x is unclear. Please add more information or update if necessary.
# Equations and symbols in the PIPA subsection are not formatted correctly. Please use the same formatting for all equations, so they read as mathematical equations and not text. This goes for all other sections as well.
# Use equations instead of images to represent math programs and equations in the Implicit Descent and SQP subsection.
# Apart from the steps for each solution technique, please also add a few sentences that describe each method.
* At least one numerical example
# Please define the terms like NCP, MP before abbreviating them. Also try not to unnecessarily abbreviate simple terms.
# Equations should be typed by LaTex. Images for equations are unacceptable.
# GAMS code is strongly discouraged. Please solve the problem "step-by-step".
# The selected numerical example is fine but is directly solved with the MPEC solver in GAMS. Try to solve it manually like the homework/in-class problems step by step using the steps described in the previous section by choosing any of the methods.
# Avoid using figures in the equations (subject to etc)
* A section to discuss and/or illustrate the applications
# Add references to “power management, highway pricing, chemical process engineering, and traffic planning.”
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# This Wiki contains very few references. Please check the list below and run a quick Google (Scholar) search to identify relevant literature.

== [[Wing shape optimization|Wing shape Optimization]] ==

* Author list: Remove cornell ID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# The introduction is missing several references (e.g., “software packages like computational fluid dynamics..”, sentences containing things that aren’t common knowledge, performance claims, etc.)
# Avoid discussion involving finer details of subject methods in this section.
# In the titles, please change the font from bold to normal to have consistent formatting in the site. Same applies to box of content!
* Theory, methodology, and/or algorithmic discussions
# Properly cite the CFD package, don’t just include a link.
# Properly label the figure with a figure number.
# Consider removing white space between isolated sentences to improve readability.
* At least one numerical example
# If you’ve already defined an abbreviation (CFD), there is no need to define it again. Just use the abbreviation.
# Avoid pronouns such as “we” or “they”.
# Phrases like “under the following” need to be followed by a colon.
# Properly label the figure with a figure number and consider making them larger to improve visibility. Call the reader's attention to the figures in text by referencing the figure number.
# “As seen in the video below” is stated yet there are only images present and it may be initially unclear to the reader which figure is being referenced here.
# Avoid inserting inline citations like “[4] introduces an..” as it is a bit informal when you don’t explicitly name the subject.
# Don’t just cite the reference when discussing the problem formulation, explicitly write the model formulation and solution process using LaTex or equation visual editor.
* A section to discuss and/or illustrate the applications
# Some characters are randomly capitalized in this section.
* A conclusion section
# These variables should be defined before the conclusion section, they are out of place here. Also, please use normal text when explaining variables except for the variable symbol.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Interior-point method for NLP|Interior point method for NLP]] ==

* An introduction of the topic:
* Theory, methodology, and/or algorithmic discussions
# Primal-Dual formulation and comparison to the Barrier Method is not discussed.
# Include brief discussion about big O convergence rates.
# Need discussion about the concept of “central path” and the notion of self concordance
# Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
# Graphs and images are incorrectly formatted to the page. Consider proper alignment with respect to the text body.
# Use explicitly typed Latex equations instead of images to represent math programs and equations.
# Fix typo “optimisation”.
# Use LaTex code or equation editor to display all equations and variables (e.g., “xi ”, “μ”, etc.).
* At least one numerical example:
# There are formatting issues with figures 2,3. Please make sure to embed them within their respective sections.
* A section to discuss and/or illustrate the applications
* A conclusion section
# Minor character code typos in the conclusion.
# Also, please add more discussion in this section. Future research directions is a good start.
# There is a box "􏰐"
* References

== [[AdaGrad|Adagrad]] ==

* An introduction of the topic:
* Theory, methodology, and/or algorithmic discussions
# Include discussion on its variants (most important is AdaDelta).
# Include disadvantages of Adagrad, since this provides motivation for the discussion on the variants and improvements of Adagrad
# Include comparisons to other popular optimizers (particularly important is comparisons to regular SGD and Adam)
# Different convergence rates are possible depending on the setting where Adagrad is used, but this is not mentioned on the page currently. As such the regret bound section should be more thoroughly explained.
* At least one numerical example
# In the first sentence, “..take the following numerical example” should be followed by a colon.
# Fix typo “trayectory”.
* A section to discuss and/or illustrate the applications
# This section is too short; include specific applications in which input features are sparse and Adagrad excels.
# Add reference to the claim “Mainly, it is a good choice for deep learning models with sparse input features”.
* A conclusion section
* References

# Too few references overall, you should aggregate information from multiple sources (even if the base algorithm itself comes from a singular paper)

== [[McCormick envelopes|McCormick Envelopes]] ==

* Author list: OK but I suggest removing NetID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# First sentence is hard to read. Please consider keeping sentences below 25-30 words.
# No references provided. Please cite all sources.
# Figure 1 is provided in the middle between two sections. Please include in the introduction section.
* Theory, methodology, and/or algorithmic discussions
# References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# When using mathematical expressions and symbols, please use the equation editor. (e.g., x*y, exy + y, sin (x+y) - x2)
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# For the sample GAMS code, please place it in a code box
* A section to discuss and/or illustrate the applications
# Having a list is not enough. Please explain at least three applications in a few sentences each.
# This section should be at least a paragraph to discuss relevant applications. Each application should be explicitly linked to the page topic. A few keywords do not meet the requirement at all.
* A conclusion section:
* References
# References are not expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please follow the standard reference style - the current format is incorrect.

2021 Cornell Optimization Open Textbook Feedback

2021-12-05T20:07:30Z

Asa273: /* Momentum */

== [[Lagrangean duality|Lagrangian duality]] ==
* Author list, sections and TOC
# Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.
# Remove cornell ID from Author list
* An introduction of the topic
# This section includes sentences on constructing the dual problem and is referred to as Lagrangian relaxation (LR). This is incorrect, please fix the definition of LR.
# Definitions of LR and its relation to duality should be double checked and re-written.
# Only one reference is present in this section. Please add more relevant references by expanding this section.
# Consider merging the “introduction” and “history” sections.
# In the titles, please change the font from bold to normal to have consistent formatting in the site.
* Theory, methodology, and/or algorithmic discussions
# The Lagrangian variables associated with equality constraints h(x) are unbounded but the Lagrangian dual problem states them as non-negative. Please fix the same.
# Also to construct a dual, we do not change minimization to maximization directly. We observed such things in the examples in lecture notes due to simplification. The lagrangian dual problem would be minimize (,).
# Adding to the previous point, the Lagrangian is a lower bound on the original objective; the solution to the primal and dual or only equivalent if the duality gap is 0. You reference this in one section, but this is after your statement “Hence, solving the dual problem, which is a function of the Lagrangian multipliers (𝜆*) yields the same solution as the primal problem, which is a function of the original variables (x*). “. Please clarify the specific conditions that must hold for the solution of the dual to be equal to the primal’s.
# You refer to the “Complementary Slackness Theorem”, but don’t actually write the mathematical representation of complementary slackness. Please fix this. Also consider including the derivation of the complementary slackness condition, as it is both easy and short. Boyd is a good reference for this.
# Last step of the “process” subsection also needs updating according to the previous comments.
# The inline notations should also be typed using LaTex.
# Please use the LaTex code or equation editor for min, s.t., etc.
* At least one numerical example
# Only one dual variable is associated with each constraint. The numerical example uses two for the first and second constraint which is unnecessary. Please update it accordingly for both constraints. This particular example will only have two dual variables instead of the five dual variables used currently.
# All consecutive steps need to be updated since the dual variables would be updated.
# After substitution the nonlinear function should be further simplified. The current expression reads like a highly nonlinear function but can be easily simplified.
# Similar to the comments in the methodology section, inverting minimize to maximize is incorrect. Please update the dual objective function and domain of dual variables accordingly.
# Please use the LaTex code or equation editor for min, s.t., etc.
* A section to discuss and/or illustrate the applications
# Bullet points could be used to state the last four real-world examples that explain the physical meaning of the primal and dual problems.
# Add references for the last set of applications.
* A conclusion section
# This section contains a few typos. Please fix the same.
* References
# Some citations' hyperlinks are displaying.

== [[Disjunctive inequalities|Disjunctive Inequalities]] ==

* Author list
# Missing course section and semester
# Remove cornell ID
* An introduction of the topic
# No citations are present in this section.
# “mixed-integer programming (MIP)” should be used instead of “multiple integer programming (MIP)”. Please fix this error.
* Theory, methodology, and/or algorithmic discussions
# The abbreviation MILP is not previously defined. Please fix this issue.
# You consistently use the negative sign instead of the NOT operator for y (-y instead of ¬y).
# Some inconsistencies with the spacing of variables, constraints, etc., under the “General” section that need to be fixed.
# Typo in “This is shown below by M1, M2, y1, and y1:” where y1 needs to be changed to y2. Why use two different Big-M variables here? Elsewhere in the Wiki you only use one so this could lead to confusion with a general audience. Also if this was taken from the lecture notes then it needs to be cited.
* At least one numerical example
# Please reformulate and solve a complete numerical example rather than just reformulating a general example. Demonstrate the use of Big-M and Convex Hull formulation in an optimization problem that provides details such as individual steps in the problem solving process and final results.
# Add space between vee (V) operator and brackets in first line of Latex
# Please format variables correctly, for example, use <math>x_1</math> instead of x1.
* A section to discuss and/or illustrate the applications
# Please format the equations appropriately either by using latex code or the visual editor. These images are NOT acceptable!
* A conclusion section
# There is no conclusion presented in this section at all.
* References
# The included references have NOT been used anywhere in the Wiki. Add references for sentences that are not common knowledge and please link them appropriately with the text in Wiki. If the figures used here were not original works, you must also cite them.
# There are many papers on this topic. A simple Google (Scholar) search could provide you with sufficient references to cite.
# Many important references of this topic are missing.
# Please consider linking the references as demonstrated in the Wiki tutorial on Canvas and in this template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

==[[Stochastic programming|Stochastic Programming]] ==

* Author list: Remove cornell IDs
* An introduction of the topic
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
# This section only includes two sentences on Stochastic programming (SP), while the rest gives examples of uncertainty. Please discuss the need for SP in the presence of uncertainty. Also, discussion on robust optimization and its limitations should be removed since it is out of place.
* Theory, methodology, and/or algorithmic discussions
# Please avoid direct inline linkbacks to Wikipedia.
# The symbol “xi” in the methodology subsection should be explained.
* At least one numerical example
# Copying a numerical example "entirely" from a textbook is inappropriate. Your team should come up with a "numerical" case.
# No specific application context is needed for a numerical example.
# The inline notations (`x1`, `s1`) should also be typed using LaTex.
# Label all tables with a table number for better readability.
# Properly format the solution table with the label attached rather than the following sentence. The solution table looks different from the others, please fix this for consistency.
* A section to discuss and/or illustrate the applications;
# I suggest eliminating citing the last name of the first author (i.e. Zhou et al.)
* A conclusion section
* References
# URLs of some citations are not properly formatted (not showing the hyperlinks).

== [[Exponential transformation|Exponential Transformation]] ==

* Author list
# Missing course section
# Remove cornell ID
* An introduction of the topic
# Please expand the introduction.
# Please aim for a maximum average sentence length of ~25 words. Last sentence with 51 words is hard to read.
# Second Sentence: please change the word “they” as it could make the meaning ambiguous
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
# If you use abbreviations, please introduce them (e.g. NLP,MINLP)
* Theory, methodology, and/or algorithmic discussions
# Please explain the transformation in words along with equations
# Terms like posynomial should be described in detail.
# Please move the numerical example to the section below
# The “(eq 1)” is not needed here.
# Please expand this section.
* At least one numerical example
# In the third equation of the numerical example, it is confusing to have coefficients after numbers. Some readers may read it as an exponent.
# Last equation in this section after “further linearization” is incorrect. This equation cannot be further linearized, please fix this.
# Please explain the steps in the numerical examples in detail. The step-by-step solution should be provided.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# Missing part of text: “Proof of convexity of with positive definite test of Hessian…”
# Applications are not numerical examples. Please refer to this link for example of applications: [[Duality|https://optimization.cbe.cornell.edu/index.php?title=Duality]]
# Citation 7 is missing in current applications
# The section current applications is redundant
# Please use the LaTex code or equation editor for min, s.t., etc.
# Under current applications, do not just use a hyperlink to describe an application. Actually describe it. And properly inline citation style should be used instead of the hyperlink.
# The convexification application of MINLP can be further simplified for binary variables. Please refer to the lecture slides for more information.
* A conclusion section
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
* References
# Please consider linking the references by using this as Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Citation 7 is missing in current applications

== [[Sparse Reconstruction with Compressed Sensing|Sparse reconstruction with Compressed Sensing]] ==
This Wiki needs a significant rewrite. Please go through the comments for details.

* An introduction of the topic
# The introduction section should include information about the problem and its implications presented briefly. Please use full sentences to write this Wiki. You may use tools like Grammarly to check sentence formation and grammar.
# This section includes several typos like “sub modual”. Please fix them throughout the wiki and delete them if not required.
# Many abbreviations are used before previously defining them. Please define these abbreviations before using them in the text.
# This section is incomprehensible in its current form. Please rewrite with proper comprehension.
# Equations and math symbols need proper reformatting. The current version reads like text (along with equations) copy-pasted from a specific source. All mathematical symbols and equations should be formatted via LaTex - this is a learning objective of the Wiki assignment. You can find some useful links on converting your equations/symbols into LaTex code here: (https://optimization.cbe.cornell.edu/index.php?title=Help:Contents).
# Try to place the figure at the top of the Wiki between the main text.
# Avoid pronouns such as “we”.
# I suggest the use of more formal abstract illustrations.
* Theory, methodology, and/or algorithmic discussions
# Equations and symbols need proper reformatting.
# Lemmas and theorems are not expected for this Wiki. Sparse reconstruction is a straightforward concept but is unnecessarily complicated here. Please refer to other Wiki examples to get an idea of what the Wiki should convey.
# All equations need to be better formatted.

* At least one numerical example
# Numerical example is missing.
# Every iteration should be clearly presented, and solved "step-by-step".
* A section to discuss and/or illustrate the applications
# Having a list is not enough. Please explain at least three applications in a few sentences each.
* A conclusion section
# Conclusion section is missing.
* References
# The current reference list is not correctly formatted. References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Portfolio optimization|Portfolio Optimization]] ==

* Author list
# Remove cornell id
* An introduction of the topic
# The introductory sentence should be rephrased. The action of minimizing the risks does not inherently maximize the gains, rather PO aims to maximize gains whilst minimizing risks.
# Amount of whitespace can be reduced by changing the orientation of Figure 1 and the sentences in this section.
# Define terms such as risk, return, portfolio, etc., when you introduce them. Assume that the reader may not know much about finance. This goes for all other sections as well.
* Theory, methodology, and/or algorithmic discussions
# A brief mention of modern portfolio theory (i.e.. Markowitz) would be appropriate in this section.
# Several grammatical errors here involving sentence structure and clarity. Some questionable semantics (e.g., “The portfolio optimization mainly assumes two directions.”) and syntax (phrases such as “.. is as follows” should be followed by a colon). Misuse of commas and missing commas in this section. Two sentences introducing E(rp) and w should be combined into one.
# Use LaTex to distinguish variables written within a sentence, such as m and n.
# Rephrase “Cut the relevant information and conditions in the portfolio optimization, as well as the final requirements into the relevant variables, constraints and linear functions of the linear programming problem.”
# An explanation of a few common constraints would be helpful, rather than just including a table.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Solving the numerical example by GAMS is inappropriate. Please provide detailed step-by-step calculation results.
# All tables need to be labeled.
# Include figure number in label for consistency.
# Fix misspelling “dolling decision variables”.
# Use LaTex for all variables, equations, and constraints here.
# Example 2 table is hard to read, so making it bigger would help.
# Remove the “Using excel as the solver” part from the sentence before the solution discussion.
# Some grammatical errors here (phrases such as “.. is as follows” should be followed by a colon).
* A section to discuss and/or illustrate the applications
# Rephrase “Portfolio optimization can be used to screen investment projects that meet investors, rationally allocate investment amounts, etc.”
# Not sure “relevant” is the correct word choice here.
# You need more specific examples with the utility of portfolio optimization, this section is quite general as is. Some more detail and focus on real-world applications in the financial industry that relate to retirement planning, financial security, economic stability, etc., would be helpful.
* A conclusion section
# Need some commas here.
# The sentence “Linear programming has been around since the 1940’s and has such a wide base of applications” is not necessary.
* References
# Please consider linking the references as demonstrated in the Wiki tutorial on Canvas and in this template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove white space between end of sentences and reference numbers.

== [[Chance-constraint method|Chance constraint method]] ==

* Author list:
* An introduction of the topic
# Please consider correcting a few grammatical errors: “pre-planned for”, “god”, “certain levels of feasibility is guaranteed in what are”, and “Performance of a system”
# In “Chance-constraint”, it is capitalized randomly throughout the introduction. Please correct.
# Please use technical language to briefly introduce chance-constrained programming. Words like “acts of god”, “cost of doing business” are not appropriate for a technical Wiki.
* Theory, methodology, and/or algorithmic discussions
# Please add a citation to the first sentence.
# Xi is an uncertainty/randomness variable. It is better to use clear language.
# Please use the mathematical editor for adding explanations in the text. Using “ x is a decision variable” is hard to read. Same for f(x) and others.
# Theory is insufficient. Please expand and explain different approaches.
# Please add pros and cons explicitly as a list.
# Explain the physical meaning for examples of chance constraints along with all the notations used.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please remove this example as it is directly from this book. The example should be purely numerical without any background.
# Please use the equation editor for min, st., etc.
# Please use the mathematical editor for adding explanations in the text. Using “ x is a decision variable” is hard to read. Same for f(x) and others.
# Please change the table format so as not to confuse the reader.
# Multiple instances of [Chart to be added] are missing.
# Example is incomplete.
# Avoid pronouns such as “we”.
* A section to discuss and/or illustrate the applications
# Please connect several grammatical and spelling errors: “real life application”, Energy creation, particularly in renewable sources, have high variabilities”, and others
# “Zhao, Xue, Cao, and Zhang”. No need to list all authors within the article. Provide a reference is sufficient. If authors must be mentioned, (Zhao et al.) should be ok.
* A conclusion section
# Uniqueness and universality earlier are not clear to me. If they are not discussed earlier in the application, it would be better not to introduce new discussions in the conclusion.
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
* References
# References seem to vary in format. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Bayesian Optimization]] ==
* Section titles should not be "bold". Please double check using source editor on the section titles.
* Contents: Subheadings for EI and the algorithm should not be bolded, Random words should not be capitalized.
* Author list: Remove cornell ID, Please check names
* Introduction
# The introduction is too general and not substantial enough. For example, simply saying BayesOpt is useful when the objective function is unknown obscures exactly HOW it is useful (namely, computational efficiency in applications where ground truth sampling is expensive). Discussion on applications should be moved to a separate section.
# Machine learning rarely includes black-box functions to be optimized. Bayesian optimization is almost never used for optimizing ML loss functions but can instead be used for hyperparameter optimization. Please update such claims in this section.
* Theory, methodology, and/or algorithmic discussions
# Captions need reformatting.
# Consider italicizing keywords rather than bolding.
# Please add a citation to the first sentence.
# Discussion on acquisition functions should include comparisons, tradeoffs, and reasons to use one over the other. Should also note that expected improvement is the most widely used in practice, and explain.
# Avoid pronouns such as “we”.
# Please write equations in the Wiki instead of attaching images for equations.
# Acquisition function figure could be made larger and clearer to improve readability.
* At least one numerical example
# Any references to functions or methods in code ‘e.g. fmin’ should be properly formatted as code-stylized text.
# Please use the equation editor for min, st., etc.
# Avoid including a figure of the code for this example and explicitly describe the steps to the modeling and solution process instead.
# Avoid pronouns such as “our” and “we”.
* A section to discuss and/or illustrate the applications
* A conclusion section
# Please do not use brackets to enclose lists.
# Some claims here should be supported by references. Please cite each source after its sentence.
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Try to avoid references to “pop” machine learning blogs where anyone can be an author. (e.g. towardsdatascience)
# All references are URLs. Please cite publications and literature.
# A simple Google Scholar search would give you many references.

Notes on grammar: Needs some work. Several instances where colons are inappropriately inserted mid sentence or in subheadings. Explanations are not terse. Several instances of switching between personal and impersonal style of writing, which is distracting.

== [[Conjugate gradient methods]] ==

* Author list: Remove cornell ID
* Introduction
# All inline notations (e.g., `x`, `A`) should be typed using LaTex.
* Theory, methodology, and/or algorithmic discussions
# All equations need to be better formatted.
# Is Gauss-Newton no longer referenced?
# Theorems listed in the first section should be accompanied with high level explanation, not just a list of the theorems themselves. The page should read like an article, with proper flow.
# Please indent equation blocks.
# Please properly format pseudocode.
* At least one numerical example
# Steps should be accompanied with explanation, or reference to the corresponding step in the pseudocode.
# Please properly format in a more organized manner, aligning equations appropriately and demarcating steps appropriately.
* A section to discuss and/or illustrate the applications
# Consider including 2 additional examples of applications
* A conclusion section
# Consider adding future research directions
* References
# Reference primary sources rather than Wikipedia
# Too few references.
# More references should be added. A simple Google Scholar search would give you many references.

== [[Geometric programming|Geometric Programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Examples of applications in this section use the same reference. Please cite their individual sources.
* Theory, methodology, and/or algorithmic discussions
# The symbol denoting the domain in the definition of a monomial is unclear. Please clarify it or fix this if it is incorrect.
# Definition of posynomial refers to section 2.1 which is missing from the Wiki (sections are not numbered in the main text).
# In the generalized posynomial subsection, bullet points do not tell us why h(x) is posynomial. Either provide reasons or simply state that h(x) is posynomial. Also explain why h3 is a generalized posynomial.
# Additional theory on the feasibility analysis could be provided in this section.
* At least one numerical example
# In the transformation example, the last two constraints could also be simplified by applying a natural logarithm on both sides. Please update them as well.
* A section to discuss and/or illustrate the applications
# The figure in this section needs to be labeled.
# The figure needs to be resized and perhaps aligned to the center.
* A conclusion section:
# Please avoid vague language such as: “This makes”.
# Please avoid opinionated statements: “one of the best ways”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# This Wiki has very few references. A quick Google Scholar search may provide relevant references.

== [[Adam]] ==

* Author list
* An introduction of the topic
# Some grammatical errors here, mostly related to the need for commas in certain places (e.g., “Before Adam..”).
# Some minor errors with parts of speech throughout the section, need to revisit phrases such as “which has broader scope in future for”, etc.
# Try splitting up some of the longer sentences in this section, a couple are hard to read.
# Avoid definitive statements about Adam being the best or always better solver, as this is simply not true (the choice of the “best” optimizer is setting-dependent). Use language such as “Research has shown that Adam has demonstrated superior experimental performance over..” and then cite academic references to back this claim.
# What does adam stand for? Introduction is insufficient. Please expand.
* Theory, methodology, and/or algorithmic discussions
# Revise grammar here, noticing some missing commas and uncapitalized word after period.
# Rephrase “second one is to update the old position with the updated position”.
# Use LaTex code or equation editor to display all equations and variables in this section, and actual subscripts instead of “m_t”, etc.
# Avoid inserting inline citations after words like “According to..” or “This article..” as it is a bit informal. This could be rephrased or changed to something like “According to author,^[2] …” with author name inserted.
# Remove white space before the period in RMSP discussion.
# Please provide a pseudocode.
# Please use list the two methods here “Adam is a combination of two gradient descent methods which are explained below”
# Please expand the theory section significantly. Theoretical convergence properties should be discussed, even if briefly.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
* A section to discuss and/or illustrate the applications
# Same comment as before, consider replacing inline citations after words like “According to..”.
* A conclusion section
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Try to avoid references to blogs and use peer-reviewed academic references instead.
# Too few references.
# More references should be added. A simple Google Scholar search would give you many references.

== [[A-star algorithm|a* algorithm]] ==

* Author list: Remove cornell ID
* Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.
* An introduction of the topic:
# Weird spacing between paragraphs. Please fix this issue.
# In the titles, please change the font from bold to normal to have consistent formatting in the site.
# Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.
# There are no citations in the introduction. Please cite every source.
* Theory, methodology, and/or algorithmic discussions
# Please add the mathematical description of the algorithm.
# Reference style varies in sentences. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please fix grammatical and spelling errors as (“from current position to the goal”, “There are a lot of discussions”, etc). Also, many hyphens are missing as “non playable”.
# In algorithms, it is a standard to add high-level description (i.e. pseudocode or flowchart). Please incorporate it.
# Use LaTex code or equation editor to display all equations and variables in this section (e.g., “f(n)...”, “h(n)..”, etc.). This goes for other sections as well.
* At least one numerical example
# The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.
# Instead of writing things like “The above image..”, label each figure and use the figure number to refer to it in text.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# No references in the applications. Please cite every source
# Preferably, add at least an additional application.
* A conclusion section
# Conclusion should summarize descriptions. Please modify it to provide a summary.
# Please pay attention to the length and structure of sentences here and in the full page. First sentence is hard to read.
* References
# References seem to vary in format and are not linked correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Incorrect reference style. Please follow the example and use the template.

== [[Job shop scheduling|Job-Shop Scheduling Problem]] ==

* An introduction of the topic
# The current introduction to the jobshop scheduling problem has only two sentences in addition to the parameter description. Introduction typically contains information about the problem, its importance in the real-world, and some information about the solution techniques and their types to solve the problem. Please add some information that covers the above.
* Theory, methodology, and/or algorithmic discussions
# It is unclear whether the assumptions stated in this section are required to apply the following solution techniques. Please clarify the same. Also use complete sentences to state them.
# The branch and bounds method described in this section only discusses the solution technique for problems with one machines. However, branch and bound is a general technique that can be applied to any MILP problems with varying scales. Please update the “methods” section to be as general as possible.
# Since this Wiki focuses on jobshop scheduling, at least two methods are expected. Branch and bound is a general MILP technique, so, it is recommended to add a tailored technique that can only solve specific jobshop scheduling problems. Solving the numerical example with this technique is not necessary.
# Reference to the branch and bound technique described in this section is a “youtube” video. Please add references in literature that describe this method in detail. The method used in this video is highly tailored for a single machine application. This is also an incorrect way to cite a reference. Please keep this section as general as possible.
# Use LaTex code or equation editor to display all equations and variables in this section and all other sections as well.
# Check grammar in this section. For example, phrases like “are as follows” need to be followed by a colon and not a period.
# Consider rewriting the assumptions as a list in this section.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# The example used in this section is exactly the same as the one in the youtube video. Please use a modification of this example or choose another example/method to demonstrate the solution technique. Your team should ideally create a numerical example independently. If you take a numerical example directly from a particular source, you will need to get explicit permission from the textbook author in writing and share that written permission with the instructors.
# The figure in this section is not numbered when all others are. Relabel this figure for consistency and its number to refer to it in-text.
# A numerical example should be simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments).
* A section to discuss and/or illustrate the applications
# This section should only focus on real-world applications of the jobshop scheduling problem. But currently, this section includes additional information on solution techniques/complexity that is appropriate for the Introduction section. Please discuss the applications of the problem in this section.
* A conclusion section
# The meaning of “Operations applications” is unclear. Please explain or update if necessary.
# The current conclusion section does not properly summarize the problem. Please refer to other Wiki examples for an idea to update the section accordingly.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please reference media sources like reference 5 appropriately.
# A simple Google Scholar search would give you many "formal" references.

== [[Optimization in game theory]] ==

* Author list: remove cornell IDs.
* An introduction of the topic
# References are not linked. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
* Theory, methodology, and/or algorithmic discussions
# Why only a subsection on "Nash Equilibrium" is included in "Theory" section? Please re-format.
# Please edit references.
# Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm.
# Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.
* At least one numerical example
# Please organize the last part in a more readable format. Questions may be in bold and numbered, answers are more direct, etc.
# Remember to cite all images and tables.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# Very good, link the reference and cite all sources.
* A conclusion section
# Please add more summarizing especially from theory sentences and avoid long sentences.
* References
# Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Reference primary sources rather than Wikipedia
# Incorrect reference style. Please correct.

== [[Trust-region methods]] ==

* Author list:
# Remove cornell IDs. Author is also spelled incorrectly.
# Add the course section.
* An introduction of the topic
# References are not linked. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Use LaTex code or equation editor to display all equations and variables (e.g., “xk”, “f`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “we”. This goes for all other sections as well.
* Theory, methodology, and/or algorithmic discussions
# Organization of ideas in this section needs work.
# You have not defined explicitly why the Cauchy point is important to compute beyond a vague allusion to performance improvements, which is also wrong (it is useful because of its guarantees for convergence, not performance) It is also misspelled.
# Each approach should have accompanying explanation and motivation for why it is being discussed. It is not enough to outline the algorithm.
# Please make sure symbols are properly subscripted and superscripted (e.g. “pk” should be “p_k”
# Please format the algorithm in proper algorithmic pseudocode format.
# Little to no discussion on global convergence guarantees
# Please include discussion about the advantages and disadvantages of the algorithm
# Fix typo “couchy point”.
* At least one numerical example
# Any code functions (uminfunc) should have proper text formatting.
# The graph needs a better caption explaining how the axes are labeled and what data points are being shown.
# Please increase the quality of the figure. It is hard to see the red line.
# Add citation to “The Rosenbrock function is a non-convex function, introduced by Howard H. Rosenbrock in 1960, which is often used as a performance test problem for optimization algorithms.”
* A section to discuss and/or illustrate the applications
# The content in this section as it is currently does NOT describe applications, but rather different approaches within the trust region methodology. Please provide specific applications (e.g. TRPO in reinforcement learning).
* A conclusion section
# Please add more summary, future research directions for example is a good start.
* References
# Incorrect reference style.
# Please consider having the references as this Wiki template, <nowiki>https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization</nowiki>
# More references should be added. A simple Google Scholar search would give you many references.

*There are numerous misspellings, grammatical errors, and incorrect claims. Please fix these.

== [[Momentum]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Apart from an explanation on momentum, it is necessary to briefly point out the limitations of SGD and why momentum could help with these limitations. Please update it accordingly.
# Remove bold on “Momentum”.
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
* Theory, methodology, and/or algorithmic discussions
# Equation formatting is very poor and should be formalized.
# It is important to use technical language for this Wiki. Although a layman’s explanation is appreciated, it would be better to skip using words like “zig zagging”. Try to explain all concepts in a technical language with few simplifications but NOT vice versa.
# The definition of the update rule for SGD with momentum looks incorrect, specifically the first expression. Please fix it and also explain all the parameters used.
# Use LaTex code or equation editor to display all equations and variables (e.g., “W”, “V`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “you”.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step". Since writing all iterations is not feasible, at least present a few iterations for both cases.
# Please try to label the plots that explains what each line color means.
# Starting point for SGD with momentum is different in explanation and the table. Please fix the same.
* A section to discuss and/or illustrate the applications
# Please use correct terminology like “optimizing non-convex functions” and not “training non-convex models”.
# Adam, Adadelta, and RMSprop are variants of SGD that already use momentum. Please double check the writing and update if necessary.
* A conclusion section
# Please refrain from using words like “zig zag” effects.
* References
# Almost all references used are URLs. Please try to add journal/conference articles or books for references, instead of directly citing the URLs. Please check the list below and run a quick Google (Scholar) search to identify relevant literature.

== [[Stochastic dynamic programming|Stochastic Dynamic programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Discussion on applications should be moved to a separate section.
* Theory, methodology, and/or algorithmic discussions
# Remove the grey box background of equations.
* At least one numerical example
* A section to discuss and/or illustrate the applications
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Outer-approximation (OA)|Outer-approximation]] ==

* An introduction of the topic
# See formatting guideline below
# Avoid opinionated statements such as “MINLP problems are usually the hardest to solve”.
# Rearrange the text such that the MINLP formulation is in the theory section and keep the introduction in words only.
* Theory, methodology, and/or algorithmic discussions
# Consider left aligning equations and optimization problem formulations by the “=”. See [[Stochastic programming|https://optimization.cbe.cornell.edu/index.php?title=Stochastic_programming]] for an example
# The sentence “The Outer-Approximation (OA) algorithm was first proposed by Duran and and Grossmann in 1986 to solve MINLP problems.” needs a reference.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# “Minimize” and “subject to” should be “min” and “s.t.” in MathType
* A section to discuss and/or illustrate the applications
# Does not explicitly point out why OA is applicable (and/or preferred) in these applications, rather than other MINLP approaches (show that the problem formulations are amenable to a solution approach through OA)
# The sentence “... an active research area and there exists a vast number of applications in fields such as engineering, computational chemistry, and finance.” needs references.
# Place GAMS code in a single code box or remove it.
# Consider reformatting to make steps more readable. Inserting spaces and breaking down steps would help.
* A conclusion section
# Too short. Consider discussion on future research direction and discussion on uncertainty
# Please review abbreviations throughout the page. Why is MINLP redefined here? “Outer-Approximation is a well known efficient approach for solving convex mixed-integer nonlinear programs (MINLP)”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove "Template:Reflist"

== [[Unit commitment problem]] ==

* Author list
* An introduction of the topic
# Please expand the introduction and avoid discussions of examples or specific applications in this section.
# The sentence “Nonlinear, Non-convex programming optimization problem.” doesn’t make sense by itself and Non-convex shouldn’t be capitalized.
* Theory, methodology, and/or algorithmic discussions
# Figure/image format should be revised to better display the content.
# Uppercase characters are used randomly (e.g., “non-convex transmission Constraints”) . Please follow correct language conventions for sentence structure.
# Avoid inserting inline citations after words like “written in matrix form as equation [3]..” or “presented in [3]...” as it is a bit informal when you don’t explicitly name the subject. Also these two sentences are grammatically incorrect and appear to be missing an ending period and comma, respectively.
# Don’t say “written in matrix form as equation..” and just cite the reference, actually write out the equation.
# Properly label the figure in this section with a figure number and improve visibility by making it larger.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Label the figures in this section properly with figure numbers.
# Fix typo “while minimize” to “while minimizing”.
# Avoid pronouns such as “we”.
# Use the equation editor when typing equations.
* A section to discuss and/or illustrate the applications:
# I suggest changing the order of the subtitles here. For example, Single-Period Unit Commitment.
* A conclusion section
* References

== [[Frank-Wolfe]] ==

* Author list:
* An introduction of the topic
# I suggest highlighting disadvantages along with advantages.
* Theory, methodology, and/or algorithmic discussions
# “[n x 1] matrix” please use the equation editor to express mathematical descriptions and symbols (p,b, etc)
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please show at least a few iterations. Even for smaller examples if needed. Report the final solution.
# Please use the LaTex code or equation editor for min and include s.t., etc.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps. For your example, please explicitly state that the derivative is taken etc.
* A section to discuss and/or illustrate the applications:
* A conclusion section
# Same as the introduction. Pros and cons should be evaluated together!
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Line search methods|Line Search Method]] ==

* Author list
* An introduction of the topic
# Expand the introduction and avoid discussion on some of the specific steps in the solution process.
# Provide references here.
* Theory, methodology, and/or algorithmic discussions
# The phrase “are as follows” in the steepest descent method discussion needs to be followed by a colon.
# Rephrase “has a nice convergence theory” and cite a reference for this claim.
# Avoid pronouns such as “we”.
# Add citation after “.. proposed by Phillip Wolfe in 1969.”
# Figure 1 is between two sections. Please fix this issue.
* At least one numerical example:
# Add some space between iterations or subsection break
* A section to discuss and/or illustrate the applications:
# Too few references in this section.
# Last paragraph makes some claims without references.
* A conclusion section
* References
# References should be properly formatted. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Piecewise linear approximation|Piecewise Linear Approximation]]==

* Author list
* An introduction of the topic
# The content of this section is good, but there are some issues with sentence clarity and some other grammatical errors. Please revisit this section and make changes accordingly.
* Theory, methodology, and/or algorithmic discussions
# Fix typo “to force the x’ values become associated with”.
* At least one numerical example
* A section to discuss and/or illustrate the applications
# Please aim for a maximum average sentence length of ~25 words. Some of these longer sentences are hard to read.
* A conclusion section
# Expand the conclusion section to be longer than one sentence. The conclusion section to include a brief summary of what was discussed above, an emphasis on it’s significance, and a brief discussion of future extensions and research direction if applicable.
* References
# Include hyperlinks to sources when possible.

== [[Mathematical programming with equilibrium constraints|Mathematical Programming with Equilibrium constraints]] ==

* An introduction of the topic
# This section includes several terms like variational inequalities, constraint qualifications that were not discussed in the class. Please add a sentence to explain them before using them.
* Theory, methodology, and/or algorithmic discussions
# The meaning of parameter vector x is unclear. Please add more information or update if necessary.
# Equations and symbols in the PIPA subsection are not formatted correctly. Please use the same formatting for all equations, so they read as mathematical equations and not text. This goes for all other sections as well.
# Use equations instead of images to represent math programs and equations in the Implicit Descent and SQP subsection.
# Apart from the steps for each solution technique, please also add a few sentences that describe each method.
* At least one numerical example
# Please define the terms like NCP, MP before abbreviating them. Also try not to unnecessarily abbreviate simple terms.
# Equations should be typed by LaTex. Images for equations are unacceptable.
# GAMS code is strongly discouraged. Please solve the problem "step-by-step".
# The selected numerical example is fine but is directly solved with the MPEC solver in GAMS. Try to solve it manually like the homework/in-class problems step by step using the steps described in the previous section by choosing any of the methods.
# Avoid using figures in the equations (subject to etc)
* A section to discuss and/or illustrate the applications
# Add references to “power management, highway pricing, chemical process engineering, and traffic planning.”
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Wing shape optimization|Wing shape Optimization]] ==

* Author list: Remove cornell ID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# The introduction is missing several references (e.g., “software packages like computational fluid dynamics..”, sentences containing things that aren’t common knowledge, performance claims, etc.)
# Avoid discussion involving finer details of subject methods in this section.
# In the titles, please change the font from bold to normal to have consistent formatting in the site. Same applies to box of content!
* Theory, methodology, and/or algorithmic discussions
# Properly cite the CFD package, don’t just include a link.
# Properly label the figure with a figure number.
# Consider removing white space between isolated sentences to improve readability.
* At least one numerical example
# If you’ve already defined an abbreviation (CFD), there is no need to define it again. Just use the abbreviation.
# Avoid pronouns such as “we” or “they”.
# Phrases like “under the following” need to be followed by a colon.
# Properly label the figure with a figure number and consider making them larger to improve visibility. Call the reader's attention to the figures in text by referencing the figure number.
# “As seen in the video below” is stated yet there are only images present and it may be initially unclear to the reader which figure is being referenced here.
# Avoid inserting inline citations like “[4] introduces an..” as it is a bit informal when you don’t explicitly name the subject.
# Don’t just cite the reference when discussing the problem formulation, explicitly write the model formulation and solution process using LaTex or equation visual editor.
* A section to discuss and/or illustrate the applications
# Some characters are randomly capitalized in this section.
* A conclusion section
# These variables should be defined before the conclusion section, they are out of place here. Also, please use normal text when explaining variables except for the variable symbol.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Interior-point method for NLP|Interior point method for NLP]] ==

* An introduction of the topic:
* Theory, methodology, and/or algorithmic discussions
# Primal-Dual formulation and comparison to the Barrier Method is not discussed.
# Include brief discussion about big O convergence rates.
# Need discussion about the concept of “central path” and the notion of self concordance
# Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
# Graphs and images are incorrectly formatted to the page. Consider proper alignment with respect to the text body.
# Use explicitly typed Latex equations instead of images to represent math programs and equations.
# Fix typo “optimisation”.
# Use LaTex code or equation editor to display all equations and variables (e.g., “xi ”, “μ”, etc.).
* At least one numerical example:
# There are formatting issues with figures 2,3. Please make sure to embed them within their respective sections.
* A section to discuss and/or illustrate the applications
* A conclusion section
# Minor character code typos in the conclusion.
# Also, please add more discussion in this section. Future research directions is a good start.
# There is a box "􏰐"
* References

== [[AdaGrad|Adagrad]] ==

* An introduction of the topic:
* Theory, methodology, and/or algorithmic discussions
# Include discussion on its variants (most important is AdaDelta).
# Include disadvantages of Adagrad, since this provides motivation for the discussion on the variants and improvements of Adagrad
# Include comparisons to other popular optimizers (particularly important is comparisons to regular SGD and Adam)
# Different convergence rates are possible depending on the setting where Adagrad is used, but this is not mentioned on the page currently. As such the regret bound section should be more thoroughly explained.
* At least one numerical example
# In the first sentence, “..take the following numerical example” should be followed by a colon.
# Fix typo “trayectory”.
* A section to discuss and/or illustrate the applications
# This section is too short; include specific applications in which input features are sparse and Adagrad excels.
# Add reference to the claim “Mainly, it is a good choice for deep learning models with sparse input features”.
* A conclusion section
* References

# Too few references overall, you should aggregate information from multiple sources (even if the base algorithm itself comes from a singular paper)

== [[McCormick envelopes|McCormick Envelopes]] ==

* Author list: OK but I suggest removing NetID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# First sentence is hard to read. Please consider keeping sentences below 25-30 words.
# No references provided. Please cite all sources.
# Figure 1 is provided in the middle between two sections. Please include in the introduction section.
* Theory, methodology, and/or algorithmic discussions
# References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# When using mathematical expressions and symbols, please use the equation editor. (e.g., x*y, exy + y, sin (x+y) - x2)
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# For the sample GAMS code, please place it in a code box
* A section to discuss and/or illustrate the applications
# Having a list is not enough. Please explain at least three applications in a few sentences each.
# This section should be at least a paragraph to discuss relevant applications. Each application should be explicitly linked to the page topic. A few keywords do not meet the requirement at all.
* A conclusion section:
* References
# References are not expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please follow the standard reference style - the current format is incorrect.

2021 Cornell Optimization Open Textbook Feedback

2021-12-05T20:05:39Z

Asa273: /* Momentum */

== [[Lagrangean duality|Lagrangian duality]] ==
* Author list, sections and TOC
# Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.
# Remove cornell ID from Author list
* An introduction of the topic
# This section includes sentences on constructing the dual problem and is referred to as Lagrangian relaxation (LR). This is incorrect, please fix the definition of LR.
# Definitions of LR and its relation to duality should be double checked and re-written.
# Only one reference is present in this section. Please add more relevant references by expanding this section.
# Consider merging the “introduction” and “history” sections.
# In the titles, please change the font from bold to normal to have consistent formatting in the site.
* Theory, methodology, and/or algorithmic discussions
# The Lagrangian variables associated with equality constraints h(x) are unbounded but the Lagrangian dual problem states them as non-negative. Please fix the same.
# Also to construct a dual, we do not change minimization to maximization directly. We observed such things in the examples in lecture notes due to simplification. The lagrangian dual problem would be minimize (,).
# Adding to the previous point, the Lagrangian is a lower bound on the original objective; the solution to the primal and dual or only equivalent if the duality gap is 0. You reference this in one section, but this is after your statement “Hence, solving the dual problem, which is a function of the Lagrangian multipliers (𝜆*) yields the same solution as the primal problem, which is a function of the original variables (x*). “. Please clarify the specific conditions that must hold for the solution of the dual to be equal to the primal’s.
# You refer to the “Complementary Slackness Theorem”, but don’t actually write the mathematical representation of complementary slackness. Please fix this. Also consider including the derivation of the complementary slackness condition, as it is both easy and short. Boyd is a good reference for this.
# Last step of the “process” subsection also needs updating according to the previous comments.
# The inline notations should also be typed using LaTex.
# Please use the LaTex code or equation editor for min, s.t., etc.
* At least one numerical example
# Only one dual variable is associated with each constraint. The numerical example uses two for the first and second constraint which is unnecessary. Please update it accordingly for both constraints. This particular example will only have two dual variables instead of the five dual variables used currently.
# All consecutive steps need to be updated since the dual variables would be updated.
# After substitution the nonlinear function should be further simplified. The current expression reads like a highly nonlinear function but can be easily simplified.
# Similar to the comments in the methodology section, inverting minimize to maximize is incorrect. Please update the dual objective function and domain of dual variables accordingly.
# Please use the LaTex code or equation editor for min, s.t., etc.
* A section to discuss and/or illustrate the applications
# Bullet points could be used to state the last four real-world examples that explain the physical meaning of the primal and dual problems.
# Add references for the last set of applications.
* A conclusion section
# This section contains a few typos. Please fix the same.
* References
# Some citations' hyperlinks are displaying.

== [[Disjunctive inequalities|Disjunctive Inequalities]] ==

* Author list
# Missing course section and semester
# Remove cornell ID
* An introduction of the topic
# No citations are present in this section.
# “mixed-integer programming (MIP)” should be used instead of “multiple integer programming (MIP)”. Please fix this error.
* Theory, methodology, and/or algorithmic discussions
# The abbreviation MILP is not previously defined. Please fix this issue.
# You consistently use the negative sign instead of the NOT operator for y (-y instead of ¬y).
# Some inconsistencies with the spacing of variables, constraints, etc., under the “General” section that need to be fixed.
# Typo in “This is shown below by M1, M2, y1, and y1:” where y1 needs to be changed to y2. Why use two different Big-M variables here? Elsewhere in the Wiki you only use one so this could lead to confusion with a general audience. Also if this was taken from the lecture notes then it needs to be cited.
* At least one numerical example
# Please reformulate and solve a complete numerical example rather than just reformulating a general example. Demonstrate the use of Big-M and Convex Hull formulation in an optimization problem that provides details such as individual steps in the problem solving process and final results.
# Add space between vee (V) operator and brackets in first line of Latex
# Please format variables correctly, for example, use <math>x_1</math> instead of x1.
* A section to discuss and/or illustrate the applications
# Please format the equations appropriately either by using latex code or the visual editor. These images are NOT acceptable!
* A conclusion section
# There is no conclusion presented in this section at all.
* References
# The included references have NOT been used anywhere in the Wiki. Add references for sentences that are not common knowledge and please link them appropriately with the text in Wiki. If the figures used here were not original works, you must also cite them.
# There are many papers on this topic. A simple Google (Scholar) search could provide you with sufficient references to cite.
# Many important references of this topic are missing.
# Please consider linking the references as demonstrated in the Wiki tutorial on Canvas and in this template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

==[[Stochastic programming|Stochastic Programming]] ==

* Author list: Remove cornell IDs
* An introduction of the topic
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
# This section only includes two sentences on Stochastic programming (SP), while the rest gives examples of uncertainty. Please discuss the need for SP in the presence of uncertainty. Also, discussion on robust optimization and its limitations should be removed since it is out of place.
* Theory, methodology, and/or algorithmic discussions
# Please avoid direct inline linkbacks to Wikipedia.
# The symbol “xi” in the methodology subsection should be explained.
* At least one numerical example
# Copying a numerical example "entirely" from a textbook is inappropriate. Your team should come up with a "numerical" case.
# No specific application context is needed for a numerical example.
# The inline notations (`x1`, `s1`) should also be typed using LaTex.
# Label all tables with a table number for better readability.
# Properly format the solution table with the label attached rather than the following sentence. The solution table looks different from the others, please fix this for consistency.
* A section to discuss and/or illustrate the applications;
# I suggest eliminating citing the last name of the first author (i.e. Zhou et al.)
* A conclusion section
* References
# URLs of some citations are not properly formatted (not showing the hyperlinks).

== [[Exponential transformation|Exponential Transformation]] ==

* Author list
# Missing course section
# Remove cornell ID
* An introduction of the topic
# Please expand the introduction.
# Please aim for a maximum average sentence length of ~25 words. Last sentence with 51 words is hard to read.
# Second Sentence: please change the word “they” as it could make the meaning ambiguous
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
# If you use abbreviations, please introduce them (e.g. NLP,MINLP)
* Theory, methodology, and/or algorithmic discussions
# Please explain the transformation in words along with equations
# Terms like posynomial should be described in detail.
# Please move the numerical example to the section below
# The “(eq 1)” is not needed here.
# Please expand this section.
* At least one numerical example
# In the third equation of the numerical example, it is confusing to have coefficients after numbers. Some readers may read it as an exponent.
# Last equation in this section after “further linearization” is incorrect. This equation cannot be further linearized, please fix this.
# Please explain the steps in the numerical examples in detail. The step-by-step solution should be provided.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# Missing part of text: “Proof of convexity of with positive definite test of Hessian…”
# Applications are not numerical examples. Please refer to this link for example of applications: [[Duality|https://optimization.cbe.cornell.edu/index.php?title=Duality]]
# Citation 7 is missing in current applications
# The section current applications is redundant
# Please use the LaTex code or equation editor for min, s.t., etc.
# Under current applications, do not just use a hyperlink to describe an application. Actually describe it. And properly inline citation style should be used instead of the hyperlink.
# The convexification application of MINLP can be further simplified for binary variables. Please refer to the lecture slides for more information.
* A conclusion section
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
* References
# Please consider linking the references by using this as Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Citation 7 is missing in current applications

== [[Sparse Reconstruction with Compressed Sensing|Sparse reconstruction with Compressed Sensing]] ==
This Wiki needs a significant rewrite. Please go through the comments for details.

* An introduction of the topic
# The introduction section should include information about the problem and its implications presented briefly. Please use full sentences to write this Wiki. You may use tools like Grammarly to check sentence formation and grammar.
# This section includes several typos like “sub modual”. Please fix them throughout the wiki and delete them if not required.
# Many abbreviations are used before previously defining them. Please define these abbreviations before using them in the text.
# This section is incomprehensible in its current form. Please rewrite with proper comprehension.
# Equations and math symbols need proper reformatting. The current version reads like text (along with equations) copy-pasted from a specific source. All mathematical symbols and equations should be formatted via LaTex - this is a learning objective of the Wiki assignment. You can find some useful links on converting your equations/symbols into LaTex code here: (https://optimization.cbe.cornell.edu/index.php?title=Help:Contents).
# Try to place the figure at the top of the Wiki between the main text.
# Avoid pronouns such as “we”.
# I suggest the use of more formal abstract illustrations.
* Theory, methodology, and/or algorithmic discussions
# Equations and symbols need proper reformatting.
# Lemmas and theorems are not expected for this Wiki. Sparse reconstruction is a straightforward concept but is unnecessarily complicated here. Please refer to other Wiki examples to get an idea of what the Wiki should convey.
# All equations need to be better formatted.

* At least one numerical example
# Numerical example is missing.
# Every iteration should be clearly presented, and solved "step-by-step".
* A section to discuss and/or illustrate the applications
# Having a list is not enough. Please explain at least three applications in a few sentences each.
* A conclusion section
# Conclusion section is missing.
* References
# The current reference list is not correctly formatted. References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Portfolio optimization|Portfolio Optimization]] ==

* Author list
# Remove cornell id
* An introduction of the topic
# The introductory sentence should be rephrased. The action of minimizing the risks does not inherently maximize the gains, rather PO aims to maximize gains whilst minimizing risks.
# Amount of whitespace can be reduced by changing the orientation of Figure 1 and the sentences in this section.
# Define terms such as risk, return, portfolio, etc., when you introduce them. Assume that the reader may not know much about finance. This goes for all other sections as well.
* Theory, methodology, and/or algorithmic discussions
# A brief mention of modern portfolio theory (i.e.. Markowitz) would be appropriate in this section.
# Several grammatical errors here involving sentence structure and clarity. Some questionable semantics (e.g., “The portfolio optimization mainly assumes two directions.”) and syntax (phrases such as “.. is as follows” should be followed by a colon). Misuse of commas and missing commas in this section. Two sentences introducing E(rp) and w should be combined into one.
# Use LaTex to distinguish variables written within a sentence, such as m and n.
# Rephrase “Cut the relevant information and conditions in the portfolio optimization, as well as the final requirements into the relevant variables, constraints and linear functions of the linear programming problem.”
# An explanation of a few common constraints would be helpful, rather than just including a table.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Solving the numerical example by GAMS is inappropriate. Please provide detailed step-by-step calculation results.
# All tables need to be labeled.
# Include figure number in label for consistency.
# Fix misspelling “dolling decision variables”.
# Use LaTex for all variables, equations, and constraints here.
# Example 2 table is hard to read, so making it bigger would help.
# Remove the “Using excel as the solver” part from the sentence before the solution discussion.
# Some grammatical errors here (phrases such as “.. is as follows” should be followed by a colon).
* A section to discuss and/or illustrate the applications
# Rephrase “Portfolio optimization can be used to screen investment projects that meet investors, rationally allocate investment amounts, etc.”
# Not sure “relevant” is the correct word choice here.
# You need more specific examples with the utility of portfolio optimization, this section is quite general as is. Some more detail and focus on real-world applications in the financial industry that relate to retirement planning, financial security, economic stability, etc., would be helpful.
* A conclusion section
# Need some commas here.
# The sentence “Linear programming has been around since the 1940’s and has such a wide base of applications” is not necessary.
* References
# Please consider linking the references as demonstrated in the Wiki tutorial on Canvas and in this template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove white space between end of sentences and reference numbers.

== [[Chance-constraint method|Chance constraint method]] ==

* Author list:
* An introduction of the topic
# Please consider correcting a few grammatical errors: “pre-planned for”, “god”, “certain levels of feasibility is guaranteed in what are”, and “Performance of a system”
# In “Chance-constraint”, it is capitalized randomly throughout the introduction. Please correct.
# Please use technical language to briefly introduce chance-constrained programming. Words like “acts of god”, “cost of doing business” are not appropriate for a technical Wiki.
* Theory, methodology, and/or algorithmic discussions
# Please add a citation to the first sentence.
# Xi is an uncertainty/randomness variable. It is better to use clear language.
# Please use the mathematical editor for adding explanations in the text. Using “ x is a decision variable” is hard to read. Same for f(x) and others.
# Theory is insufficient. Please expand and explain different approaches.
# Please add pros and cons explicitly as a list.
# Explain the physical meaning for examples of chance constraints along with all the notations used.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please remove this example as it is directly from this book. The example should be purely numerical without any background.
# Please use the equation editor for min, st., etc.
# Please use the mathematical editor for adding explanations in the text. Using “ x is a decision variable” is hard to read. Same for f(x) and others.
# Please change the table format so as not to confuse the reader.
# Multiple instances of [Chart to be added] are missing.
# Example is incomplete.
# Avoid pronouns such as “we”.
* A section to discuss and/or illustrate the applications
# Please connect several grammatical and spelling errors: “real life application”, Energy creation, particularly in renewable sources, have high variabilities”, and others
# “Zhao, Xue, Cao, and Zhang”. No need to list all authors within the article. Provide a reference is sufficient. If authors must be mentioned, (Zhao et al.) should be ok.
* A conclusion section
# Uniqueness and universality earlier are not clear to me. If they are not discussed earlier in the application, it would be better not to introduce new discussions in the conclusion.
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
* References
# References seem to vary in format. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Bayesian Optimization]] ==
* Section titles should not be "bold". Please double check using source editor on the section titles.
* Contents: Subheadings for EI and the algorithm should not be bolded, Random words should not be capitalized.
* Author list: Remove cornell ID, Please check names
* Introduction
# The introduction is too general and not substantial enough. For example, simply saying BayesOpt is useful when the objective function is unknown obscures exactly HOW it is useful (namely, computational efficiency in applications where ground truth sampling is expensive). Discussion on applications should be moved to a separate section.
# Machine learning rarely includes black-box functions to be optimized. Bayesian optimization is almost never used for optimizing ML loss functions but can instead be used for hyperparameter optimization. Please update such claims in this section.
* Theory, methodology, and/or algorithmic discussions
# Captions need reformatting.
# Consider italicizing keywords rather than bolding.
# Please add a citation to the first sentence.
# Discussion on acquisition functions should include comparisons, tradeoffs, and reasons to use one over the other. Should also note that expected improvement is the most widely used in practice, and explain.
# Avoid pronouns such as “we”.
# Please write equations in the Wiki instead of attaching images for equations.
# Acquisition function figure could be made larger and clearer to improve readability.
* At least one numerical example
# Any references to functions or methods in code ‘e.g. fmin’ should be properly formatted as code-stylized text.
# Please use the equation editor for min, st., etc.
# Avoid including a figure of the code for this example and explicitly describe the steps to the modeling and solution process instead.
# Avoid pronouns such as “our” and “we”.
* A section to discuss and/or illustrate the applications
* A conclusion section
# Please do not use brackets to enclose lists.
# Some claims here should be supported by references. Please cite each source after its sentence.
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Try to avoid references to “pop” machine learning blogs where anyone can be an author. (e.g. towardsdatascience)
# All references are URLs. Please cite publications and literature.
# A simple Google Scholar search would give you many references.

Notes on grammar: Needs some work. Several instances where colons are inappropriately inserted mid sentence or in subheadings. Explanations are not terse. Several instances of switching between personal and impersonal style of writing, which is distracting.

== [[Conjugate gradient methods]] ==

* Author list: Remove cornell ID
* Introduction
# All inline notations (e.g., `x`, `A`) should be typed using LaTex.
* Theory, methodology, and/or algorithmic discussions
# All equations need to be better formatted.
# Is Gauss-Newton no longer referenced?
# Theorems listed in the first section should be accompanied with high level explanation, not just a list of the theorems themselves. The page should read like an article, with proper flow.
# Please indent equation blocks.
# Please properly format pseudocode.
* At least one numerical example
# Steps should be accompanied with explanation, or reference to the corresponding step in the pseudocode.
# Please properly format in a more organized manner, aligning equations appropriately and demarcating steps appropriately.
* A section to discuss and/or illustrate the applications
# Consider including 2 additional examples of applications
* A conclusion section
# Consider adding future research directions
* References
# Reference primary sources rather than Wikipedia
# Too few references.
# More references should be added. A simple Google Scholar search would give you many references.

== [[Geometric programming|Geometric Programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Examples of applications in this section use the same reference. Please cite their individual sources.
* Theory, methodology, and/or algorithmic discussions
# The symbol denoting the domain in the definition of a monomial is unclear. Please clarify it or fix this if it is incorrect.
# Definition of posynomial refers to section 2.1 which is missing from the Wiki (sections are not numbered in the main text).
# In the generalized posynomial subsection, bullet points do not tell us why h(x) is posynomial. Either provide reasons or simply state that h(x) is posynomial. Also explain why h3 is a generalized posynomial.
# Additional theory on the feasibility analysis could be provided in this section.
* At least one numerical example
# In the transformation example, the last two constraints could also be simplified by applying a natural logarithm on both sides. Please update them as well.
* A section to discuss and/or illustrate the applications
# The figure in this section needs to be labeled.
# The figure needs to be resized and perhaps aligned to the center.
* A conclusion section:
# Please avoid vague language such as: “This makes”.
# Please avoid opinionated statements: “one of the best ways”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# This Wiki has very few references. A quick Google Scholar search may provide relevant references.

== [[Adam]] ==

* Author list
* An introduction of the topic
# Some grammatical errors here, mostly related to the need for commas in certain places (e.g., “Before Adam..”).
# Some minor errors with parts of speech throughout the section, need to revisit phrases such as “which has broader scope in future for”, etc.
# Try splitting up some of the longer sentences in this section, a couple are hard to read.
# Avoid definitive statements about Adam being the best or always better solver, as this is simply not true (the choice of the “best” optimizer is setting-dependent). Use language such as “Research has shown that Adam has demonstrated superior experimental performance over..” and then cite academic references to back this claim.
# What does adam stand for? Introduction is insufficient. Please expand.
* Theory, methodology, and/or algorithmic discussions
# Revise grammar here, noticing some missing commas and uncapitalized word after period.
# Rephrase “second one is to update the old position with the updated position”.
# Use LaTex code or equation editor to display all equations and variables in this section, and actual subscripts instead of “m_t”, etc.
# Avoid inserting inline citations after words like “According to..” or “This article..” as it is a bit informal. This could be rephrased or changed to something like “According to author,^[2] …” with author name inserted.
# Remove white space before the period in RMSP discussion.
# Please provide a pseudocode.
# Please use list the two methods here “Adam is a combination of two gradient descent methods which are explained below”
# Please expand the theory section significantly. Theoretical convergence properties should be discussed, even if briefly.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
* A section to discuss and/or illustrate the applications
# Same comment as before, consider replacing inline citations after words like “According to..”.
* A conclusion section
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Try to avoid references to blogs and use peer-reviewed academic references instead.
# Too few references.
# More references should be added. A simple Google Scholar search would give you many references.

== [[A-star algorithm|a* algorithm]] ==

* Author list: Remove cornell ID
* Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.
* An introduction of the topic:
# Weird spacing between paragraphs. Please fix this issue.
# In the titles, please change the font from bold to normal to have consistent formatting in the site.
# Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.
# There are no citations in the introduction. Please cite every source.
* Theory, methodology, and/or algorithmic discussions
# Please add the mathematical description of the algorithm.
# Reference style varies in sentences. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please fix grammatical and spelling errors as (“from current position to the goal”, “There are a lot of discussions”, etc). Also, many hyphens are missing as “non playable”.
# In algorithms, it is a standard to add high-level description (i.e. pseudocode or flowchart). Please incorporate it.
# Use LaTex code or equation editor to display all equations and variables in this section (e.g., “f(n)...”, “h(n)..”, etc.). This goes for other sections as well.
* At least one numerical example
# The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.
# Instead of writing things like “The above image..”, label each figure and use the figure number to refer to it in text.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# No references in the applications. Please cite every source
# Preferably, add at least an additional application.
* A conclusion section
# Conclusion should summarize descriptions. Please modify it to provide a summary.
# Please pay attention to the length and structure of sentences here and in the full page. First sentence is hard to read.
* References
# References seem to vary in format and are not linked correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Incorrect reference style. Please follow the example and use the template.

== [[Job shop scheduling|Job-Shop Scheduling Problem]] ==

* An introduction of the topic
# The current introduction to the jobshop scheduling problem has only two sentences in addition to the parameter description. Introduction typically contains information about the problem, its importance in the real-world, and some information about the solution techniques and their types to solve the problem. Please add some information that covers the above.
* Theory, methodology, and/or algorithmic discussions
# It is unclear whether the assumptions stated in this section are required to apply the following solution techniques. Please clarify the same. Also use complete sentences to state them.
# The branch and bounds method described in this section only discusses the solution technique for problems with one machines. However, branch and bound is a general technique that can be applied to any MILP problems with varying scales. Please update the “methods” section to be as general as possible.
# Since this Wiki focuses on jobshop scheduling, at least two methods are expected. Branch and bound is a general MILP technique, so, it is recommended to add a tailored technique that can only solve specific jobshop scheduling problems. Solving the numerical example with this technique is not necessary.
# Reference to the branch and bound technique described in this section is a “youtube” video. Please add references in literature that describe this method in detail. The method used in this video is highly tailored for a single machine application. This is also an incorrect way to cite a reference. Please keep this section as general as possible.
# Use LaTex code or equation editor to display all equations and variables in this section and all other sections as well.
# Check grammar in this section. For example, phrases like “are as follows” need to be followed by a colon and not a period.
# Consider rewriting the assumptions as a list in this section.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# The example used in this section is exactly the same as the one in the youtube video. Please use a modification of this example or choose another example/method to demonstrate the solution technique. Your team should ideally create a numerical example independently. If you take a numerical example directly from a particular source, you will need to get explicit permission from the textbook author in writing and share that written permission with the instructors.
# The figure in this section is not numbered when all others are. Relabel this figure for consistency and its number to refer to it in-text.
# A numerical example should be simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments).
* A section to discuss and/or illustrate the applications
# This section should only focus on real-world applications of the jobshop scheduling problem. But currently, this section includes additional information on solution techniques/complexity that is appropriate for the Introduction section. Please discuss the applications of the problem in this section.
* A conclusion section
# The meaning of “Operations applications” is unclear. Please explain or update if necessary.
# The current conclusion section does not properly summarize the problem. Please refer to other Wiki examples for an idea to update the section accordingly.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please reference media sources like reference 5 appropriately.
# A simple Google Scholar search would give you many "formal" references.

== [[Optimization in game theory]] ==

* Author list: remove cornell IDs.
* An introduction of the topic
# References are not linked. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
* Theory, methodology, and/or algorithmic discussions
# Why only a subsection on "Nash Equilibrium" is included in "Theory" section? Please re-format.
# Please edit references.
# Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm.
# Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.
* At least one numerical example
# Please organize the last part in a more readable format. Questions may be in bold and numbered, answers are more direct, etc.
# Remember to cite all images and tables.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# Very good, link the reference and cite all sources.
* A conclusion section
# Please add more summarizing especially from theory sentences and avoid long sentences.
* References
# Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Reference primary sources rather than Wikipedia
# Incorrect reference style. Please correct.

== [[Trust-region methods]] ==

* Author list:
# Remove cornell IDs. Author is also spelled incorrectly.
# Add the course section.
* An introduction of the topic
# References are not linked. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Use LaTex code or equation editor to display all equations and variables (e.g., “xk”, “f`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “we”. This goes for all other sections as well.
* Theory, methodology, and/or algorithmic discussions
# Organization of ideas in this section needs work.
# You have not defined explicitly why the Cauchy point is important to compute beyond a vague allusion to performance improvements, which is also wrong (it is useful because of its guarantees for convergence, not performance) It is also misspelled.
# Each approach should have accompanying explanation and motivation for why it is being discussed. It is not enough to outline the algorithm.
# Please make sure symbols are properly subscripted and superscripted (e.g. “pk” should be “p_k”
# Please format the algorithm in proper algorithmic pseudocode format.
# Little to no discussion on global convergence guarantees
# Please include discussion about the advantages and disadvantages of the algorithm
# Fix typo “couchy point”.
* At least one numerical example
# Any code functions (uminfunc) should have proper text formatting.
# The graph needs a better caption explaining how the axes are labeled and what data points are being shown.
# Please increase the quality of the figure. It is hard to see the red line.
# Add citation to “The Rosenbrock function is a non-convex function, introduced by Howard H. Rosenbrock in 1960, which is often used as a performance test problem for optimization algorithms.”
* A section to discuss and/or illustrate the applications
# The content in this section as it is currently does NOT describe applications, but rather different approaches within the trust region methodology. Please provide specific applications (e.g. TRPO in reinforcement learning).
* A conclusion section
# Please add more summary, future research directions for example is a good start.
* References
# Incorrect reference style.
# Please consider having the references as this Wiki template, <nowiki>https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization</nowiki>
# More references should be added. A simple Google Scholar search would give you many references.

*There are numerous misspellings, grammatical errors, and incorrect claims. Please fix these.

== [[Momentum]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Apart from an explanation on momentum, it is necessary to briefly point out the limitations of SGD and why momentum could help with these limitations. Please update it accordingly.
# Remove bold on “Momentum”.
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
* Theory, methodology, and/or algorithmic discussions
# Equation formatting is very poor and should be formalized.
# It is important to use technical language for this Wiki. Although a layman’s explanation is appreciated, it would be better to skip using words like “zig zagging”. Try to explain all concepts in a technical language with few simplifications but NOT vice versa.
# The definition of the update rule for SGD with momentum looks incorrect, specifically the first expression. Please fix it and also explain all the parameters used.
# Use LaTex code or equation editor to display all equations and variables (e.g., “W”, “V`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “you”.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step". Since writing all iterations is not feasible, at least present a few iterations for both cases.
# Please try to label the plots that explains what each line color means.
# Starting point for SGD with momentum is different in explanation and the table. Please fix the same.
* A section to discuss and/or illustrate the applications
# Please use correct terminology like “optimizing non-convex functions” and not “training non-convex models”.
# Adam, Adadelta, and RMSprop are variants of SGD that already use momentum. Please double check the writing and update if necessary.
* A conclusion section
# Please refrain from using words like “zig zag” effects.
* References
# Almost all references used are URLs. Please try to add journal/conference articles or books for references, instead of directly citing the URLs.

== [[Stochastic dynamic programming|Stochastic Dynamic programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Discussion on applications should be moved to a separate section.
* Theory, methodology, and/or algorithmic discussions
# Remove the grey box background of equations.
* At least one numerical example
* A section to discuss and/or illustrate the applications
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Outer-approximation (OA)|Outer-approximation]] ==

* An introduction of the topic
# See formatting guideline below
# Avoid opinionated statements such as “MINLP problems are usually the hardest to solve”.
# Rearrange the text such that the MINLP formulation is in the theory section and keep the introduction in words only.
* Theory, methodology, and/or algorithmic discussions
# Consider left aligning equations and optimization problem formulations by the “=”. See [[Stochastic programming|https://optimization.cbe.cornell.edu/index.php?title=Stochastic_programming]] for an example
# The sentence “The Outer-Approximation (OA) algorithm was first proposed by Duran and and Grossmann in 1986 to solve MINLP problems.” needs a reference.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# “Minimize” and “subject to” should be “min” and “s.t.” in MathType
* A section to discuss and/or illustrate the applications
# Does not explicitly point out why OA is applicable (and/or preferred) in these applications, rather than other MINLP approaches (show that the problem formulations are amenable to a solution approach through OA)
# The sentence “... an active research area and there exists a vast number of applications in fields such as engineering, computational chemistry, and finance.” needs references.
# Place GAMS code in a single code box or remove it.
# Consider reformatting to make steps more readable. Inserting spaces and breaking down steps would help.
* A conclusion section
# Too short. Consider discussion on future research direction and discussion on uncertainty
# Please review abbreviations throughout the page. Why is MINLP redefined here? “Outer-Approximation is a well known efficient approach for solving convex mixed-integer nonlinear programs (MINLP)”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove "Template:Reflist"

== [[Unit commitment problem]] ==

* Author list
* An introduction of the topic
# Please expand the introduction and avoid discussions of examples or specific applications in this section.
# The sentence “Nonlinear, Non-convex programming optimization problem.” doesn’t make sense by itself and Non-convex shouldn’t be capitalized.
* Theory, methodology, and/or algorithmic discussions
# Figure/image format should be revised to better display the content.
# Uppercase characters are used randomly (e.g., “non-convex transmission Constraints”) . Please follow correct language conventions for sentence structure.
# Avoid inserting inline citations after words like “written in matrix form as equation [3]..” or “presented in [3]...” as it is a bit informal when you don’t explicitly name the subject. Also these two sentences are grammatically incorrect and appear to be missing an ending period and comma, respectively.
# Don’t say “written in matrix form as equation..” and just cite the reference, actually write out the equation.
# Properly label the figure in this section with a figure number and improve visibility by making it larger.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Label the figures in this section properly with figure numbers.
# Fix typo “while minimize” to “while minimizing”.
# Avoid pronouns such as “we”.
# Use the equation editor when typing equations.
* A section to discuss and/or illustrate the applications:
# I suggest changing the order of the subtitles here. For example, Single-Period Unit Commitment.
* A conclusion section
* References

== [[Frank-Wolfe]] ==

* Author list:
* An introduction of the topic
# I suggest highlighting disadvantages along with advantages.
* Theory, methodology, and/or algorithmic discussions
# “[n x 1] matrix” please use the equation editor to express mathematical descriptions and symbols (p,b, etc)
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please show at least a few iterations. Even for smaller examples if needed. Report the final solution.
# Please use the LaTex code or equation editor for min and include s.t., etc.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps. For your example, please explicitly state that the derivative is taken etc.
* A section to discuss and/or illustrate the applications:
* A conclusion section
# Same as the introduction. Pros and cons should be evaluated together!
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Line search methods|Line Search Method]] ==

* Author list
* An introduction of the topic
# Expand the introduction and avoid discussion on some of the specific steps in the solution process.
# Provide references here.
* Theory, methodology, and/or algorithmic discussions
# The phrase “are as follows” in the steepest descent method discussion needs to be followed by a colon.
# Rephrase “has a nice convergence theory” and cite a reference for this claim.
# Avoid pronouns such as “we”.
# Add citation after “.. proposed by Phillip Wolfe in 1969.”
# Figure 1 is between two sections. Please fix this issue.
* At least one numerical example:
# Add some space between iterations or subsection break
* A section to discuss and/or illustrate the applications:
# Too few references in this section.
# Last paragraph makes some claims without references.
* A conclusion section
* References
# References should be properly formatted. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Piecewise linear approximation|Piecewise Linear Approximation]]==

* Author list
* An introduction of the topic
# The content of this section is good, but there are some issues with sentence clarity and some other grammatical errors. Please revisit this section and make changes accordingly.
* Theory, methodology, and/or algorithmic discussions
# Fix typo “to force the x’ values become associated with”.
* At least one numerical example
* A section to discuss and/or illustrate the applications
# Please aim for a maximum average sentence length of ~25 words. Some of these longer sentences are hard to read.
* A conclusion section
# Expand the conclusion section to be longer than one sentence. The conclusion section to include a brief summary of what was discussed above, an emphasis on it’s significance, and a brief discussion of future extensions and research direction if applicable.
* References
# Include hyperlinks to sources when possible.

== [[Mathematical programming with equilibrium constraints|Mathematical Programming with Equilibrium constraints]] ==

* An introduction of the topic
# This section includes several terms like variational inequalities, constraint qualifications that were not discussed in the class. Please add a sentence to explain them before using them.
* Theory, methodology, and/or algorithmic discussions
# The meaning of parameter vector x is unclear. Please add more information or update if necessary.
# Equations and symbols in the PIPA subsection are not formatted correctly. Please use the same formatting for all equations, so they read as mathematical equations and not text. This goes for all other sections as well.
# Use equations instead of images to represent math programs and equations in the Implicit Descent and SQP subsection.
# Apart from the steps for each solution technique, please also add a few sentences that describe each method.
* At least one numerical example
# Please define the terms like NCP, MP before abbreviating them. Also try not to unnecessarily abbreviate simple terms.
# Equations should be typed by LaTex. Images for equations are unacceptable.
# GAMS code is strongly discouraged. Please solve the problem "step-by-step".
# The selected numerical example is fine but is directly solved with the MPEC solver in GAMS. Try to solve it manually like the homework/in-class problems step by step using the steps described in the previous section by choosing any of the methods.
# Avoid using figures in the equations (subject to etc)
* A section to discuss and/or illustrate the applications
# Add references to “power management, highway pricing, chemical process engineering, and traffic planning.”
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Wing shape optimization|Wing shape Optimization]] ==

* Author list: Remove cornell ID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# The introduction is missing several references (e.g., “software packages like computational fluid dynamics..”, sentences containing things that aren’t common knowledge, performance claims, etc.)
# Avoid discussion involving finer details of subject methods in this section.
# In the titles, please change the font from bold to normal to have consistent formatting in the site. Same applies to box of content!
* Theory, methodology, and/or algorithmic discussions
# Properly cite the CFD package, don’t just include a link.
# Properly label the figure with a figure number.
# Consider removing white space between isolated sentences to improve readability.
* At least one numerical example
# If you’ve already defined an abbreviation (CFD), there is no need to define it again. Just use the abbreviation.
# Avoid pronouns such as “we” or “they”.
# Phrases like “under the following” need to be followed by a colon.
# Properly label the figure with a figure number and consider making them larger to improve visibility. Call the reader's attention to the figures in text by referencing the figure number.
# “As seen in the video below” is stated yet there are only images present and it may be initially unclear to the reader which figure is being referenced here.
# Avoid inserting inline citations like “[4] introduces an..” as it is a bit informal when you don’t explicitly name the subject.
# Don’t just cite the reference when discussing the problem formulation, explicitly write the model formulation and solution process using LaTex or equation visual editor.
* A section to discuss and/or illustrate the applications
# Some characters are randomly capitalized in this section.
* A conclusion section
# These variables should be defined before the conclusion section, they are out of place here. Also, please use normal text when explaining variables except for the variable symbol.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Interior-point method for NLP|Interior point method for NLP]] ==

* An introduction of the topic:
* Theory, methodology, and/or algorithmic discussions
# Primal-Dual formulation and comparison to the Barrier Method is not discussed.
# Include brief discussion about big O convergence rates.
# Need discussion about the concept of “central path” and the notion of self concordance
# Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
# Graphs and images are incorrectly formatted to the page. Consider proper alignment with respect to the text body.
# Use explicitly typed Latex equations instead of images to represent math programs and equations.
# Fix typo “optimisation”.
# Use LaTex code or equation editor to display all equations and variables (e.g., “xi ”, “μ”, etc.).
* At least one numerical example:
# There are formatting issues with figures 2,3. Please make sure to embed them within their respective sections.
* A section to discuss and/or illustrate the applications
* A conclusion section
# Minor character code typos in the conclusion.
# Also, please add more discussion in this section. Future research directions is a good start.
# There is a box "􏰐"
* References

== [[AdaGrad|Adagrad]] ==

* An introduction of the topic:
* Theory, methodology, and/or algorithmic discussions
# Include discussion on its variants (most important is AdaDelta).
# Include disadvantages of Adagrad, since this provides motivation for the discussion on the variants and improvements of Adagrad
# Include comparisons to other popular optimizers (particularly important is comparisons to regular SGD and Adam)
# Different convergence rates are possible depending on the setting where Adagrad is used, but this is not mentioned on the page currently. As such the regret bound section should be more thoroughly explained.
* At least one numerical example
# In the first sentence, “..take the following numerical example” should be followed by a colon.
# Fix typo “trayectory”.
* A section to discuss and/or illustrate the applications
# This section is too short; include specific applications in which input features are sparse and Adagrad excels.
# Add reference to the claim “Mainly, it is a good choice for deep learning models with sparse input features”.
* A conclusion section
* References

# Too few references overall, you should aggregate information from multiple sources (even if the base algorithm itself comes from a singular paper)

== [[McCormick envelopes|McCormick Envelopes]] ==

* Author list: OK but I suggest removing NetID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# First sentence is hard to read. Please consider keeping sentences below 25-30 words.
# No references provided. Please cite all sources.
# Figure 1 is provided in the middle between two sections. Please include in the introduction section.
* Theory, methodology, and/or algorithmic discussions
# References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# When using mathematical expressions and symbols, please use the equation editor. (e.g., x*y, exy + y, sin (x+y) - x2)
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# For the sample GAMS code, please place it in a code box
* A section to discuss and/or illustrate the applications
# Having a list is not enough. Please explain at least three applications in a few sentences each.
# This section should be at least a paragraph to discuss relevant applications. Each application should be explicitly linked to the page topic. A few keywords do not meet the requirement at all.
* A conclusion section:
* References
# References are not expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please follow the standard reference style - the current format is incorrect.

2021 Cornell Optimization Open Textbook Feedback

2021-12-05T19:58:08Z

Asa273: /* Job-Shop Scheduling Problem */

== [[Lagrangean duality|Lagrangian duality]] ==
* Author list, sections and TOC
# Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.
# Remove cornell ID from Author list
* An introduction of the topic
# This section includes sentences on constructing the dual problem and is referred to as Lagrangian relaxation (LR). This is incorrect, please fix the definition of LR.
# Definitions of LR and its relation to duality should be double checked and re-written.
# Only one reference is present in this section. Please add more relevant references by expanding this section.
# Consider merging the “introduction” and “history” sections.
# In the titles, please change the font from bold to normal to have consistent formatting in the site.
* Theory, methodology, and/or algorithmic discussions
# The Lagrangian variables associated with equality constraints h(x) are unbounded but the Lagrangian dual problem states them as non-negative. Please fix the same.
# Also to construct a dual, we do not change minimization to maximization directly. We observed such things in the examples in lecture notes due to simplification. The lagrangian dual problem would be minimize (,).
# Adding to the previous point, the Lagrangian is a lower bound on the original objective; the solution to the primal and dual or only equivalent if the duality gap is 0. You reference this in one section, but this is after your statement “Hence, solving the dual problem, which is a function of the Lagrangian multipliers (𝜆*) yields the same solution as the primal problem, which is a function of the original variables (x*). “. Please clarify the specific conditions that must hold for the solution of the dual to be equal to the primal’s.
# You refer to the “Complementary Slackness Theorem”, but don’t actually write the mathematical representation of complementary slackness. Please fix this. Also consider including the derivation of the complementary slackness condition, as it is both easy and short. Boyd is a good reference for this.
# Last step of the “process” subsection also needs updating according to the previous comments.
# The inline notations should also be typed using LaTex.
# Please use the LaTex code or equation editor for min, s.t., etc.
* At least one numerical example
# Only one dual variable is associated with each constraint. The numerical example uses two for the first and second constraint which is unnecessary. Please update it accordingly for both constraints. This particular example will only have two dual variables instead of the five dual variables used currently.
# All consecutive steps need to be updated since the dual variables would be updated.
# After substitution the nonlinear function should be further simplified. The current expression reads like a highly nonlinear function but can be easily simplified.
# Similar to the comments in the methodology section, inverting minimize to maximize is incorrect. Please update the dual objective function and domain of dual variables accordingly.
# Please use the LaTex code or equation editor for min, s.t., etc.
* A section to discuss and/or illustrate the applications
# Bullet points could be used to state the last four real-world examples that explain the physical meaning of the primal and dual problems.
# Add references for the last set of applications.
* A conclusion section
# This section contains a few typos. Please fix the same.
* References
# Some citations' hyperlinks are displaying.

== [[Disjunctive inequalities|Disjunctive Inequalities]] ==

* Author list
# Missing course section and semester
# Remove cornell ID
* An introduction of the topic
# No citations are present in this section.
# “mixed-integer programming (MIP)” should be used instead of “multiple integer programming (MIP)”. Please fix this error.
* Theory, methodology, and/or algorithmic discussions
# The abbreviation MILP is not previously defined. Please fix this issue.
# You consistently use the negative sign instead of the NOT operator for y (-y instead of ¬y).
# Some inconsistencies with the spacing of variables, constraints, etc., under the “General” section that need to be fixed.
# Typo in “This is shown below by M1, M2, y1, and y1:” where y1 needs to be changed to y2. Why use two different Big-M variables here? Elsewhere in the Wiki you only use one so this could lead to confusion with a general audience. Also if this was taken from the lecture notes then it needs to be cited.
* At least one numerical example
# Please reformulate and solve a complete numerical example rather than just reformulating a general example. Demonstrate the use of Big-M and Convex Hull formulation in an optimization problem that provides details such as individual steps in the problem solving process and final results.
# Add space between vee (V) operator and brackets in first line of Latex
# Please format variables correctly, for example, use <math>x_1</math> instead of x1.
* A section to discuss and/or illustrate the applications
# Please format the equations appropriately either by using latex code or the visual editor. These images are NOT acceptable!
* A conclusion section
# There is no conclusion presented in this section at all.
* References
# The included references have NOT been used anywhere in the Wiki. Add references for sentences that are not common knowledge and please link them appropriately with the text in Wiki. If the figures used here were not original works, you must also cite them.
# There are many papers on this topic. A simple Google (Scholar) search could provide you with sufficient references to cite.
# Many important references of this topic are missing.
# Please consider linking the references as demonstrated in the Wiki tutorial on Canvas and in this template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

==[[Stochastic programming|Stochastic Programming]] ==

* Author list: Remove cornell IDs
* An introduction of the topic
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
# This section only includes two sentences on Stochastic programming (SP), while the rest gives examples of uncertainty. Please discuss the need for SP in the presence of uncertainty. Also, discussion on robust optimization and its limitations should be removed since it is out of place.
* Theory, methodology, and/or algorithmic discussions
# Please avoid direct inline linkbacks to Wikipedia.
# The symbol “xi” in the methodology subsection should be explained.
* At least one numerical example
# Copying a numerical example "entirely" from a textbook is inappropriate. Your team should come up with a "numerical" case.
# No specific application context is needed for a numerical example.
# The inline notations (`x1`, `s1`) should also be typed using LaTex.
# Label all tables with a table number for better readability.
# Properly format the solution table with the label attached rather than the following sentence. The solution table looks different from the others, please fix this for consistency.
* A section to discuss and/or illustrate the applications;
# I suggest eliminating citing the last name of the first author (i.e. Zhou et al.)
* A conclusion section
* References
# URLs of some citations are not properly formatted (not showing the hyperlinks).

== [[Exponential transformation|Exponential Transformation]] ==

* Author list
# Missing course section
# Remove cornell ID
* An introduction of the topic
# Please expand the introduction.
# Please aim for a maximum average sentence length of ~25 words. Last sentence with 51 words is hard to read.
# Second Sentence: please change the word “they” as it could make the meaning ambiguous
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
# If you use abbreviations, please introduce them (e.g. NLP,MINLP)
* Theory, methodology, and/or algorithmic discussions
# Please explain the transformation in words along with equations
# Terms like posynomial should be described in detail.
# Please move the numerical example to the section below
# The “(eq 1)” is not needed here.
# Please expand this section.
* At least one numerical example
# In the third equation of the numerical example, it is confusing to have coefficients after numbers. Some readers may read it as an exponent.
# Last equation in this section after “further linearization” is incorrect. This equation cannot be further linearized, please fix this.
# Please explain the steps in the numerical examples in detail. The step-by-step solution should be provided.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# Missing part of text: “Proof of convexity of with positive definite test of Hessian…”
# Applications are not numerical examples. Please refer to this link for example of applications: [[Duality|https://optimization.cbe.cornell.edu/index.php?title=Duality]]
# Citation 7 is missing in current applications
# The section current applications is redundant
# Please use the LaTex code or equation editor for min, s.t., etc.
# Under current applications, do not just use a hyperlink to describe an application. Actually describe it. And properly inline citation style should be used instead of the hyperlink.
# The convexification application of MINLP can be further simplified for binary variables. Please refer to the lecture slides for more information.
* A conclusion section
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
* References
# Please consider linking the references by using this as Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Citation 7 is missing in current applications

== [[Sparse Reconstruction with Compressed Sensing|Sparse reconstruction with Compressed Sensing]] ==
This Wiki needs a significant rewrite. Please go through the comments for details.

* An introduction of the topic
# The introduction section should include information about the problem and its implications presented briefly. Please use full sentences to write this Wiki. You may use tools like Grammarly to check sentence formation and grammar.
# This section includes several typos like “sub modual”. Please fix them throughout the wiki and delete them if not required.
# Many abbreviations are used before previously defining them. Please define these abbreviations before using them in the text.
# This section is incomprehensible in its current form. Please rewrite with proper comprehension.
# Equations and math symbols need proper reformatting. The current version reads like text (along with equations) copy-pasted from a specific source. All mathematical symbols and equations should be formatted via LaTex - this is a learning objective of the Wiki assignment. You can find some useful links on converting your equations/symbols into LaTex code here: (https://optimization.cbe.cornell.edu/index.php?title=Help:Contents).
# Try to place the figure at the top of the Wiki between the main text.
# Avoid pronouns such as “we”.
# I suggest the use of more formal abstract illustrations.
* Theory, methodology, and/or algorithmic discussions
# Equations and symbols need proper reformatting.
# Lemmas and theorems are not expected for this Wiki. Sparse reconstruction is a straightforward concept but is unnecessarily complicated here. Please refer to other Wiki examples to get an idea of what the Wiki should convey.
# All equations need to be better formatted.

* At least one numerical example
# Numerical example is missing.
# Every iteration should be clearly presented, and solved "step-by-step".
* A section to discuss and/or illustrate the applications
# Having a list is not enough. Please explain at least three applications in a few sentences each.
* A conclusion section
# Conclusion section is missing.
* References
# The current reference list is not correctly formatted. References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Portfolio optimization|Portfolio Optimization]] ==

* Author list
# Remove cornell id
* An introduction of the topic
# The introductory sentence should be rephrased. The action of minimizing the risks does not inherently maximize the gains, rather PO aims to maximize gains whilst minimizing risks.
# Amount of whitespace can be reduced by changing the orientation of Figure 1 and the sentences in this section.
# Define terms such as risk, return, portfolio, etc., when you introduce them. Assume that the reader may not know much about finance. This goes for all other sections as well.
* Theory, methodology, and/or algorithmic discussions
# A brief mention of modern portfolio theory (i.e.. Markowitz) would be appropriate in this section.
# Several grammatical errors here involving sentence structure and clarity. Some questionable semantics (e.g., “The portfolio optimization mainly assumes two directions.”) and syntax (phrases such as “.. is as follows” should be followed by a colon). Misuse of commas and missing commas in this section. Two sentences introducing E(rp) and w should be combined into one.
# Use LaTex to distinguish variables written within a sentence, such as m and n.
# Rephrase “Cut the relevant information and conditions in the portfolio optimization, as well as the final requirements into the relevant variables, constraints and linear functions of the linear programming problem.”
# An explanation of a few common constraints would be helpful, rather than just including a table.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Solving the numerical example by GAMS is inappropriate. Please provide detailed step-by-step calculation results.
# All tables need to be labeled.
# Include figure number in label for consistency.
# Fix misspelling “dolling decision variables”.
# Use LaTex for all variables, equations, and constraints here.
# Example 2 table is hard to read, so making it bigger would help.
# Remove the “Using excel as the solver” part from the sentence before the solution discussion.
# Some grammatical errors here (phrases such as “.. is as follows” should be followed by a colon).
* A section to discuss and/or illustrate the applications
# Rephrase “Portfolio optimization can be used to screen investment projects that meet investors, rationally allocate investment amounts, etc.”
# Not sure “relevant” is the correct word choice here.
# You need more specific examples with the utility of portfolio optimization, this section is quite general as is. Some more detail and focus on real-world applications in the financial industry that relate to retirement planning, financial security, economic stability, etc., would be helpful.
* A conclusion section
# Need some commas here.
# The sentence “Linear programming has been around since the 1940’s and has such a wide base of applications” is not necessary.
* References
# Please consider linking the references as demonstrated in the Wiki tutorial on Canvas and in this template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove white space between end of sentences and reference numbers.

== [[Chance-constraint method|Chance constraint method]] ==

* Author list:
* An introduction of the topic
# Please consider correcting a few grammatical errors: “pre-planned for”, “god”, “certain levels of feasibility is guaranteed in what are”, and “Performance of a system”
# In “Chance-constraint”, it is capitalized randomly throughout the introduction. Please correct.
# Please use technical language to briefly introduce chance-constrained programming. Words like “acts of god”, “cost of doing business” are not appropriate for a technical Wiki.
* Theory, methodology, and/or algorithmic discussions
# Please add a citation to the first sentence.
# Xi is an uncertainty/randomness variable. It is better to use clear language.
# Please use the mathematical editor for adding explanations in the text. Using “ x is a decision variable” is hard to read. Same for f(x) and others.
# Theory is insufficient. Please expand and explain different approaches.
# Please add pros and cons explicitly as a list.
# Explain the physical meaning for examples of chance constraints along with all the notations used.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please remove this example as it is directly from this book. The example should be purely numerical without any background.
# Please use the equation editor for min, st., etc.
# Please use the mathematical editor for adding explanations in the text. Using “ x is a decision variable” is hard to read. Same for f(x) and others.
# Please change the table format so as not to confuse the reader.
# Multiple instances of [Chart to be added] are missing.
# Example is incomplete.
# Avoid pronouns such as “we”.
* A section to discuss and/or illustrate the applications
# Please connect several grammatical and spelling errors: “real life application”, Energy creation, particularly in renewable sources, have high variabilities”, and others
# “Zhao, Xue, Cao, and Zhang”. No need to list all authors within the article. Provide a reference is sufficient. If authors must be mentioned, (Zhao et al.) should be ok.
* A conclusion section
# Uniqueness and universality earlier are not clear to me. If they are not discussed earlier in the application, it would be better not to introduce new discussions in the conclusion.
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
* References
# References seem to vary in format. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Bayesian Optimization]] ==
* Section titles should not be "bold". Please double check using source editor on the section titles.
* Contents: Subheadings for EI and the algorithm should not be bolded, Random words should not be capitalized.
* Author list: Remove cornell ID, Please check names
* Introduction
# The introduction is too general and not substantial enough. For example, simply saying BayesOpt is useful when the objective function is unknown obscures exactly HOW it is useful (namely, computational efficiency in applications where ground truth sampling is expensive). Discussion on applications should be moved to a separate section.
# Machine learning rarely includes black-box functions to be optimized. Bayesian optimization is almost never used for optimizing ML loss functions but can instead be used for hyperparameter optimization. Please update such claims in this section.
* Theory, methodology, and/or algorithmic discussions
# Captions need reformatting.
# Consider italicizing keywords rather than bolding.
# Please add a citation to the first sentence.
# Discussion on acquisition functions should include comparisons, tradeoffs, and reasons to use one over the other. Should also note that expected improvement is the most widely used in practice, and explain.
# Avoid pronouns such as “we”.
# Please write equations in the Wiki instead of attaching images for equations.
# Acquisition function figure could be made larger and clearer to improve readability.
* At least one numerical example
# Any references to functions or methods in code ‘e.g. fmin’ should be properly formatted as code-stylized text.
# Please use the equation editor for min, st., etc.
# Avoid including a figure of the code for this example and explicitly describe the steps to the modeling and solution process instead.
# Avoid pronouns such as “our” and “we”.
* A section to discuss and/or illustrate the applications
* A conclusion section
# Please do not use brackets to enclose lists.
# Some claims here should be supported by references. Please cite each source after its sentence.
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Try to avoid references to “pop” machine learning blogs where anyone can be an author. (e.g. towardsdatascience)
# All references are URLs. Please cite publications and literature.
# A simple Google Scholar search would give you many references.

Notes on grammar: Needs some work. Several instances where colons are inappropriately inserted mid sentence or in subheadings. Explanations are not terse. Several instances of switching between personal and impersonal style of writing, which is distracting.

== [[Conjugate gradient methods]] ==

* Author list: Remove cornell ID
* Introduction
# All inline notations (e.g., `x`, `A`) should be typed using LaTex.
* Theory, methodology, and/or algorithmic discussions
# All equations need to be better formatted.
# Is Gauss-Newton no longer referenced?
# Theorems listed in the first section should be accompanied with high level explanation, not just a list of the theorems themselves. The page should read like an article, with proper flow.
# Please indent equation blocks.
# Please properly format pseudocode.
* At least one numerical example
# Steps should be accompanied with explanation, or reference to the corresponding step in the pseudocode.
# Please properly format in a more organized manner, aligning equations appropriately and demarcating steps appropriately.
* A section to discuss and/or illustrate the applications
# Consider including 2 additional examples of applications
* A conclusion section
# Consider adding future research directions
* References
# Reference primary sources rather than Wikipedia
# Too few references.
# More references should be added. A simple Google Scholar search would give you many references.

== [[Geometric programming|Geometric Programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Examples of applications in this section use the same reference. Please cite their individual sources.
* Theory, methodology, and/or algorithmic discussions
# The symbol denoting the domain in the definition of a monomial is unclear. Please clarify it or fix this if it is incorrect.
# Definition of posynomial refers to section 2.1 which is missing from the Wiki (sections are not numbered in the main text).
# In the generalized posynomial subsection, bullet points do not tell us why h(x) is posynomial. Either provide reasons or simply state that h(x) is posynomial. Also explain why h3 is a generalized posynomial.
# Additional theory on the feasibility analysis could be provided in this section.
* At least one numerical example
# In the transformation example, the last two constraints could also be simplified by applying a natural logarithm on both sides. Please update them as well.
* A section to discuss and/or illustrate the applications
# The figure in this section needs to be labeled.
# The figure needs to be resized and perhaps aligned to the center.
* A conclusion section:
# Please avoid vague language such as: “This makes”.
# Please avoid opinionated statements: “one of the best ways”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# This Wiki has very few references. A quick Google Scholar search may provide relevant references.

== [[Adam]] ==

* Author list
* An introduction of the topic
# Some grammatical errors here, mostly related to the need for commas in certain places (e.g., “Before Adam..”).
# Some minor errors with parts of speech throughout the section, need to revisit phrases such as “which has broader scope in future for”, etc.
# Try splitting up some of the longer sentences in this section, a couple are hard to read.
# Avoid definitive statements about Adam being the best or always better solver, as this is simply not true (the choice of the “best” optimizer is setting-dependent). Use language such as “Research has shown that Adam has demonstrated superior experimental performance over..” and then cite academic references to back this claim.
# What does adam stand for? Introduction is insufficient. Please expand.
* Theory, methodology, and/or algorithmic discussions
# Revise grammar here, noticing some missing commas and uncapitalized word after period.
# Rephrase “second one is to update the old position with the updated position”.
# Use LaTex code or equation editor to display all equations and variables in this section, and actual subscripts instead of “m_t”, etc.
# Avoid inserting inline citations after words like “According to..” or “This article..” as it is a bit informal. This could be rephrased or changed to something like “According to author,^[2] …” with author name inserted.
# Remove white space before the period in RMSP discussion.
# Please provide a pseudocode.
# Please use list the two methods here “Adam is a combination of two gradient descent methods which are explained below”
# Please expand the theory section significantly. Theoretical convergence properties should be discussed, even if briefly.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
* A section to discuss and/or illustrate the applications
# Same comment as before, consider replacing inline citations after words like “According to..”.
* A conclusion section
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Try to avoid references to blogs and use peer-reviewed academic references instead.
# Too few references.
# More references should be added. A simple Google Scholar search would give you many references.

== [[A-star algorithm|a* algorithm]] ==

* Author list: Remove cornell ID
* Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.
* An introduction of the topic:
# Weird spacing between paragraphs. Please fix this issue.
# In the titles, please change the font from bold to normal to have consistent formatting in the site.
# Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.
# There are no citations in the introduction. Please cite every source.
* Theory, methodology, and/or algorithmic discussions
# Please add the mathematical description of the algorithm.
# Reference style varies in sentences. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please fix grammatical and spelling errors as (“from current position to the goal”, “There are a lot of discussions”, etc). Also, many hyphens are missing as “non playable”.
# In algorithms, it is a standard to add high-level description (i.e. pseudocode or flowchart). Please incorporate it.
# Use LaTex code or equation editor to display all equations and variables in this section (e.g., “f(n)...”, “h(n)..”, etc.). This goes for other sections as well.
* At least one numerical example
# The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.
# Instead of writing things like “The above image..”, label each figure and use the figure number to refer to it in text.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# No references in the applications. Please cite every source
# Preferably, add at least an additional application.
* A conclusion section
# Conclusion should summarize descriptions. Please modify it to provide a summary.
# Please pay attention to the length and structure of sentences here and in the full page. First sentence is hard to read.
* References
# References seem to vary in format and are not linked correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Incorrect reference style. Please follow the example and use the template.

== [[Job shop scheduling|Job-Shop Scheduling Problem]] ==

* An introduction of the topic
# The current introduction to the jobshop scheduling problem has only two sentences in addition to the parameter description. Introduction typically contains information about the problem, its importance in the real-world, and some information about the solution techniques and their types to solve the problem. Please add some information that covers the above.
* Theory, methodology, and/or algorithmic discussions
# It is unclear whether the assumptions stated in this section are required to apply the following solution techniques. Please clarify the same. Also use complete sentences to state them.
# The branch and bounds method described in this section only discusses the solution technique for problems with one machines. However, branch and bound is a general technique that can be applied to any MILP problems with varying scales. Please update the “methods” section to be as general as possible.
# Since this Wiki focuses on jobshop scheduling, at least two methods are expected. Branch and bound is a general MILP technique, so, it is recommended to add a tailored technique that can only solve specific jobshop scheduling problems. Solving the numerical example with this technique is not necessary.
# Reference to the branch and bound technique described in this section is a “youtube” video. Please add references in literature that describe this method in detail. The method used in this video is highly tailored for a single machine application. This is also an incorrect way to cite a reference. Please keep this section as general as possible.
# Use LaTex code or equation editor to display all equations and variables in this section and all other sections as well.
# Check grammar in this section. For example, phrases like “are as follows” need to be followed by a colon and not a period.
# Consider rewriting the assumptions as a list in this section.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# The example used in this section is exactly the same as the one in the youtube video. Please use a modification of this example or choose another example/method to demonstrate the solution technique. Your team should ideally create a numerical example independently. If you take a numerical example directly from a particular source, you will need to get explicit permission from the textbook author in writing and share that written permission with the instructors.
# The figure in this section is not numbered when all others are. Relabel this figure for consistency and its number to refer to it in-text.
# A numerical example should be simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments).
* A section to discuss and/or illustrate the applications
# This section should only focus on real-world applications of the jobshop scheduling problem. But currently, this section includes additional information on solution techniques/complexity that is appropriate for the Introduction section. Please discuss the applications of the problem in this section.
* A conclusion section
# The meaning of “Operations applications” is unclear. Please explain or update if necessary.
# The current conclusion section does not properly summarize the problem. Please refer to other Wiki examples for an idea to update the section accordingly.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please reference media sources like reference 5 appropriately.
# A simple Google Scholar search would give you many "formal" references.

== [[Optimization in game theory]] ==

* Author list: remove cornell IDs.
* An introduction of the topic
# References are not linked. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
* Theory, methodology, and/or algorithmic discussions
# Why only a subsection on "Nash Equilibrium" is included in "Theory" section? Please re-format.
# Please edit references.
# Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm.
# Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.
* At least one numerical example
# Please organize the last part in a more readable format. Questions may be in bold and numbered, answers are more direct, etc.
# Remember to cite all images and tables.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# Very good, link the reference and cite all sources.
* A conclusion section
# Please add more summarizing especially from theory sentences and avoid long sentences.
* References
# Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Reference primary sources rather than Wikipedia
# Incorrect reference style. Please correct.

== [[Trust-region methods]] ==

* Author list:
# Remove cornell IDs. Author is also spelled incorrectly.
# Add the course section.
* An introduction of the topic
# References are not linked. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Use LaTex code or equation editor to display all equations and variables (e.g., “xk”, “f`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “we”. This goes for all other sections as well.
* Theory, methodology, and/or algorithmic discussions
# Organization of ideas in this section needs work.
# You have not defined explicitly why the Cauchy point is important to compute beyond a vague allusion to performance improvements, which is also wrong (it is useful because of its guarantees for convergence, not performance) It is also misspelled.
# Each approach should have accompanying explanation and motivation for why it is being discussed. It is not enough to outline the algorithm.
# Please make sure symbols are properly subscripted and superscripted (e.g. “pk” should be “p_k”
# Please format the algorithm in proper algorithmic pseudocode format.
# Little to no discussion on global convergence guarantees
# Please include discussion about the advantages and disadvantages of the algorithm
# Fix typo “couchy point”.
* At least one numerical example
# Any code functions (uminfunc) should have proper text formatting.
# The graph needs a better caption explaining how the axes are labeled and what data points are being shown.
# Please increase the quality of the figure. It is hard to see the red line.
# Add citation to “The Rosenbrock function is a non-convex function, introduced by Howard H. Rosenbrock in 1960, which is often used as a performance test problem for optimization algorithms.”
* A section to discuss and/or illustrate the applications
# The content in this section as it is currently does NOT describe applications, but rather different approaches within the trust region methodology. Please provide specific applications (e.g. TRPO in reinforcement learning).
* A conclusion section
# Please add more summary, future research directions for example is a good start.
* References
# Incorrect reference style.
# Please consider having the references as this Wiki template, <nowiki>https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization</nowiki>
# More references should be added. A simple Google Scholar search would give you many references.

*There are numerous misspellings, grammatical errors, and incorrect claims. Please fix these.

== [[Momentum]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Apart from an explanation on momentum, it is necessary to briefly point out the limitations of SGD and why momentum could help with these limitations. Please update it accordingly.
# Remove bold on “Momentum”.
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
* Theory, methodology, and/or algorithmic discussions
# Equation formatting is very poor and should be formalized.
# It is important to use technical language for this Wiki. Although a layman’s explanation is appreciated, it would be better to skip using words like “zig zagging”. Try to explain all concepts in a technical language with few simplifications but NOT vice versa.
# The definition of the update rule for SGD with momentum looks incorrect, specifically the first expression. Please fix it and also explain all the parameters used.
# Use LaTex code or equation editor to display all equations and variables (e.g., “W”, “V`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “you”.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please try to label the plots that explains what each line color means.
* A section to discuss and/or illustrate the applications
# Please use correct terminology like “optimizing non-convex functions” and not “training non-convex models”.
# Adam, Adadelta, and RMSprop are variants of SGD that already use momentum. Please double check the writing and update if necessary.
* A conclusion section
# Please refrain from using words like “zig zag” effects.
* References
# Almost all references used are URLs. Please try to add journal/conference articles or books for references, instead of directly citing the URLs.

== [[Stochastic dynamic programming|Stochastic Dynamic programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Discussion on applications should be moved to a separate section.
* Theory, methodology, and/or algorithmic discussions
# Remove the grey box background of equations.
* At least one numerical example
* A section to discuss and/or illustrate the applications
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Outer-approximation (OA)|Outer-approximation]] ==

* An introduction of the topic
# See formatting guideline below
# Avoid opinionated statements such as “MINLP problems are usually the hardest to solve”.
# Rearrange the text such that the MINLP formulation is in the theory section and keep the introduction in words only.
* Theory, methodology, and/or algorithmic discussions
# Consider left aligning equations and optimization problem formulations by the “=”. See [[Stochastic programming|https://optimization.cbe.cornell.edu/index.php?title=Stochastic_programming]] for an example
# The sentence “The Outer-Approximation (OA) algorithm was first proposed by Duran and and Grossmann in 1986 to solve MINLP problems.” needs a reference.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# “Minimize” and “subject to” should be “min” and “s.t.” in MathType
* A section to discuss and/or illustrate the applications
# Does not explicitly point out why OA is applicable (and/or preferred) in these applications, rather than other MINLP approaches (show that the problem formulations are amenable to a solution approach through OA)
# The sentence “... an active research area and there exists a vast number of applications in fields such as engineering, computational chemistry, and finance.” needs references.
# Place GAMS code in a single code box or remove it.
# Consider reformatting to make steps more readable. Inserting spaces and breaking down steps would help.
* A conclusion section
# Too short. Consider discussion on future research direction and discussion on uncertainty
# Please review abbreviations throughout the page. Why is MINLP redefined here? “Outer-Approximation is a well known efficient approach for solving convex mixed-integer nonlinear programs (MINLP)”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove "Template:Reflist"

== [[Unit commitment problem]] ==

* Author list
* An introduction of the topic
# Please expand the introduction and avoid discussions of examples or specific applications in this section.
# The sentence “Nonlinear, Non-convex programming optimization problem.” doesn’t make sense by itself and Non-convex shouldn’t be capitalized.
* Theory, methodology, and/or algorithmic discussions
# Figure/image format should be revised to better display the content.
# Uppercase characters are used randomly (e.g., “non-convex transmission Constraints”) . Please follow correct language conventions for sentence structure.
# Avoid inserting inline citations after words like “written in matrix form as equation [3]..” or “presented in [3]...” as it is a bit informal when you don’t explicitly name the subject. Also these two sentences are grammatically incorrect and appear to be missing an ending period and comma, respectively.
# Don’t say “written in matrix form as equation..” and just cite the reference, actually write out the equation.
# Properly label the figure in this section with a figure number and improve visibility by making it larger.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Label the figures in this section properly with figure numbers.
# Fix typo “while minimize” to “while minimizing”.
# Avoid pronouns such as “we”.
# Use the equation editor when typing equations.
* A section to discuss and/or illustrate the applications:
# I suggest changing the order of the subtitles here. For example, Single-Period Unit Commitment.
* A conclusion section
* References

== [[Frank-Wolfe]] ==

* Author list:
* An introduction of the topic
# I suggest highlighting disadvantages along with advantages.
* Theory, methodology, and/or algorithmic discussions
# “[n x 1] matrix” please use the equation editor to express mathematical descriptions and symbols (p,b, etc)
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please show at least a few iterations. Even for smaller examples if needed. Report the final solution.
# Please use the LaTex code or equation editor for min and include s.t., etc.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps. For your example, please explicitly state that the derivative is taken etc.
* A section to discuss and/or illustrate the applications:
* A conclusion section
# Same as the introduction. Pros and cons should be evaluated together!
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Line search methods|Line Search Method]] ==

* Author list
* An introduction of the topic
# Expand the introduction and avoid discussion on some of the specific steps in the solution process.
# Provide references here.
* Theory, methodology, and/or algorithmic discussions
# The phrase “are as follows” in the steepest descent method discussion needs to be followed by a colon.
# Rephrase “has a nice convergence theory” and cite a reference for this claim.
# Avoid pronouns such as “we”.
# Add citation after “.. proposed by Phillip Wolfe in 1969.”
# Figure 1 is between two sections. Please fix this issue.
* At least one numerical example:
# Add some space between iterations or subsection break
* A section to discuss and/or illustrate the applications:
# Too few references in this section.
# Last paragraph makes some claims without references.
* A conclusion section
* References
# References should be properly formatted. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Piecewise linear approximation|Piecewise Linear Approximation]]==

* Author list
* An introduction of the topic
# The content of this section is good, but there are some issues with sentence clarity and some other grammatical errors. Please revisit this section and make changes accordingly.
* Theory, methodology, and/or algorithmic discussions
# Fix typo “to force the x’ values become associated with”.
* At least one numerical example
* A section to discuss and/or illustrate the applications
# Please aim for a maximum average sentence length of ~25 words. Some of these longer sentences are hard to read.
* A conclusion section
# Expand the conclusion section to be longer than one sentence. The conclusion section to include a brief summary of what was discussed above, an emphasis on it’s significance, and a brief discussion of future extensions and research direction if applicable.
* References
# Include hyperlinks to sources when possible.

== [[Mathematical programming with equilibrium constraints|Mathematical Programming with Equilibrium constraints]] ==

* An introduction of the topic
# This section includes several terms like variational inequalities, constraint qualifications that were not discussed in the class. Please add a sentence to explain them before using them.
* Theory, methodology, and/or algorithmic discussions
# The meaning of parameter vector x is unclear. Please add more information or update if necessary.
# Equations and symbols in the PIPA subsection are not formatted correctly. Please use the same formatting for all equations, so they read as mathematical equations and not text. This goes for all other sections as well.
# Use equations instead of images to represent math programs and equations in the Implicit Descent and SQP subsection.
# Apart from the steps for each solution technique, please also add a few sentences that describe each method.
* At least one numerical example
# Please define the terms like NCP, MP before abbreviating them. Also try not to unnecessarily abbreviate simple terms.
# Equations should be typed by LaTex. Images for equations are unacceptable.
# GAMS code is strongly discouraged. Please solve the problem "step-by-step".
# The selected numerical example is fine but is directly solved with the MPEC solver in GAMS. Try to solve it manually like the homework/in-class problems step by step using the steps described in the previous section by choosing any of the methods.
# Avoid using figures in the equations (subject to etc)
* A section to discuss and/or illustrate the applications
# Add references to “power management, highway pricing, chemical process engineering, and traffic planning.”
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Wing shape optimization|Wing shape Optimization]] ==

* Author list: Remove cornell ID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# The introduction is missing several references (e.g., “software packages like computational fluid dynamics..”, sentences containing things that aren’t common knowledge, performance claims, etc.)
# Avoid discussion involving finer details of subject methods in this section.
# In the titles, please change the font from bold to normal to have consistent formatting in the site. Same applies to box of content!
* Theory, methodology, and/or algorithmic discussions
# Properly cite the CFD package, don’t just include a link.
# Properly label the figure with a figure number.
# Consider removing white space between isolated sentences to improve readability.
* At least one numerical example
# If you’ve already defined an abbreviation (CFD), there is no need to define it again. Just use the abbreviation.
# Avoid pronouns such as “we” or “they”.
# Phrases like “under the following” need to be followed by a colon.
# Properly label the figure with a figure number and consider making them larger to improve visibility. Call the reader's attention to the figures in text by referencing the figure number.
# “As seen in the video below” is stated yet there are only images present and it may be initially unclear to the reader which figure is being referenced here.
# Avoid inserting inline citations like “[4] introduces an..” as it is a bit informal when you don’t explicitly name the subject.
# Don’t just cite the reference when discussing the problem formulation, explicitly write the model formulation and solution process using LaTex or equation visual editor.
* A section to discuss and/or illustrate the applications
# Some characters are randomly capitalized in this section.
* A conclusion section
# These variables should be defined before the conclusion section, they are out of place here. Also, please use normal text when explaining variables except for the variable symbol.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Interior-point method for NLP|Interior point method for NLP]] ==

* An introduction of the topic:
* Theory, methodology, and/or algorithmic discussions
# Primal-Dual formulation and comparison to the Barrier Method is not discussed.
# Include brief discussion about big O convergence rates.
# Need discussion about the concept of “central path” and the notion of self concordance
# Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
# Graphs and images are incorrectly formatted to the page. Consider proper alignment with respect to the text body.
# Use explicitly typed Latex equations instead of images to represent math programs and equations.
# Fix typo “optimisation”.
# Use LaTex code or equation editor to display all equations and variables (e.g., “xi ”, “μ”, etc.).
* At least one numerical example:
# There are formatting issues with figures 2,3. Please make sure to embed them within their respective sections.
* A section to discuss and/or illustrate the applications
* A conclusion section
# Minor character code typos in the conclusion.
# Also, please add more discussion in this section. Future research directions is a good start.
# There is a box "􏰐"
* References

== [[AdaGrad|Adagrad]] ==

* An introduction of the topic:
* Theory, methodology, and/or algorithmic discussions
# Include discussion on its variants (most important is AdaDelta).
# Include disadvantages of Adagrad, since this provides motivation for the discussion on the variants and improvements of Adagrad
# Include comparisons to other popular optimizers (particularly important is comparisons to regular SGD and Adam)
# Different convergence rates are possible depending on the setting where Adagrad is used, but this is not mentioned on the page currently. As such the regret bound section should be more thoroughly explained.
* At least one numerical example
# In the first sentence, “..take the following numerical example” should be followed by a colon.
# Fix typo “trayectory”.
* A section to discuss and/or illustrate the applications
# This section is too short; include specific applications in which input features are sparse and Adagrad excels.
# Add reference to the claim “Mainly, it is a good choice for deep learning models with sparse input features”.
* A conclusion section
* References

# Too few references overall, you should aggregate information from multiple sources (even if the base algorithm itself comes from a singular paper)

== [[McCormick envelopes|McCormick Envelopes]] ==

* Author list: OK but I suggest removing NetID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# First sentence is hard to read. Please consider keeping sentences below 25-30 words.
# No references provided. Please cite all sources.
# Figure 1 is provided in the middle between two sections. Please include in the introduction section.
* Theory, methodology, and/or algorithmic discussions
# References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# When using mathematical expressions and symbols, please use the equation editor. (e.g., x*y, exy + y, sin (x+y) - x2)
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# For the sample GAMS code, please place it in a code box
* A section to discuss and/or illustrate the applications
# Having a list is not enough. Please explain at least three applications in a few sentences each.
# This section should be at least a paragraph to discuss relevant applications. Each application should be explicitly linked to the page topic. A few keywords do not meet the requirement at all.
* A conclusion section:
* References
# References are not expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please follow the standard reference style - the current format is incorrect.

2021 Cornell Optimization Open Textbook Feedback

2021-12-05T19:54:47Z

Asa273: /* Geometric Programming */

== [[Lagrangean duality|Lagrangian duality]] ==
* Author list, sections and TOC
# Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.
# Remove cornell ID from Author list
* An introduction of the topic
# This section includes sentences on constructing the dual problem and is referred to as Lagrangian relaxation (LR). This is incorrect, please fix the definition of LR.
# Definitions of LR and its relation to duality should be double checked and re-written.
# Only one reference is present in this section. Please add more relevant references by expanding this section.
# Consider merging the “introduction” and “history” sections.
# In the titles, please change the font from bold to normal to have consistent formatting in the site.
* Theory, methodology, and/or algorithmic discussions
# The Lagrangian variables associated with equality constraints h(x) are unbounded but the Lagrangian dual problem states them as non-negative. Please fix the same.
# Also to construct a dual, we do not change minimization to maximization directly. We observed such things in the examples in lecture notes due to simplification. The lagrangian dual problem would be minimize (,).
# Adding to the previous point, the Lagrangian is a lower bound on the original objective; the solution to the primal and dual or only equivalent if the duality gap is 0. You reference this in one section, but this is after your statement “Hence, solving the dual problem, which is a function of the Lagrangian multipliers (𝜆*) yields the same solution as the primal problem, which is a function of the original variables (x*). “. Please clarify the specific conditions that must hold for the solution of the dual to be equal to the primal’s.
# You refer to the “Complementary Slackness Theorem”, but don’t actually write the mathematical representation of complementary slackness. Please fix this. Also consider including the derivation of the complementary slackness condition, as it is both easy and short. Boyd is a good reference for this.
# Last step of the “process” subsection also needs updating according to the previous comments.
# The inline notations should also be typed using LaTex.
# Please use the LaTex code or equation editor for min, s.t., etc.
* At least one numerical example
# Only one dual variable is associated with each constraint. The numerical example uses two for the first and second constraint which is unnecessary. Please update it accordingly for both constraints. This particular example will only have two dual variables instead of the five dual variables used currently.
# All consecutive steps need to be updated since the dual variables would be updated.
# After substitution the nonlinear function should be further simplified. The current expression reads like a highly nonlinear function but can be easily simplified.
# Similar to the comments in the methodology section, inverting minimize to maximize is incorrect. Please update the dual objective function and domain of dual variables accordingly.
# Please use the LaTex code or equation editor for min, s.t., etc.
* A section to discuss and/or illustrate the applications
# Bullet points could be used to state the last four real-world examples that explain the physical meaning of the primal and dual problems.
# Add references for the last set of applications.
* A conclusion section
# This section contains a few typos. Please fix the same.
* References
# Some citations' hyperlinks are displaying.

== [[Disjunctive inequalities|Disjunctive Inequalities]] ==

* Author list
# Missing course section and semester
# Remove cornell ID
* An introduction of the topic
# No citations are present in this section.
# “mixed-integer programming (MIP)” should be used instead of “multiple integer programming (MIP)”. Please fix this error.
* Theory, methodology, and/or algorithmic discussions
# The abbreviation MILP is not previously defined. Please fix this issue.
# You consistently use the negative sign instead of the NOT operator for y (-y instead of ¬y).
# Some inconsistencies with the spacing of variables, constraints, etc., under the “General” section that need to be fixed.
# Typo in “This is shown below by M1, M2, y1, and y1:” where y1 needs to be changed to y2. Why use two different Big-M variables here? Elsewhere in the Wiki you only use one so this could lead to confusion with a general audience. Also if this was taken from the lecture notes then it needs to be cited.
* At least one numerical example
# Please reformulate and solve a complete numerical example rather than just reformulating a general example. Demonstrate the use of Big-M and Convex Hull formulation in an optimization problem that provides details such as individual steps in the problem solving process and final results.
# Add space between vee (V) operator and brackets in first line of Latex
# Please format variables correctly, for example, use <math>x_1</math> instead of x1.
* A section to discuss and/or illustrate the applications
# Please format the equations appropriately either by using latex code or the visual editor. These images are NOT acceptable!
* A conclusion section
# There is no conclusion presented in this section at all.
* References
# The included references have NOT been used anywhere in the Wiki. Add references for sentences that are not common knowledge and please link them appropriately with the text in Wiki. If the figures used here were not original works, you must also cite them.
# There are many papers on this topic. A simple Google (Scholar) search could provide you with sufficient references to cite.
# Many important references of this topic are missing.
# Please consider linking the references as demonstrated in the Wiki tutorial on Canvas and in this template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

==[[Stochastic programming|Stochastic Programming]] ==

* Author list: Remove cornell IDs
* An introduction of the topic
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
# This section only includes two sentences on Stochastic programming (SP), while the rest gives examples of uncertainty. Please discuss the need for SP in the presence of uncertainty. Also, discussion on robust optimization and its limitations should be removed since it is out of place.
* Theory, methodology, and/or algorithmic discussions
# Please avoid direct inline linkbacks to Wikipedia.
# The symbol “xi” in the methodology subsection should be explained.
* At least one numerical example
# Copying a numerical example "entirely" from a textbook is inappropriate. Your team should come up with a "numerical" case.
# No specific application context is needed for a numerical example.
# The inline notations (`x1`, `s1`) should also be typed using LaTex.
# Label all tables with a table number for better readability.
# Properly format the solution table with the label attached rather than the following sentence. The solution table looks different from the others, please fix this for consistency.
* A section to discuss and/or illustrate the applications;
# I suggest eliminating citing the last name of the first author (i.e. Zhou et al.)
* A conclusion section
* References
# URLs of some citations are not properly formatted (not showing the hyperlinks).

== [[Exponential transformation|Exponential Transformation]] ==

* Author list
# Missing course section
# Remove cornell ID
* An introduction of the topic
# Please expand the introduction.
# Please aim for a maximum average sentence length of ~25 words. Last sentence with 51 words is hard to read.
# Second Sentence: please change the word “they” as it could make the meaning ambiguous
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
# If you use abbreviations, please introduce them (e.g. NLP,MINLP)
* Theory, methodology, and/or algorithmic discussions
# Please explain the transformation in words along with equations
# Terms like posynomial should be described in detail.
# Please move the numerical example to the section below
# The “(eq 1)” is not needed here.
# Please expand this section.
* At least one numerical example
# In the third equation of the numerical example, it is confusing to have coefficients after numbers. Some readers may read it as an exponent.
# Last equation in this section after “further linearization” is incorrect. This equation cannot be further linearized, please fix this.
# Please explain the steps in the numerical examples in detail. The step-by-step solution should be provided.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# Missing part of text: “Proof of convexity of with positive definite test of Hessian…”
# Applications are not numerical examples. Please refer to this link for example of applications: [[Duality|https://optimization.cbe.cornell.edu/index.php?title=Duality]]
# Citation 7 is missing in current applications
# The section current applications is redundant
# Please use the LaTex code or equation editor for min, s.t., etc.
# Under current applications, do not just use a hyperlink to describe an application. Actually describe it. And properly inline citation style should be used instead of the hyperlink.
# The convexification application of MINLP can be further simplified for binary variables. Please refer to the lecture slides for more information.
* A conclusion section
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
* References
# Please consider linking the references by using this as Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Citation 7 is missing in current applications

== [[Sparse Reconstruction with Compressed Sensing|Sparse reconstruction with Compressed Sensing]] ==
This Wiki needs a significant rewrite. Please go through the comments for details.

* An introduction of the topic
# The introduction section should include information about the problem and its implications presented briefly. Please use full sentences to write this Wiki. You may use tools like Grammarly to check sentence formation and grammar.
# This section includes several typos like “sub modual”. Please fix them throughout the wiki and delete them if not required.
# Many abbreviations are used before previously defining them. Please define these abbreviations before using them in the text.
# This section is incomprehensible in its current form. Please rewrite with proper comprehension.
# Equations and math symbols need proper reformatting. The current version reads like text (along with equations) copy-pasted from a specific source. All mathematical symbols and equations should be formatted via LaTex - this is a learning objective of the Wiki assignment. You can find some useful links on converting your equations/symbols into LaTex code here: (https://optimization.cbe.cornell.edu/index.php?title=Help:Contents).
# Try to place the figure at the top of the Wiki between the main text.
# Avoid pronouns such as “we”.
# I suggest the use of more formal abstract illustrations.
* Theory, methodology, and/or algorithmic discussions
# Equations and symbols need proper reformatting.
# Lemmas and theorems are not expected for this Wiki. Sparse reconstruction is a straightforward concept but is unnecessarily complicated here. Please refer to other Wiki examples to get an idea of what the Wiki should convey.
# All equations need to be better formatted.

* At least one numerical example
# Numerical example is missing.
# Every iteration should be clearly presented, and solved "step-by-step".
* A section to discuss and/or illustrate the applications
# Having a list is not enough. Please explain at least three applications in a few sentences each.
* A conclusion section
# Conclusion section is missing.
* References
# The current reference list is not correctly formatted. References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Portfolio optimization|Portfolio Optimization]] ==

* Author list
# Remove cornell id
* An introduction of the topic
# The introductory sentence should be rephrased. The action of minimizing the risks does not inherently maximize the gains, rather PO aims to maximize gains whilst minimizing risks.
# Amount of whitespace can be reduced by changing the orientation of Figure 1 and the sentences in this section.
# Define terms such as risk, return, portfolio, etc., when you introduce them. Assume that the reader may not know much about finance. This goes for all other sections as well.
* Theory, methodology, and/or algorithmic discussions
# A brief mention of modern portfolio theory (i.e.. Markowitz) would be appropriate in this section.
# Several grammatical errors here involving sentence structure and clarity. Some questionable semantics (e.g., “The portfolio optimization mainly assumes two directions.”) and syntax (phrases such as “.. is as follows” should be followed by a colon). Misuse of commas and missing commas in this section. Two sentences introducing E(rp) and w should be combined into one.
# Use LaTex to distinguish variables written within a sentence, such as m and n.
# Rephrase “Cut the relevant information and conditions in the portfolio optimization, as well as the final requirements into the relevant variables, constraints and linear functions of the linear programming problem.”
# An explanation of a few common constraints would be helpful, rather than just including a table.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Solving the numerical example by GAMS is inappropriate. Please provide detailed step-by-step calculation results.
# All tables need to be labeled.
# Include figure number in label for consistency.
# Fix misspelling “dolling decision variables”.
# Use LaTex for all variables, equations, and constraints here.
# Example 2 table is hard to read, so making it bigger would help.
# Remove the “Using excel as the solver” part from the sentence before the solution discussion.
# Some grammatical errors here (phrases such as “.. is as follows” should be followed by a colon).
* A section to discuss and/or illustrate the applications
# Rephrase “Portfolio optimization can be used to screen investment projects that meet investors, rationally allocate investment amounts, etc.”
# Not sure “relevant” is the correct word choice here.
# You need more specific examples with the utility of portfolio optimization, this section is quite general as is. Some more detail and focus on real-world applications in the financial industry that relate to retirement planning, financial security, economic stability, etc., would be helpful.
* A conclusion section
# Need some commas here.
# The sentence “Linear programming has been around since the 1940’s and has such a wide base of applications” is not necessary.
* References
# Please consider linking the references as demonstrated in the Wiki tutorial on Canvas and in this template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove white space between end of sentences and reference numbers.

== [[Chance-constraint method|Chance constraint method]] ==

* Author list:
* An introduction of the topic
# Please consider correcting a few grammatical errors: “pre-planned for”, “god”, “certain levels of feasibility is guaranteed in what are”, and “Performance of a system”
# In “Chance-constraint”, it is capitalized randomly throughout the introduction. Please correct.
# Please use technical language to briefly introduce chance-constrained programming. Words like “acts of god”, “cost of doing business” are not appropriate for a technical Wiki.
* Theory, methodology, and/or algorithmic discussions
# Please add a citation to the first sentence.
# Xi is an uncertainty/randomness variable. It is better to use clear language.
# Please use the mathematical editor for adding explanations in the text. Using “ x is a decision variable” is hard to read. Same for f(x) and others.
# Theory is insufficient. Please expand and explain different approaches.
# Please add pros and cons explicitly as a list.
# Explain the physical meaning for examples of chance constraints along with all the notations used.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please remove this example as it is directly from this book. The example should be purely numerical without any background.
# Please use the equation editor for min, st., etc.
# Please use the mathematical editor for adding explanations in the text. Using “ x is a decision variable” is hard to read. Same for f(x) and others.
# Please change the table format so as not to confuse the reader.
# Multiple instances of [Chart to be added] are missing.
# Example is incomplete.
# Avoid pronouns such as “we”.
* A section to discuss and/or illustrate the applications
# Please connect several grammatical and spelling errors: “real life application”, Energy creation, particularly in renewable sources, have high variabilities”, and others
# “Zhao, Xue, Cao, and Zhang”. No need to list all authors within the article. Provide a reference is sufficient. If authors must be mentioned, (Zhao et al.) should be ok.
* A conclusion section
# Uniqueness and universality earlier are not clear to me. If they are not discussed earlier in the application, it would be better not to introduce new discussions in the conclusion.
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
* References
# References seem to vary in format. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Bayesian Optimization]] ==
* Section titles should not be "bold". Please double check using source editor on the section titles.
* Contents: Subheadings for EI and the algorithm should not be bolded, Random words should not be capitalized.
* Author list: Remove cornell ID, Please check names
* Introduction
# The introduction is too general and not substantial enough. For example, simply saying BayesOpt is useful when the objective function is unknown obscures exactly HOW it is useful (namely, computational efficiency in applications where ground truth sampling is expensive). Discussion on applications should be moved to a separate section.
# Machine learning rarely includes black-box functions to be optimized. Bayesian optimization is almost never used for optimizing ML loss functions but can instead be used for hyperparameter optimization. Please update such claims in this section.
* Theory, methodology, and/or algorithmic discussions
# Captions need reformatting.
# Consider italicizing keywords rather than bolding.
# Please add a citation to the first sentence.
# Discussion on acquisition functions should include comparisons, tradeoffs, and reasons to use one over the other. Should also note that expected improvement is the most widely used in practice, and explain.
# Avoid pronouns such as “we”.
# Please write equations in the Wiki instead of attaching images for equations.
# Acquisition function figure could be made larger and clearer to improve readability.
* At least one numerical example
# Any references to functions or methods in code ‘e.g. fmin’ should be properly formatted as code-stylized text.
# Please use the equation editor for min, st., etc.
# Avoid including a figure of the code for this example and explicitly describe the steps to the modeling and solution process instead.
# Avoid pronouns such as “our” and “we”.
* A section to discuss and/or illustrate the applications
* A conclusion section
# Please do not use brackets to enclose lists.
# Some claims here should be supported by references. Please cite each source after its sentence.
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Try to avoid references to “pop” machine learning blogs where anyone can be an author. (e.g. towardsdatascience)
# All references are URLs. Please cite publications and literature.
# A simple Google Scholar search would give you many references.

Notes on grammar: Needs some work. Several instances where colons are inappropriately inserted mid sentence or in subheadings. Explanations are not terse. Several instances of switching between personal and impersonal style of writing, which is distracting.

== [[Conjugate gradient methods]] ==

* Author list: Remove cornell ID
* Introduction
# All inline notations (e.g., `x`, `A`) should be typed using LaTex.
* Theory, methodology, and/or algorithmic discussions
# All equations need to be better formatted.
# Is Gauss-Newton no longer referenced?
# Theorems listed in the first section should be accompanied with high level explanation, not just a list of the theorems themselves. The page should read like an article, with proper flow.
# Please indent equation blocks.
# Please properly format pseudocode.
* At least one numerical example
# Steps should be accompanied with explanation, or reference to the corresponding step in the pseudocode.
# Please properly format in a more organized manner, aligning equations appropriately and demarcating steps appropriately.
* A section to discuss and/or illustrate the applications
# Consider including 2 additional examples of applications
* A conclusion section
# Consider adding future research directions
* References
# Reference primary sources rather than Wikipedia
# Too few references.
# More references should be added. A simple Google Scholar search would give you many references.

== [[Geometric programming|Geometric Programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Examples of applications in this section use the same reference. Please cite their individual sources.
* Theory, methodology, and/or algorithmic discussions
# The symbol denoting the domain in the definition of a monomial is unclear. Please clarify it or fix this if it is incorrect.
# Definition of posynomial refers to section 2.1 which is missing from the Wiki (sections are not numbered in the main text).
# In the generalized posynomial subsection, bullet points do not tell us why h(x) is posynomial. Either provide reasons or simply state that h(x) is posynomial. Also explain why h3 is a generalized posynomial.
# Additional theory on the feasibility analysis could be provided in this section.
* At least one numerical example
# In the transformation example, the last two constraints could also be simplified by applying a natural logarithm on both sides. Please update them as well.
* A section to discuss and/or illustrate the applications
# The figure in this section needs to be labeled.
# The figure needs to be resized and perhaps aligned to the center.
* A conclusion section:
# Please avoid vague language such as: “This makes”.
# Please avoid opinionated statements: “one of the best ways”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# This Wiki has very few references. A quick Google Scholar search may provide relevant references.

== [[Adam]] ==

* Author list
* An introduction of the topic
# Some grammatical errors here, mostly related to the need for commas in certain places (e.g., “Before Adam..”).
# Some minor errors with parts of speech throughout the section, need to revisit phrases such as “which has broader scope in future for”, etc.
# Try splitting up some of the longer sentences in this section, a couple are hard to read.
# Avoid definitive statements about Adam being the best or always better solver, as this is simply not true (the choice of the “best” optimizer is setting-dependent). Use language such as “Research has shown that Adam has demonstrated superior experimental performance over..” and then cite academic references to back this claim.
# What does adam stand for? Introduction is insufficient. Please expand.
* Theory, methodology, and/or algorithmic discussions
# Revise grammar here, noticing some missing commas and uncapitalized word after period.
# Rephrase “second one is to update the old position with the updated position”.
# Use LaTex code or equation editor to display all equations and variables in this section, and actual subscripts instead of “m_t”, etc.
# Avoid inserting inline citations after words like “According to..” or “This article..” as it is a bit informal. This could be rephrased or changed to something like “According to author,^[2] …” with author name inserted.
# Remove white space before the period in RMSP discussion.
# Please provide a pseudocode.
# Please use list the two methods here “Adam is a combination of two gradient descent methods which are explained below”
# Please expand the theory section significantly. Theoretical convergence properties should be discussed, even if briefly.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
* A section to discuss and/or illustrate the applications
# Same comment as before, consider replacing inline citations after words like “According to..”.
* A conclusion section
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Try to avoid references to blogs and use peer-reviewed academic references instead.
# Too few references.
# More references should be added. A simple Google Scholar search would give you many references.

== [[A-star algorithm|a* algorithm]] ==

* Author list: Remove cornell ID
* Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.
* An introduction of the topic:
# Weird spacing between paragraphs. Please fix this issue.
# In the titles, please change the font from bold to normal to have consistent formatting in the site.
# Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.
# There are no citations in the introduction. Please cite every source.
* Theory, methodology, and/or algorithmic discussions
# Please add the mathematical description of the algorithm.
# Reference style varies in sentences. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please fix grammatical and spelling errors as (“from current position to the goal”, “There are a lot of discussions”, etc). Also, many hyphens are missing as “non playable”.
# In algorithms, it is a standard to add high-level description (i.e. pseudocode or flowchart). Please incorporate it.
# Use LaTex code or equation editor to display all equations and variables in this section (e.g., “f(n)...”, “h(n)..”, etc.). This goes for other sections as well.
* At least one numerical example
# The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.
# Instead of writing things like “The above image..”, label each figure and use the figure number to refer to it in text.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# No references in the applications. Please cite every source
# Preferably, add at least an additional application.
* A conclusion section
# Conclusion should summarize descriptions. Please modify it to provide a summary.
# Please pay attention to the length and structure of sentences here and in the full page. First sentence is hard to read.
* References
# References seem to vary in format and are not linked correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Incorrect reference style. Please follow the example and use the template.

== [[Job shop scheduling|Job-Shop Scheduling Problem]] ==

* An introduction of the topic
# The current introduction to the jobshop scheduling problem has only two sentences in addition to the parameter description. Introduction typically contains information about the problem, its importance in the real-world, and some information about the solution techniques and their types to solve the problem. Please add some information that covers the above.
* Theory, methodology, and/or algorithmic discussions
# It is unclear whether the assumptions stated in this section are required to apply the following solution techniques. Please clarify the same. Also use complete sentences to state them.
# The branch and bounds method described in this section only discusses the solution technique for problems with one machines. However, branch and bound is a general technique that can be applied to any MILP problems with varying scales. Please update the “methods” section to be as general as possible.
# Since this Wiki focuses on jobshop scheduling, at least two methods are expected. Branch and bound is a general MILP technique, so, it is recommended to add a tailored technique that can only solve specific jobshop scheduling problems. Solving the numerical example with this technique is not necessary.
# Reference to the branch and bound technique described in this section is a “youtube” video. Please add references in literature that describe this method in detail. The method used in this video is highly tailored for a single machine application. This is also an incorrect way to cite a reference. Please keep this section as general as possible.
# Use LaTex code or equation editor to display all equations and variables in this section and all other sections as well.
# Check grammar in this section. For example, phrases like “are as follows” need to be followed by a colon and not a period.
# Consider rewriting the assumptions as a list in this section.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# The example used in this section is exactly the same as the one in the youtube video. Please use a modification of this example or choose another example/method to demonstrate the solution technique.
# The figure in this section is not numbered when all others are. Relabel this figure for consistency and its number to refer to it in-text.
* A section to discuss and/or illustrate the applications
# This section should only focus on real-world applications of the jobshop scheduling problem. But currently, this section includes additional information on solution techniques/complexity that is appropriate for the Introduction section. Please discuss the applications of the problem in this section.
* A conclusion section
# The meaning of “Operations applications” is unclear. Please explain or update if necessary.
# The current conclusion section does not properly summarize the problem. Please refer to other Wiki examples for an idea to update the section accordingly.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please reference media sources like reference 5 appropriately.
# A simple Google Scholar search would give you many "formal" references.

== [[Optimization in game theory]] ==

* Author list: remove cornell IDs.
* An introduction of the topic
# References are not linked. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
* Theory, methodology, and/or algorithmic discussions
# Why only a subsection on "Nash Equilibrium" is included in "Theory" section? Please re-format.
# Please edit references.
# Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm.
# Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.
* At least one numerical example
# Please organize the last part in a more readable format. Questions may be in bold and numbered, answers are more direct, etc.
# Remember to cite all images and tables.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# Very good, link the reference and cite all sources.
* A conclusion section
# Please add more summarizing especially from theory sentences and avoid long sentences.
* References
# Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Reference primary sources rather than Wikipedia
# Incorrect reference style. Please correct.

== [[Trust-region methods]] ==

* Author list:
# Remove cornell IDs. Author is also spelled incorrectly.
# Add the course section.
* An introduction of the topic
# References are not linked. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Use LaTex code or equation editor to display all equations and variables (e.g., “xk”, “f`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “we”. This goes for all other sections as well.
* Theory, methodology, and/or algorithmic discussions
# Organization of ideas in this section needs work.
# You have not defined explicitly why the Cauchy point is important to compute beyond a vague allusion to performance improvements, which is also wrong (it is useful because of its guarantees for convergence, not performance) It is also misspelled.
# Each approach should have accompanying explanation and motivation for why it is being discussed. It is not enough to outline the algorithm.
# Please make sure symbols are properly subscripted and superscripted (e.g. “pk” should be “p_k”
# Please format the algorithm in proper algorithmic pseudocode format.
# Little to no discussion on global convergence guarantees
# Please include discussion about the advantages and disadvantages of the algorithm
# Fix typo “couchy point”.
* At least one numerical example
# Any code functions (uminfunc) should have proper text formatting.
# The graph needs a better caption explaining how the axes are labeled and what data points are being shown.
# Please increase the quality of the figure. It is hard to see the red line.
# Add citation to “The Rosenbrock function is a non-convex function, introduced by Howard H. Rosenbrock in 1960, which is often used as a performance test problem for optimization algorithms.”
* A section to discuss and/or illustrate the applications
# The content in this section as it is currently does NOT describe applications, but rather different approaches within the trust region methodology. Please provide specific applications (e.g. TRPO in reinforcement learning).
* A conclusion section
# Please add more summary, future research directions for example is a good start.
* References
# Incorrect reference style.
# Please consider having the references as this Wiki template, <nowiki>https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization</nowiki>
# More references should be added. A simple Google Scholar search would give you many references.

*There are numerous misspellings, grammatical errors, and incorrect claims. Please fix these.

== [[Momentum]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Apart from an explanation on momentum, it is necessary to briefly point out the limitations of SGD and why momentum could help with these limitations. Please update it accordingly.
# Remove bold on “Momentum”.
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
* Theory, methodology, and/or algorithmic discussions
# Equation formatting is very poor and should be formalized.
# It is important to use technical language for this Wiki. Although a layman’s explanation is appreciated, it would be better to skip using words like “zig zagging”. Try to explain all concepts in a technical language with few simplifications but NOT vice versa.
# The definition of the update rule for SGD with momentum looks incorrect, specifically the first expression. Please fix it and also explain all the parameters used.
# Use LaTex code or equation editor to display all equations and variables (e.g., “W”, “V`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “you”.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please try to label the plots that explains what each line color means.
* A section to discuss and/or illustrate the applications
# Please use correct terminology like “optimizing non-convex functions” and not “training non-convex models”.
# Adam, Adadelta, and RMSprop are variants of SGD that already use momentum. Please double check the writing and update if necessary.
* A conclusion section
# Please refrain from using words like “zig zag” effects.
* References
# Almost all references used are URLs. Please try to add journal/conference articles or books for references, instead of directly citing the URLs.

== [[Stochastic dynamic programming|Stochastic Dynamic programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Discussion on applications should be moved to a separate section.
* Theory, methodology, and/or algorithmic discussions
# Remove the grey box background of equations.
* At least one numerical example
* A section to discuss and/or illustrate the applications
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Outer-approximation (OA)|Outer-approximation]] ==

* An introduction of the topic
# See formatting guideline below
# Avoid opinionated statements such as “MINLP problems are usually the hardest to solve”.
# Rearrange the text such that the MINLP formulation is in the theory section and keep the introduction in words only.
* Theory, methodology, and/or algorithmic discussions
# Consider left aligning equations and optimization problem formulations by the “=”. See [[Stochastic programming|https://optimization.cbe.cornell.edu/index.php?title=Stochastic_programming]] for an example
# The sentence “The Outer-Approximation (OA) algorithm was first proposed by Duran and and Grossmann in 1986 to solve MINLP problems.” needs a reference.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# “Minimize” and “subject to” should be “min” and “s.t.” in MathType
* A section to discuss and/or illustrate the applications
# Does not explicitly point out why OA is applicable (and/or preferred) in these applications, rather than other MINLP approaches (show that the problem formulations are amenable to a solution approach through OA)
# The sentence “... an active research area and there exists a vast number of applications in fields such as engineering, computational chemistry, and finance.” needs references.
# Place GAMS code in a single code box or remove it.
# Consider reformatting to make steps more readable. Inserting spaces and breaking down steps would help.
* A conclusion section
# Too short. Consider discussion on future research direction and discussion on uncertainty
# Please review abbreviations throughout the page. Why is MINLP redefined here? “Outer-Approximation is a well known efficient approach for solving convex mixed-integer nonlinear programs (MINLP)”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove "Template:Reflist"

== [[Unit commitment problem]] ==

* Author list
* An introduction of the topic
# Please expand the introduction and avoid discussions of examples or specific applications in this section.
# The sentence “Nonlinear, Non-convex programming optimization problem.” doesn’t make sense by itself and Non-convex shouldn’t be capitalized.
* Theory, methodology, and/or algorithmic discussions
# Figure/image format should be revised to better display the content.
# Uppercase characters are used randomly (e.g., “non-convex transmission Constraints”) . Please follow correct language conventions for sentence structure.
# Avoid inserting inline citations after words like “written in matrix form as equation [3]..” or “presented in [3]...” as it is a bit informal when you don’t explicitly name the subject. Also these two sentences are grammatically incorrect and appear to be missing an ending period and comma, respectively.
# Don’t say “written in matrix form as equation..” and just cite the reference, actually write out the equation.
# Properly label the figure in this section with a figure number and improve visibility by making it larger.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Label the figures in this section properly with figure numbers.
# Fix typo “while minimize” to “while minimizing”.
# Avoid pronouns such as “we”.
# Use the equation editor when typing equations.
* A section to discuss and/or illustrate the applications:
# I suggest changing the order of the subtitles here. For example, Single-Period Unit Commitment.
* A conclusion section
* References

== [[Frank-Wolfe]] ==

* Author list:
* An introduction of the topic
# I suggest highlighting disadvantages along with advantages.
* Theory, methodology, and/or algorithmic discussions
# “[n x 1] matrix” please use the equation editor to express mathematical descriptions and symbols (p,b, etc)
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please show at least a few iterations. Even for smaller examples if needed. Report the final solution.
# Please use the LaTex code or equation editor for min and include s.t., etc.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps. For your example, please explicitly state that the derivative is taken etc.
* A section to discuss and/or illustrate the applications:
* A conclusion section
# Same as the introduction. Pros and cons should be evaluated together!
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Line search methods|Line Search Method]] ==

* Author list
* An introduction of the topic
# Expand the introduction and avoid discussion on some of the specific steps in the solution process.
# Provide references here.
* Theory, methodology, and/or algorithmic discussions
# The phrase “are as follows” in the steepest descent method discussion needs to be followed by a colon.
# Rephrase “has a nice convergence theory” and cite a reference for this claim.
# Avoid pronouns such as “we”.
# Add citation after “.. proposed by Phillip Wolfe in 1969.”
# Figure 1 is between two sections. Please fix this issue.
* At least one numerical example:
# Add some space between iterations or subsection break
* A section to discuss and/or illustrate the applications:
# Too few references in this section.
# Last paragraph makes some claims without references.
* A conclusion section
* References
# References should be properly formatted. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Piecewise linear approximation|Piecewise Linear Approximation]]==

* Author list
* An introduction of the topic
# The content of this section is good, but there are some issues with sentence clarity and some other grammatical errors. Please revisit this section and make changes accordingly.
* Theory, methodology, and/or algorithmic discussions
# Fix typo “to force the x’ values become associated with”.
* At least one numerical example
* A section to discuss and/or illustrate the applications
# Please aim for a maximum average sentence length of ~25 words. Some of these longer sentences are hard to read.
* A conclusion section
# Expand the conclusion section to be longer than one sentence. The conclusion section to include a brief summary of what was discussed above, an emphasis on it’s significance, and a brief discussion of future extensions and research direction if applicable.
* References
# Include hyperlinks to sources when possible.

== [[Mathematical programming with equilibrium constraints|Mathematical Programming with Equilibrium constraints]] ==

* An introduction of the topic
# This section includes several terms like variational inequalities, constraint qualifications that were not discussed in the class. Please add a sentence to explain them before using them.
* Theory, methodology, and/or algorithmic discussions
# The meaning of parameter vector x is unclear. Please add more information or update if necessary.
# Equations and symbols in the PIPA subsection are not formatted correctly. Please use the same formatting for all equations, so they read as mathematical equations and not text. This goes for all other sections as well.
# Use equations instead of images to represent math programs and equations in the Implicit Descent and SQP subsection.
# Apart from the steps for each solution technique, please also add a few sentences that describe each method.
* At least one numerical example
# Please define the terms like NCP, MP before abbreviating them. Also try not to unnecessarily abbreviate simple terms.
# Equations should be typed by LaTex. Images for equations are unacceptable.
# GAMS code is strongly discouraged. Please solve the problem "step-by-step".
# The selected numerical example is fine but is directly solved with the MPEC solver in GAMS. Try to solve it manually like the homework/in-class problems step by step using the steps described in the previous section by choosing any of the methods.
# Avoid using figures in the equations (subject to etc)
* A section to discuss and/or illustrate the applications
# Add references to “power management, highway pricing, chemical process engineering, and traffic planning.”
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Wing shape optimization|Wing shape Optimization]] ==

* Author list: Remove cornell ID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# The introduction is missing several references (e.g., “software packages like computational fluid dynamics..”, sentences containing things that aren’t common knowledge, performance claims, etc.)
# Avoid discussion involving finer details of subject methods in this section.
# In the titles, please change the font from bold to normal to have consistent formatting in the site. Same applies to box of content!
* Theory, methodology, and/or algorithmic discussions
# Properly cite the CFD package, don’t just include a link.
# Properly label the figure with a figure number.
# Consider removing white space between isolated sentences to improve readability.
* At least one numerical example
# If you’ve already defined an abbreviation (CFD), there is no need to define it again. Just use the abbreviation.
# Avoid pronouns such as “we” or “they”.
# Phrases like “under the following” need to be followed by a colon.
# Properly label the figure with a figure number and consider making them larger to improve visibility. Call the reader's attention to the figures in text by referencing the figure number.
# “As seen in the video below” is stated yet there are only images present and it may be initially unclear to the reader which figure is being referenced here.
# Avoid inserting inline citations like “[4] introduces an..” as it is a bit informal when you don’t explicitly name the subject.
# Don’t just cite the reference when discussing the problem formulation, explicitly write the model formulation and solution process using LaTex or equation visual editor.
* A section to discuss and/or illustrate the applications
# Some characters are randomly capitalized in this section.
* A conclusion section
# These variables should be defined before the conclusion section, they are out of place here. Also, please use normal text when explaining variables except for the variable symbol.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Interior-point method for NLP|Interior point method for NLP]] ==

* An introduction of the topic:
* Theory, methodology, and/or algorithmic discussions
# Primal-Dual formulation and comparison to the Barrier Method is not discussed.
# Include brief discussion about big O convergence rates.
# Need discussion about the concept of “central path” and the notion of self concordance
# Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
# Graphs and images are incorrectly formatted to the page. Consider proper alignment with respect to the text body.
# Use explicitly typed Latex equations instead of images to represent math programs and equations.
# Fix typo “optimisation”.
# Use LaTex code or equation editor to display all equations and variables (e.g., “xi ”, “μ”, etc.).
* At least one numerical example:
# There are formatting issues with figures 2,3. Please make sure to embed them within their respective sections.
* A section to discuss and/or illustrate the applications
* A conclusion section
# Minor character code typos in the conclusion.
# Also, please add more discussion in this section. Future research directions is a good start.
# There is a box "􏰐"
* References

== [[AdaGrad|Adagrad]] ==

* An introduction of the topic:
* Theory, methodology, and/or algorithmic discussions
# Include discussion on its variants (most important is AdaDelta).
# Include disadvantages of Adagrad, since this provides motivation for the discussion on the variants and improvements of Adagrad
# Include comparisons to other popular optimizers (particularly important is comparisons to regular SGD and Adam)
# Different convergence rates are possible depending on the setting where Adagrad is used, but this is not mentioned on the page currently. As such the regret bound section should be more thoroughly explained.
* At least one numerical example
# In the first sentence, “..take the following numerical example” should be followed by a colon.
# Fix typo “trayectory”.
* A section to discuss and/or illustrate the applications
# This section is too short; include specific applications in which input features are sparse and Adagrad excels.
# Add reference to the claim “Mainly, it is a good choice for deep learning models with sparse input features”.
* A conclusion section
* References

# Too few references overall, you should aggregate information from multiple sources (even if the base algorithm itself comes from a singular paper)

== [[McCormick envelopes|McCormick Envelopes]] ==

* Author list: OK but I suggest removing NetID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# First sentence is hard to read. Please consider keeping sentences below 25-30 words.
# No references provided. Please cite all sources.
# Figure 1 is provided in the middle between two sections. Please include in the introduction section.
* Theory, methodology, and/or algorithmic discussions
# References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# When using mathematical expressions and symbols, please use the equation editor. (e.g., x*y, exy + y, sin (x+y) - x2)
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# For the sample GAMS code, please place it in a code box
* A section to discuss and/or illustrate the applications
# Having a list is not enough. Please explain at least three applications in a few sentences each.
# This section should be at least a paragraph to discuss relevant applications. Each application should be explicitly linked to the page topic. A few keywords do not meet the requirement at all.
* A conclusion section:
* References
# References are not expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please follow the standard reference style - the current format is incorrect.

2021 Cornell Optimization Open Textbook Feedback

2021-12-05T19:45:37Z

Asa273: /* Sparse reconstruction with Compressed Sensing */

== [[Lagrangean duality|Lagrangian duality]] ==
* Author list, sections and TOC
# Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.
# Remove cornell ID from Author list
* An introduction of the topic
# This section includes sentences on constructing the dual problem and is referred to as Lagrangian relaxation (LR). This is incorrect, please fix the definition of LR.
# Definitions of LR and its relation to duality should be double checked and re-written.
# Only one reference is present in this section. Please add more relevant references by expanding this section.
# Consider merging the “introduction” and “history” sections.
# In the titles, please change the font from bold to normal to have consistent formatting in the site.
* Theory, methodology, and/or algorithmic discussions
# The Lagrangian variables associated with equality constraints h(x) are unbounded but the Lagrangian dual problem states them as non-negative. Please fix the same.
# Also to construct a dual, we do not change minimization to maximization directly. We observed such things in the examples in lecture notes due to simplification. The lagrangian dual problem would be minimize (,).
# Adding to the previous point, the Lagrangian is a lower bound on the original objective; the solution to the primal and dual or only equivalent if the duality gap is 0. You reference this in one section, but this is after your statement “Hence, solving the dual problem, which is a function of the Lagrangian multipliers (𝜆*) yields the same solution as the primal problem, which is a function of the original variables (x*). “. Please clarify the specific conditions that must hold for the solution of the dual to be equal to the primal’s.
# You refer to the “Complementary Slackness Theorem”, but don’t actually write the mathematical representation of complementary slackness. Please fix this. Also consider including the derivation of the complementary slackness condition, as it is both easy and short. Boyd is a good reference for this.
# Last step of the “process” subsection also needs updating according to the previous comments.
# The inline notations should also be typed using LaTex.
# Please use the LaTex code or equation editor for min, s.t., etc.
* At least one numerical example
# Only one dual variable is associated with each constraint. The numerical example uses two for the first and second constraint which is unnecessary. Please update it accordingly for both constraints. This particular example will only have two dual variables instead of the five dual variables used currently.
# All consecutive steps need to be updated since the dual variables would be updated.
# After substitution the nonlinear function should be further simplified. The current expression reads like a highly nonlinear function but can be easily simplified.
# Similar to the comments in the methodology section, inverting minimize to maximize is incorrect. Please update the dual objective function and domain of dual variables accordingly.
# Please use the LaTex code or equation editor for min, s.t., etc.
* A section to discuss and/or illustrate the applications
# Bullet points could be used to state the last four real-world examples that explain the physical meaning of the primal and dual problems.
# Add references for the last set of applications.
* A conclusion section
# This section contains a few typos. Please fix the same.
* References
# Some citations' hyperlinks are displaying.

== [[Disjunctive inequalities|Disjunctive Inequalities]] ==

* Author list
# Missing course section and semester
# Remove cornell ID
* An introduction of the topic
# No citations are present in this section.
# “mixed-integer programming (MIP)” should be used instead of “multiple integer programming (MIP)”. Please fix this error.
* Theory, methodology, and/or algorithmic discussions
# The abbreviation MILP is not previously defined. Please fix this issue.
# You consistently use the negative sign instead of the NOT operator for y (-y instead of ¬y).
# Some inconsistencies with the spacing of variables, constraints, etc., under the “General” section that need to be fixed.
# Typo in “This is shown below by M1, M2, y1, and y1:” where y1 needs to be changed to y2. Why use two different Big-M variables here? Elsewhere in the Wiki you only use one so this could lead to confusion with a general audience. Also if this was taken from the lecture notes then it needs to be cited.
* At least one numerical example
# Please reformulate and solve a complete numerical example rather than just reformulating a general example. Demonstrate the use of Big-M and Convex Hull formulation in an optimization problem that provides details such as individual steps in the problem solving process and final results.
# Add space between vee (V) operator and brackets in first line of Latex
# Please format variables correctly, for example, use <math>x_1</math> instead of x1.
* A section to discuss and/or illustrate the applications
# Please format the equations appropriately either by using latex code or the visual editor. These images are NOT acceptable!
* A conclusion section
# There is no conclusion presented in this section at all.
* References
# The included references have NOT been used anywhere in the Wiki. Add references for sentences that are not common knowledge and please link them appropriately with the text in Wiki. If the figures used here were not original works, you must also cite them.
# There are many papers on this topic. A simple Google (Scholar) search could provide you with sufficient references to cite.
# Many important references of this topic are missing.
# Please consider linking the references as demonstrated in the Wiki tutorial on Canvas and in this template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

==[[Stochastic programming|Stochastic Programming]] ==

* Author list: Remove cornell IDs
* An introduction of the topic
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
# This section only includes two sentences on Stochastic programming (SP), while the rest gives examples of uncertainty. Please discuss the need for SP in the presence of uncertainty. Also, discussion on robust optimization and its limitations should be removed since it is out of place.
* Theory, methodology, and/or algorithmic discussions
# Please avoid direct inline linkbacks to Wikipedia.
# The symbol “xi” in the methodology subsection should be explained.
* At least one numerical example
# Copying a numerical example "entirely" from a textbook is inappropriate. Your team should come up with a "numerical" case.
# No specific application context is needed for a numerical example.
# The inline notations (`x1`, `s1`) should also be typed using LaTex.
# Label all tables with a table number for better readability.
# Properly format the solution table with the label attached rather than the following sentence. The solution table looks different from the others, please fix this for consistency.
* A section to discuss and/or illustrate the applications;
# I suggest eliminating citing the last name of the first author (i.e. Zhou et al.)
* A conclusion section
* References
# URLs of some citations are not properly formatted (not showing the hyperlinks).

== [[Exponential transformation|Exponential Transformation]] ==

* Author list
# Missing course section
# Remove cornell ID
* An introduction of the topic
# Please expand the introduction.
# Please aim for a maximum average sentence length of ~25 words. Last sentence with 51 words is hard to read.
# Second Sentence: please change the word “they” as it could make the meaning ambiguous
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
# If you use abbreviations, please introduce them (e.g. NLP,MINLP)
* Theory, methodology, and/or algorithmic discussions
# Please explain the transformation in words along with equations
# Terms like posynomial should be described in detail.
# Please move the numerical example to the section below
# The “(eq 1)” is not needed here.
# Please expand this section.
* At least one numerical example
# In the third equation of the numerical example, it is confusing to have coefficients after numbers. Some readers may read it as an exponent.
# Last equation in this section after “further linearization” is incorrect. This equation cannot be further linearized, please fix this.
# Please explain the steps in the numerical examples in detail. The step-by-step solution should be provided.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# Missing part of text: “Proof of convexity of with positive definite test of Hessian…”
# Applications are not numerical examples. Please refer to this link for example of applications: [[Duality|https://optimization.cbe.cornell.edu/index.php?title=Duality]]
# Citation 7 is missing in current applications
# The section current applications is redundant
# Please use the LaTex code or equation editor for min, s.t., etc.
# Under current applications, do not just use a hyperlink to describe an application. Actually describe it. And properly inline citation style should be used instead of the hyperlink.
# The convexification application of MINLP can be further simplified for binary variables. Please refer to the lecture slides for more information.
* A conclusion section
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
* References
# Please consider linking the references by using this as Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Citation 7 is missing in current applications

== [[Sparse Reconstruction with Compressed Sensing|Sparse reconstruction with Compressed Sensing]] ==
This Wiki needs a significant rewrite. Please go through the comments for details.

* An introduction of the topic
# The introduction section should include information about the problem and its implications presented briefly. Please use full sentences to write this Wiki. You may use tools like Grammarly to check sentence formation and grammar.
# This section includes several typos like “sub modual”. Please fix them throughout the wiki and delete them if not required.
# Many abbreviations are used before previously defining them. Please define these abbreviations before using them in the text.
# This section is incomprehensible in its current form. Please rewrite with proper comprehension.
# Equations and math symbols need proper reformatting. The current version reads like text (along with equations) copy-pasted from a specific source. All mathematical symbols and equations should be formatted via LaTex - this is a learning objective of the Wiki assignment. You can find some useful links on converting your equations/symbols into LaTex code here: (https://optimization.cbe.cornell.edu/index.php?title=Help:Contents).
# Try to place the figure at the top of the Wiki between the main text.
# Avoid pronouns such as “we”.
# I suggest the use of more formal abstract illustrations.
* Theory, methodology, and/or algorithmic discussions
# Equations and symbols need proper reformatting.
# Lemmas and theorems are not expected for this Wiki. Sparse reconstruction is a straightforward concept but is unnecessarily complicated here. Please refer to other Wiki examples to get an idea of what the Wiki should convey.
# All equations need to be better formatted.

* At least one numerical example
# Numerical example is missing.
# Every iteration should be clearly presented, and solved "step-by-step".
* A section to discuss and/or illustrate the applications
# Having a list is not enough. Please explain at least three applications in a few sentences each.
* A conclusion section
# Conclusion section is missing.
* References
# The current reference list is not correctly formatted. References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Portfolio optimization|Portfolio Optimization]] ==

* Author list
# Remove cornell id
* An introduction of the topic
# The introductory sentence should be rephrased. The action of minimizing the risks does not inherently maximize the gains, rather PO aims to maximize gains whilst minimizing risks.
# Amount of whitespace can be reduced by changing the orientation of Figure 1 and the sentences in this section.
# Define terms such as risk, return, portfolio, etc., when you introduce them. Assume that the reader may not know much about finance. This goes for all other sections as well.
* Theory, methodology, and/or algorithmic discussions
# A brief mention of modern portfolio theory (i.e.. Markowitz) would be appropriate in this section.
# Several grammatical errors here involving sentence structure and clarity. Some questionable semantics (e.g., “The portfolio optimization mainly assumes two directions.”) and syntax (phrases such as “.. is as follows” should be followed by a colon). Misuse of commas and missing commas in this section. Two sentences introducing E(rp) and w should be combined into one.
# Use LaTex to distinguish variables written within a sentence, such as m and n.
# Rephrase “Cut the relevant information and conditions in the portfolio optimization, as well as the final requirements into the relevant variables, constraints and linear functions of the linear programming problem.”
# An explanation of a few common constraints would be helpful, rather than just including a table.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Solving the numerical example by GAMS is inappropriate. Please provide detailed step-by-step calculation results.
# All tables need to be labeled.
# Include figure number in label for consistency.
# Fix misspelling “dolling decision variables”.
# Use LaTex for all variables, equations, and constraints here.
# Example 2 table is hard to read, so making it bigger would help.
# Remove the “Using excel as the solver” part from the sentence before the solution discussion.
# Some grammatical errors here (phrases such as “.. is as follows” should be followed by a colon).
* A section to discuss and/or illustrate the applications
# Rephrase “Portfolio optimization can be used to screen investment projects that meet investors, rationally allocate investment amounts, etc.”
# Not sure “relevant” is the correct word choice here.
# You need more specific examples with the utility of portfolio optimization, this section is quite general as is. Some more detail and focus on real-world applications in the financial industry that relate to retirement planning, financial security, economic stability, etc., would be helpful.
* A conclusion section
# Need some commas here.
# The sentence “Linear programming has been around since the 1940’s and has such a wide base of applications” is not necessary.
* References
# Please consider linking the references as demonstrated in the Wiki tutorial on Canvas and in this template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove white space between end of sentences and reference numbers.

== [[Chance-constraint method|Chance constraint method]] ==

* Author list:
* An introduction of the topic
# Please consider correcting a few grammatical errors: “pre-planned for”, “god”, “certain levels of feasibility is guaranteed in what are”, and “Performance of a system”
# In “Chance-constraint”, it is capitalized randomly throughout the introduction. Please correct.
# Please use technical language to briefly introduce chance-constrained programming. Words like “acts of god”, “cost of doing business” are not appropriate for a technical Wiki.
* Theory, methodology, and/or algorithmic discussions
# Please add a citation to the first sentence.
# Xi is an uncertainty/randomness variable. It is better to use clear language.
# Please use the mathematical editor for adding explanations in the text. Using “ x is a decision variable” is hard to read. Same for f(x) and others.
# Theory is insufficient. Please expand and explain different approaches.
# Please add pros and cons explicitly as a list.
# Explain the physical meaning for examples of chance constraints along with all the notations used.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please remove this example as it is directly from this book. The example should be purely numerical without any background.
# Please use the equation editor for min, st., etc.
# Please use the mathematical editor for adding explanations in the text. Using “ x is a decision variable” is hard to read. Same for f(x) and others.
# Please change the table format so as not to confuse the reader.
# Multiple instances of [Chart to be added] are missing.
# Example is incomplete.
# Avoid pronouns such as “we”.
* A section to discuss and/or illustrate the applications
# Please connect several grammatical and spelling errors: “real life application”, Energy creation, particularly in renewable sources, have high variabilities”, and others
# “Zhao, Xue, Cao, and Zhang”. No need to list all authors within the article. Provide a reference is sufficient. If authors must be mentioned, (Zhao et al.) should be ok.
* A conclusion section
# Uniqueness and universality earlier are not clear to me. If they are not discussed earlier in the application, it would be better not to introduce new discussions in the conclusion.
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
* References
# References seem to vary in format. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Bayesian Optimization]] ==
* Section titles should not be "bold". Please double check using source editor on the section titles.
* Contents: Subheadings for EI and the algorithm should not be bolded, Random words should not be capitalized.
* Author list: Remove cornell ID, Please check names
* Introduction
# The introduction is too general and not substantial enough. For example, simply saying BayesOpt is useful when the objective function is unknown obscures exactly HOW it is useful (namely, computational efficiency in applications where ground truth sampling is expensive). Discussion on applications should be moved to a separate section.
# Machine learning rarely includes black-box functions to be optimized. Bayesian optimization is almost never used for optimizing ML loss functions but can instead be used for hyperparameter optimization. Please update such claims in this section.
* Theory, methodology, and/or algorithmic discussions
# Captions need reformatting.
# Consider italicizing keywords rather than bolding.
# Please add a citation to the first sentence.
# Discussion on acquisition functions should include comparisons, tradeoffs, and reasons to use one over the other. Should also note that expected improvement is the most widely used in practice, and explain.
# Avoid pronouns such as “we”.
# Please write equations in the Wiki instead of attaching images for equations.
# Acquisition function figure could be made larger and clearer to improve readability.
* At least one numerical example
# Any references to functions or methods in code ‘e.g. fmin’ should be properly formatted as code-stylized text.
# Please use the equation editor for min, st., etc.
# Avoid including a figure of the code for this example and explicitly describe the steps to the modeling and solution process instead.
# Avoid pronouns such as “our” and “we”.
* A section to discuss and/or illustrate the applications
* A conclusion section
# Please do not use brackets to enclose lists.
# Some claims here should be supported by references. Please cite each source after its sentence.
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Try to avoid references to “pop” machine learning blogs where anyone can be an author. (e.g. towardsdatascience)
# All references are URLs. Please cite publications and literature.
# A simple Google Scholar search would give you many references.

Notes on grammar: Needs some work. Several instances where colons are inappropriately inserted mid sentence or in subheadings. Explanations are not terse. Several instances of switching between personal and impersonal style of writing, which is distracting.

== [[Conjugate gradient methods]] ==

* Author list: Remove cornell ID
* Introduction
# All inline notations (e.g., `x`, `A`) should be typed using LaTex.
* Theory, methodology, and/or algorithmic discussions
# All equations need to be better formatted.
# Is Gauss-Newton no longer referenced?
# Theorems listed in the first section should be accompanied with high level explanation, not just a list of the theorems themselves. The page should read like an article, with proper flow.
# Please indent equation blocks.
# Please properly format pseudocode.
* At least one numerical example
# Steps should be accompanied with explanation, or reference to the corresponding step in the pseudocode.
# Please properly format in a more organized manner, aligning equations appropriately and demarcating steps appropriately.
* A section to discuss and/or illustrate the applications
# Consider including 2 additional examples of applications
* A conclusion section
# Consider adding future research directions
* References
# Reference primary sources rather than Wikipedia
# Too few references.
# More references should be added. A simple Google Scholar search would give you many references.

== [[Geometric programming|Geometric Programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Examples of applications in this section use the same reference. Please cite their individual sources.
* Theory, methodology, and/or algorithmic discussions
# The symbol denoting the domain in the definition of a monomial is unclear. Please clarify it or fix this if it is incorrect.
# Definition of posynomial refers to section 2.1 which is missing from the Wiki (sections are not numbered in the main text).
# In the generalized posynomial subsection, bullet points do not tell us why h(x) is posynomial. Either provide reasons or simply state that h(x) is posynomial. Also explain why h3 is a generalized posynomial.
# Additional theory on the feasibility analysis could be provided in this section.
* At least one numerical example
# In the transformation example, the last two constraints could also be simplified by applying a natural logarithm on both sides. Please update them as well.
* A section to discuss and/or illustrate the applications
# The figure in this section needs to be labeled.
# The figure needs to be resized and perhaps aligned to the center.
* A conclusion section:
# Please avoid vague language such as: “This makes”.
# Please avoid opinionated statements: “one of the best ways”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Adam]] ==

* Author list
* An introduction of the topic
# Some grammatical errors here, mostly related to the need for commas in certain places (e.g., “Before Adam..”).
# Some minor errors with parts of speech throughout the section, need to revisit phrases such as “which has broader scope in future for”, etc.
# Try splitting up some of the longer sentences in this section, a couple are hard to read.
# Avoid definitive statements about Adam being the best or always better solver, as this is simply not true (the choice of the “best” optimizer is setting-dependent). Use language such as “Research has shown that Adam has demonstrated superior experimental performance over..” and then cite academic references to back this claim.
# What does adam stand for? Introduction is insufficient. Please expand.
* Theory, methodology, and/or algorithmic discussions
# Revise grammar here, noticing some missing commas and uncapitalized word after period.
# Rephrase “second one is to update the old position with the updated position”.
# Use LaTex code or equation editor to display all equations and variables in this section, and actual subscripts instead of “m_t”, etc.
# Avoid inserting inline citations after words like “According to..” or “This article..” as it is a bit informal. This could be rephrased or changed to something like “According to author,^[2] …” with author name inserted.
# Remove white space before the period in RMSP discussion.
# Please provide a pseudocode.
# Please use list the two methods here “Adam is a combination of two gradient descent methods which are explained below”
# Please expand the theory section significantly. Theoretical convergence properties should be discussed, even if briefly.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
* A section to discuss and/or illustrate the applications
# Same comment as before, consider replacing inline citations after words like “According to..”.
* A conclusion section
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Try to avoid references to blogs and use peer-reviewed academic references instead.
# Too few references.
# More references should be added. A simple Google Scholar search would give you many references.

== [[A-star algorithm|a* algorithm]] ==

* Author list: Remove cornell ID
* Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.
* An introduction of the topic:
# Weird spacing between paragraphs. Please fix this issue.
# In the titles, please change the font from bold to normal to have consistent formatting in the site.
# Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.
# There are no citations in the introduction. Please cite every source.
* Theory, methodology, and/or algorithmic discussions
# Please add the mathematical description of the algorithm.
# Reference style varies in sentences. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please fix grammatical and spelling errors as (“from current position to the goal”, “There are a lot of discussions”, etc). Also, many hyphens are missing as “non playable”.
# In algorithms, it is a standard to add high-level description (i.e. pseudocode or flowchart). Please incorporate it.
# Use LaTex code or equation editor to display all equations and variables in this section (e.g., “f(n)...”, “h(n)..”, etc.). This goes for other sections as well.
* At least one numerical example
# The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.
# Instead of writing things like “The above image..”, label each figure and use the figure number to refer to it in text.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# No references in the applications. Please cite every source
# Preferably, add at least an additional application.
* A conclusion section
# Conclusion should summarize descriptions. Please modify it to provide a summary.
# Please pay attention to the length and structure of sentences here and in the full page. First sentence is hard to read.
* References
# References seem to vary in format and are not linked correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Incorrect reference style. Please follow the example and use the template.

== [[Job shop scheduling|Job-Shop Scheduling Problem]] ==

* An introduction of the topic
# The current introduction to the jobshop scheduling problem has only two sentences in addition to the parameter description. Introduction typically contains information about the problem, its importance in the real-world, and some information about the solution techniques and their types to solve the problem. Please add some information that covers the above.
* Theory, methodology, and/or algorithmic discussions
# It is unclear whether the assumptions stated in this section are required to apply the following solution techniques. Please clarify the same. Also use complete sentences to state them.
# The branch and bounds method described in this section only discusses the solution technique for problems with one machines. However, branch and bound is a general technique that can be applied to any MILP problems with varying scales. Please update the “methods” section to be as general as possible.
# Since this Wiki focuses on jobshop scheduling, at least two methods are expected. Branch and bound is a general MILP technique, so, it is recommended to add a tailored technique that can only solve specific jobshop scheduling problems. Solving the numerical example with this technique is not necessary.
# Reference to the branch and bound technique described in this section is a “youtube” video. Please add references in literature that describe this method in detail. The method used in this video is highly tailored for a single machine application. This is also an incorrect way to cite a reference. Please keep this section as general as possible.
# Use LaTex code or equation editor to display all equations and variables in this section and all other sections as well.
# Check grammar in this section. For example, phrases like “are as follows” need to be followed by a colon and not a period.
# Consider rewriting the assumptions as a list in this section.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# The example used in this section is exactly the same as the one in the youtube video. Please use a modification of this example or choose another example/method to demonstrate the solution technique.
# The figure in this section is not numbered when all others are. Relabel this figure for consistency and its number to refer to it in-text.
* A section to discuss and/or illustrate the applications
# This section should only focus on real-world applications of the jobshop scheduling problem. But currently, this section includes additional information on solution techniques/complexity that is appropriate for the Introduction section. Please discuss the applications of the problem in this section.
* A conclusion section
# The meaning of “Operations applications” is unclear. Please explain or update if necessary.
# The current conclusion section does not properly summarize the problem. Please refer to other Wiki examples for an idea to update the section accordingly.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please reference media sources like reference 5 appropriately.
# A simple Google Scholar search would give you many "formal" references.

== [[Optimization in game theory]] ==

* Author list: remove cornell IDs.
* An introduction of the topic
# References are not linked. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
* Theory, methodology, and/or algorithmic discussions
# Why only a subsection on "Nash Equilibrium" is included in "Theory" section? Please re-format.
# Please edit references.
# Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm.
# Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.
* At least one numerical example
# Please organize the last part in a more readable format. Questions may be in bold and numbered, answers are more direct, etc.
# Remember to cite all images and tables.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# Very good, link the reference and cite all sources.
* A conclusion section
# Please add more summarizing especially from theory sentences and avoid long sentences.
* References
# Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Reference primary sources rather than Wikipedia
# Incorrect reference style. Please correct.

== [[Trust-region methods]] ==

* Author list:
# Remove cornell IDs. Author is also spelled incorrectly.
# Add the course section.
* An introduction of the topic
# References are not linked. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Use LaTex code or equation editor to display all equations and variables (e.g., “xk”, “f`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “we”. This goes for all other sections as well.
* Theory, methodology, and/or algorithmic discussions
# Organization of ideas in this section needs work.
# You have not defined explicitly why the Cauchy point is important to compute beyond a vague allusion to performance improvements, which is also wrong (it is useful because of its guarantees for convergence, not performance) It is also misspelled.
# Each approach should have accompanying explanation and motivation for why it is being discussed. It is not enough to outline the algorithm.
# Please make sure symbols are properly subscripted and superscripted (e.g. “pk” should be “p_k”
# Please format the algorithm in proper algorithmic pseudocode format.
# Little to no discussion on global convergence guarantees
# Please include discussion about the advantages and disadvantages of the algorithm
# Fix typo “couchy point”.
* At least one numerical example
# Any code functions (uminfunc) should have proper text formatting.
# The graph needs a better caption explaining how the axes are labeled and what data points are being shown.
# Please increase the quality of the figure. It is hard to see the red line.
# Add citation to “The Rosenbrock function is a non-convex function, introduced by Howard H. Rosenbrock in 1960, which is often used as a performance test problem for optimization algorithms.”
* A section to discuss and/or illustrate the applications
# The content in this section as it is currently does NOT describe applications, but rather different approaches within the trust region methodology. Please provide specific applications (e.g. TRPO in reinforcement learning).
* A conclusion section
# Please add more summary, future research directions for example is a good start.
* References
# Incorrect reference style.
# Please consider having the references as this Wiki template, <nowiki>https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization</nowiki>
# More references should be added. A simple Google Scholar search would give you many references.

*There are numerous misspellings, grammatical errors, and incorrect claims. Please fix these.

== [[Momentum]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Apart from an explanation on momentum, it is necessary to briefly point out the limitations of SGD and why momentum could help with these limitations. Please update it accordingly.
# Remove bold on “Momentum”.
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
* Theory, methodology, and/or algorithmic discussions
# Equation formatting is very poor and should be formalized.
# It is important to use technical language for this Wiki. Although a layman’s explanation is appreciated, it would be better to skip using words like “zig zagging”. Try to explain all concepts in a technical language with few simplifications but NOT vice versa.
# The definition of the update rule for SGD with momentum looks incorrect, specifically the first expression. Please fix it and also explain all the parameters used.
# Use LaTex code or equation editor to display all equations and variables (e.g., “W”, “V`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “you”.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please try to label the plots that explains what each line color means.
* A section to discuss and/or illustrate the applications
# Please use correct terminology like “optimizing non-convex functions” and not “training non-convex models”.
# Adam, Adadelta, and RMSprop are variants of SGD that already use momentum. Please double check the writing and update if necessary.
* A conclusion section
# Please refrain from using words like “zig zag” effects.
* References
# Almost all references used are URLs. Please try to add journal/conference articles or books for references, instead of directly citing the URLs.

== [[Stochastic dynamic programming|Stochastic Dynamic programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Discussion on applications should be moved to a separate section.
* Theory, methodology, and/or algorithmic discussions
# Remove the grey box background of equations.
* At least one numerical example
* A section to discuss and/or illustrate the applications
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Outer-approximation (OA)|Outer-approximation]] ==

* An introduction of the topic
# See formatting guideline below
# Avoid opinionated statements such as “MINLP problems are usually the hardest to solve”.
# Rearrange the text such that the MINLP formulation is in the theory section and keep the introduction in words only.
* Theory, methodology, and/or algorithmic discussions
# Consider left aligning equations and optimization problem formulations by the “=”. See [[Stochastic programming|https://optimization.cbe.cornell.edu/index.php?title=Stochastic_programming]] for an example
# The sentence “The Outer-Approximation (OA) algorithm was first proposed by Duran and and Grossmann in 1986 to solve MINLP problems.” needs a reference.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# “Minimize” and “subject to” should be “min” and “s.t.” in MathType
* A section to discuss and/or illustrate the applications
# Does not explicitly point out why OA is applicable (and/or preferred) in these applications, rather than other MINLP approaches (show that the problem formulations are amenable to a solution approach through OA)
# The sentence “... an active research area and there exists a vast number of applications in fields such as engineering, computational chemistry, and finance.” needs references.
# Place GAMS code in a single code box or remove it.
# Consider reformatting to make steps more readable. Inserting spaces and breaking down steps would help.
* A conclusion section
# Too short. Consider discussion on future research direction and discussion on uncertainty
# Please review abbreviations throughout the page. Why is MINLP redefined here? “Outer-Approximation is a well known efficient approach for solving convex mixed-integer nonlinear programs (MINLP)”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove "Template:Reflist"

== [[Unit commitment problem]] ==

* Author list
* An introduction of the topic
# Please expand the introduction and avoid discussions of examples or specific applications in this section.
# The sentence “Nonlinear, Non-convex programming optimization problem.” doesn’t make sense by itself and Non-convex shouldn’t be capitalized.
* Theory, methodology, and/or algorithmic discussions
# Figure/image format should be revised to better display the content.
# Uppercase characters are used randomly (e.g., “non-convex transmission Constraints”) . Please follow correct language conventions for sentence structure.
# Avoid inserting inline citations after words like “written in matrix form as equation [3]..” or “presented in [3]...” as it is a bit informal when you don’t explicitly name the subject. Also these two sentences are grammatically incorrect and appear to be missing an ending period and comma, respectively.
# Don’t say “written in matrix form as equation..” and just cite the reference, actually write out the equation.
# Properly label the figure in this section with a figure number and improve visibility by making it larger.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Label the figures in this section properly with figure numbers.
# Fix typo “while minimize” to “while minimizing”.
# Avoid pronouns such as “we”.
# Use the equation editor when typing equations.
* A section to discuss and/or illustrate the applications:
# I suggest changing the order of the subtitles here. For example, Single-Period Unit Commitment.
* A conclusion section
* References

== [[Frank-Wolfe]] ==

* Author list:
* An introduction of the topic
# I suggest highlighting disadvantages along with advantages.
* Theory, methodology, and/or algorithmic discussions
# “[n x 1] matrix” please use the equation editor to express mathematical descriptions and symbols (p,b, etc)
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please show at least a few iterations. Even for smaller examples if needed. Report the final solution.
# Please use the LaTex code or equation editor for min and include s.t., etc.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps. For your example, please explicitly state that the derivative is taken etc.
* A section to discuss and/or illustrate the applications:
* A conclusion section
# Same as the introduction. Pros and cons should be evaluated together!
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Line search methods|Line Search Method]] ==

* Author list
* An introduction of the topic
# Expand the introduction and avoid discussion on some of the specific steps in the solution process.
# Provide references here.
* Theory, methodology, and/or algorithmic discussions
# The phrase “are as follows” in the steepest descent method discussion needs to be followed by a colon.
# Rephrase “has a nice convergence theory” and cite a reference for this claim.
# Avoid pronouns such as “we”.
# Add citation after “.. proposed by Phillip Wolfe in 1969.”
# Figure 1 is between two sections. Please fix this issue.
* At least one numerical example:
# Add some space between iterations or subsection break
* A section to discuss and/or illustrate the applications:
# Too few references in this section.
# Last paragraph makes some claims without references.
* A conclusion section
* References
# References should be properly formatted. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Piecewise linear approximation|Piecewise Linear Approximation]]==

* Author list
* An introduction of the topic
# The content of this section is good, but there are some issues with sentence clarity and some other grammatical errors. Please revisit this section and make changes accordingly.
* Theory, methodology, and/or algorithmic discussions
# Fix typo “to force the x’ values become associated with”.
* At least one numerical example
* A section to discuss and/or illustrate the applications
# Please aim for a maximum average sentence length of ~25 words. Some of these longer sentences are hard to read.
* A conclusion section
# Expand the conclusion section to be longer than one sentence. The conclusion section to include a brief summary of what was discussed above, an emphasis on it’s significance, and a brief discussion of future extensions and research direction if applicable.
* References
# Include hyperlinks to sources when possible.

== [[Mathematical programming with equilibrium constraints|Mathematical Programming with Equilibrium constraints]] ==

* An introduction of the topic
# This section includes several terms like variational inequalities, constraint qualifications that were not discussed in the class. Please add a sentence to explain them before using them.
* Theory, methodology, and/or algorithmic discussions
# The meaning of parameter vector x is unclear. Please add more information or update if necessary.
# Equations and symbols in the PIPA subsection are not formatted correctly. Please use the same formatting for all equations, so they read as mathematical equations and not text. This goes for all other sections as well.
# Use equations instead of images to represent math programs and equations in the Implicit Descent and SQP subsection.
# Apart from the steps for each solution technique, please also add a few sentences that describe each method.
* At least one numerical example
# Please define the terms like NCP, MP before abbreviating them. Also try not to unnecessarily abbreviate simple terms.
# Equations should be typed by LaTex. Images for equations are unacceptable.
# GAMS code is strongly discouraged. Please solve the problem "step-by-step".
# The selected numerical example is fine but is directly solved with the MPEC solver in GAMS. Try to solve it manually like the homework/in-class problems step by step using the steps described in the previous section by choosing any of the methods.
# Avoid using figures in the equations (subject to etc)
* A section to discuss and/or illustrate the applications
# Add references to “power management, highway pricing, chemical process engineering, and traffic planning.”
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Wing shape optimization|Wing shape Optimization]] ==

* Author list: Remove cornell ID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# The introduction is missing several references (e.g., “software packages like computational fluid dynamics..”, sentences containing things that aren’t common knowledge, performance claims, etc.)
# Avoid discussion involving finer details of subject methods in this section.
# In the titles, please change the font from bold to normal to have consistent formatting in the site. Same applies to box of content!
* Theory, methodology, and/or algorithmic discussions
# Properly cite the CFD package, don’t just include a link.
# Properly label the figure with a figure number.
# Consider removing white space between isolated sentences to improve readability.
* At least one numerical example
# If you’ve already defined an abbreviation (CFD), there is no need to define it again. Just use the abbreviation.
# Avoid pronouns such as “we” or “they”.
# Phrases like “under the following” need to be followed by a colon.
# Properly label the figure with a figure number and consider making them larger to improve visibility. Call the reader's attention to the figures in text by referencing the figure number.
# “As seen in the video below” is stated yet there are only images present and it may be initially unclear to the reader which figure is being referenced here.
# Avoid inserting inline citations like “[4] introduces an..” as it is a bit informal when you don’t explicitly name the subject.
# Don’t just cite the reference when discussing the problem formulation, explicitly write the model formulation and solution process using LaTex or equation visual editor.
* A section to discuss and/or illustrate the applications
# Some characters are randomly capitalized in this section.
* A conclusion section
# These variables should be defined before the conclusion section, they are out of place here. Also, please use normal text when explaining variables except for the variable symbol.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Interior-point method for NLP|Interior point method for NLP]] ==

* An introduction of the topic:
* Theory, methodology, and/or algorithmic discussions
# Primal-Dual formulation and comparison to the Barrier Method is not discussed.
# Include brief discussion about big O convergence rates.
# Need discussion about the concept of “central path” and the notion of self concordance
# Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
# Graphs and images are incorrectly formatted to the page. Consider proper alignment with respect to the text body.
# Use explicitly typed Latex equations instead of images to represent math programs and equations.
# Fix typo “optimisation”.
# Use LaTex code or equation editor to display all equations and variables (e.g., “xi ”, “μ”, etc.).
* At least one numerical example:
# There are formatting issues with figures 2,3. Please make sure to embed them within their respective sections.
* A section to discuss and/or illustrate the applications
* A conclusion section
# Minor character code typos in the conclusion.
# Also, please add more discussion in this section. Future research directions is a good start.
# There is a box "􏰐"
* References

== [[AdaGrad|Adagrad]] ==

* An introduction of the topic:
* Theory, methodology, and/or algorithmic discussions
# Include discussion on its variants (most important is AdaDelta).
# Include disadvantages of Adagrad, since this provides motivation for the discussion on the variants and improvements of Adagrad
# Include comparisons to other popular optimizers (particularly important is comparisons to regular SGD and Adam)
# Different convergence rates are possible depending on the setting where Adagrad is used, but this is not mentioned on the page currently. As such the regret bound section should be more thoroughly explained.
* At least one numerical example
# In the first sentence, “..take the following numerical example” should be followed by a colon.
# Fix typo “trayectory”.
* A section to discuss and/or illustrate the applications
# This section is too short; include specific applications in which input features are sparse and Adagrad excels.
# Add reference to the claim “Mainly, it is a good choice for deep learning models with sparse input features”.
* A conclusion section
* References

# Too few references overall, you should aggregate information from multiple sources (even if the base algorithm itself comes from a singular paper)

== [[McCormick envelopes|McCormick Envelopes]] ==

* Author list: OK but I suggest removing NetID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# First sentence is hard to read. Please consider keeping sentences below 25-30 words.
# No references provided. Please cite all sources.
# Figure 1 is provided in the middle between two sections. Please include in the introduction section.
* Theory, methodology, and/or algorithmic discussions
# References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# When using mathematical expressions and symbols, please use the equation editor. (e.g., x*y, exy + y, sin (x+y) - x2)
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# For the sample GAMS code, please place it in a code box
* A section to discuss and/or illustrate the applications
# Having a list is not enough. Please explain at least three applications in a few sentences each.
# This section should be at least a paragraph to discuss relevant applications. Each application should be explicitly linked to the page topic. A few keywords do not meet the requirement at all.
* A conclusion section:
* References
# References are not expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please follow the standard reference style - the current format is incorrect.

2021 Cornell Optimization Open Textbook Feedback

2021-12-05T19:42:38Z

Asa273: /* Lagrangian duality */

== [[Lagrangean duality|Lagrangian duality]] ==
* Author list, sections and TOC
# Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.
# Remove cornell ID from Author list
* An introduction of the topic
# This section includes sentences on constructing the dual problem and is referred to as Lagrangian relaxation (LR). This is incorrect, please fix the definition of LR.
# Definitions of LR and its relation to duality should be double checked and re-written.
# Only one reference is present in this section. Please add more relevant references by expanding this section.
# Consider merging the “introduction” and “history” sections.
# In the titles, please change the font from bold to normal to have consistent formatting in the site.
* Theory, methodology, and/or algorithmic discussions
# The Lagrangian variables associated with equality constraints h(x) are unbounded but the Lagrangian dual problem states them as non-negative. Please fix the same.
# Also to construct a dual, we do not change minimization to maximization directly. We observed such things in the examples in lecture notes due to simplification. The lagrangian dual problem would be minimize (,).
# Adding to the previous point, the Lagrangian is a lower bound on the original objective; the solution to the primal and dual or only equivalent if the duality gap is 0. You reference this in one section, but this is after your statement “Hence, solving the dual problem, which is a function of the Lagrangian multipliers (𝜆*) yields the same solution as the primal problem, which is a function of the original variables (x*). “. Please clarify the specific conditions that must hold for the solution of the dual to be equal to the primal’s.
# You refer to the “Complementary Slackness Theorem”, but don’t actually write the mathematical representation of complementary slackness. Please fix this. Also consider including the derivation of the complementary slackness condition, as it is both easy and short. Boyd is a good reference for this.
# Last step of the “process” subsection also needs updating according to the previous comments.
# The inline notations should also be typed using LaTex.
# Please use the LaTex code or equation editor for min, s.t., etc.
* At least one numerical example
# Only one dual variable is associated with each constraint. The numerical example uses two for the first and second constraint which is unnecessary. Please update it accordingly for both constraints. This particular example will only have two dual variables instead of the five dual variables used currently.
# All consecutive steps need to be updated since the dual variables would be updated.
# After substitution the nonlinear function should be further simplified. The current expression reads like a highly nonlinear function but can be easily simplified.
# Similar to the comments in the methodology section, inverting minimize to maximize is incorrect. Please update the dual objective function and domain of dual variables accordingly.
# Please use the LaTex code or equation editor for min, s.t., etc.
* A section to discuss and/or illustrate the applications
# Bullet points could be used to state the last four real-world examples that explain the physical meaning of the primal and dual problems.
# Add references for the last set of applications.
* A conclusion section
# This section contains a few typos. Please fix the same.
* References
# Some citations' hyperlinks are displaying.

== [[Disjunctive inequalities|Disjunctive Inequalities]] ==

* Author list
# Missing course section and semester
# Remove cornell ID
* An introduction of the topic
# No citations are present in this section.
# “mixed-integer programming (MIP)” should be used instead of “multiple integer programming (MIP)”. Please fix this error.
* Theory, methodology, and/or algorithmic discussions
# The abbreviation MILP is not previously defined. Please fix this issue.
# You consistently use the negative sign instead of the NOT operator for y (-y instead of ¬y).
# Some inconsistencies with the spacing of variables, constraints, etc., under the “General” section that need to be fixed.
# Typo in “This is shown below by M1, M2, y1, and y1:” where y1 needs to be changed to y2. Why use two different Big-M variables here? Elsewhere in the Wiki you only use one so this could lead to confusion with a general audience. Also if this was taken from the lecture notes then it needs to be cited.
* At least one numerical example
# Please reformulate and solve a complete numerical example rather than just reformulating a general example. Demonstrate the use of Big-M and Convex Hull formulation in an optimization problem that provides details such as individual steps in the problem solving process and final results.
# Add space between vee (V) operator and brackets in first line of Latex
# Please format variables correctly, for example, use <math>x_1</math> instead of x1.
* A section to discuss and/or illustrate the applications
# Please format the equations appropriately either by using latex code or the visual editor. These images are NOT acceptable!
* A conclusion section
# There is no conclusion presented in this section at all.
* References
# The included references have NOT been used anywhere in the Wiki. Add references for sentences that are not common knowledge and please link them appropriately with the text in Wiki. If the figures used here were not original works, you must also cite them.
# There are many papers on this topic. A simple Google (Scholar) search could provide you with sufficient references to cite.
# Many important references of this topic are missing.
# Please consider linking the references as demonstrated in the Wiki tutorial on Canvas and in this template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

==[[Stochastic programming|Stochastic Programming]] ==

* Author list: Remove cornell IDs
* An introduction of the topic
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
# This section only includes two sentences on Stochastic programming (SP), while the rest gives examples of uncertainty. Please discuss the need for SP in the presence of uncertainty. Also, discussion on robust optimization and its limitations should be removed since it is out of place.
* Theory, methodology, and/or algorithmic discussions
# Please avoid direct inline linkbacks to Wikipedia.
# The symbol “xi” in the methodology subsection should be explained.
* At least one numerical example
# Copying a numerical example "entirely" from a textbook is inappropriate. Your team should come up with a "numerical" case.
# No specific application context is needed for a numerical example.
# The inline notations (`x1`, `s1`) should also be typed using LaTex.
# Label all tables with a table number for better readability.
# Properly format the solution table with the label attached rather than the following sentence. The solution table looks different from the others, please fix this for consistency.
* A section to discuss and/or illustrate the applications;
# I suggest eliminating citing the last name of the first author (i.e. Zhou et al.)
* A conclusion section
* References
# URLs of some citations are not properly formatted (not showing the hyperlinks).

== [[Exponential transformation|Exponential Transformation]] ==

* Author list
# Missing course section
# Remove cornell ID
* An introduction of the topic
# Please expand the introduction.
# Please aim for a maximum average sentence length of ~25 words. Last sentence with 51 words is hard to read.
# Second Sentence: please change the word “they” as it could make the meaning ambiguous
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
# If you use abbreviations, please introduce them (e.g. NLP,MINLP)
* Theory, methodology, and/or algorithmic discussions
# Please explain the transformation in words along with equations
# Terms like posynomial should be described in detail.
# Please move the numerical example to the section below
# The “(eq 1)” is not needed here.
# Please expand this section.
* At least one numerical example
# In the third equation of the numerical example, it is confusing to have coefficients after numbers. Some readers may read it as an exponent.
# Last equation in this section after “further linearization” is incorrect. This equation cannot be further linearized, please fix this.
# Please explain the steps in the numerical examples in detail. The step-by-step solution should be provided.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# Missing part of text: “Proof of convexity of with positive definite test of Hessian…”
# Applications are not numerical examples. Please refer to this link for example of applications: [[Duality|https://optimization.cbe.cornell.edu/index.php?title=Duality]]
# Citation 7 is missing in current applications
# The section current applications is redundant
# Please use the LaTex code or equation editor for min, s.t., etc.
# Under current applications, do not just use a hyperlink to describe an application. Actually describe it. And properly inline citation style should be used instead of the hyperlink.
# The convexification application of MINLP can be further simplified for binary variables. Please refer to the lecture slides for more information.
* A conclusion section
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
* References
# Please consider linking the references by using this as Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Citation 7 is missing in current applications

== [[Sparse Reconstruction with Compressed Sensing|Sparse reconstruction with Compressed Sensing]] ==
This Wiki needs a significant rewrite. Please go through the comments for details.

* An introduction of the topic
# The introduction section should include information about the problem and its implications presented briefly. Please use full sentences to write this Wiki. You may use tools like Grammarly to check sentence formation and grammar.
# This section includes several typos like “sub modual”. Please fix them throughout the wiki and delete them if not required.
# Many abbreviations are used before previously defining them. Please define these abbreviations before using them in the text.
# This section is incomprehensible in its current form. Please rewrite with proper comprehension.
# Equations and math symbols need proper reformatting. The current version reads like text (along with equations) copy-pasted from a specific source.
# Try to place the figure at the top of the Wiki between the main text.
# Avoid pronouns such as “we”.
# I suggest the use of more formal abstract illustrations.
* Theory, methodology, and/or algorithmic discussions
# Equations and symbols need proper reformatting.
# Lemmas and theorems are not expected for this Wiki. Sparse reconstruction is a straightforward concept but is unnecessarily complicated here. Please refer to other Wiki examples to get an idea of what the Wiki should convey.
# All equations need to be better formatted.

* At least one numerical example
# Numerical example is missing.
# Every iteration should be clearly presented, and solved "step-by-step".
* A section to discuss and/or illustrate the applications
# Having a list is not enough. Please explain at least three applications in a few sentences each.
* A conclusion section
# Conclusion section is missing.
* References
# The current reference list is not correctly formatted. References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Portfolio optimization|Portfolio Optimization]] ==

* Author list
# Remove cornell id
* An introduction of the topic
# The introductory sentence should be rephrased. The action of minimizing the risks does not inherently maximize the gains, rather PO aims to maximize gains whilst minimizing risks.
# Amount of whitespace can be reduced by changing the orientation of Figure 1 and the sentences in this section.
# Define terms such as risk, return, portfolio, etc., when you introduce them. Assume that the reader may not know much about finance. This goes for all other sections as well.
* Theory, methodology, and/or algorithmic discussions
# A brief mention of modern portfolio theory (i.e.. Markowitz) would be appropriate in this section.
# Several grammatical errors here involving sentence structure and clarity. Some questionable semantics (e.g., “The portfolio optimization mainly assumes two directions.”) and syntax (phrases such as “.. is as follows” should be followed by a colon). Misuse of commas and missing commas in this section. Two sentences introducing E(rp) and w should be combined into one.
# Use LaTex to distinguish variables written within a sentence, such as m and n.
# Rephrase “Cut the relevant information and conditions in the portfolio optimization, as well as the final requirements into the relevant variables, constraints and linear functions of the linear programming problem.”
# An explanation of a few common constraints would be helpful, rather than just including a table.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Solving the numerical example by GAMS is inappropriate. Please provide detailed step-by-step calculation results.
# All tables need to be labeled.
# Include figure number in label for consistency.
# Fix misspelling “dolling decision variables”.
# Use LaTex for all variables, equations, and constraints here.
# Example 2 table is hard to read, so making it bigger would help.
# Remove the “Using excel as the solver” part from the sentence before the solution discussion.
# Some grammatical errors here (phrases such as “.. is as follows” should be followed by a colon).
* A section to discuss and/or illustrate the applications
# Rephrase “Portfolio optimization can be used to screen investment projects that meet investors, rationally allocate investment amounts, etc.”
# Not sure “relevant” is the correct word choice here.
# You need more specific examples with the utility of portfolio optimization, this section is quite general as is. Some more detail and focus on real-world applications in the financial industry that relate to retirement planning, financial security, economic stability, etc., would be helpful.
* A conclusion section
# Need some commas here.
# The sentence “Linear programming has been around since the 1940’s and has such a wide base of applications” is not necessary.
* References
# Please consider linking the references as demonstrated in the Wiki tutorial on Canvas and in this template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove white space between end of sentences and reference numbers.

== [[Chance-constraint method|Chance constraint method]] ==

* Author list:
* An introduction of the topic
# Please consider correcting a few grammatical errors: “pre-planned for”, “god”, “certain levels of feasibility is guaranteed in what are”, and “Performance of a system”
# In “Chance-constraint”, it is capitalized randomly throughout the introduction. Please correct.
# Please use technical language to briefly introduce chance-constrained programming. Words like “acts of god”, “cost of doing business” are not appropriate for a technical Wiki.
* Theory, methodology, and/or algorithmic discussions
# Please add a citation to the first sentence.
# Xi is an uncertainty/randomness variable. It is better to use clear language.
# Please use the mathematical editor for adding explanations in the text. Using “ x is a decision variable” is hard to read. Same for f(x) and others.
# Theory is insufficient. Please expand and explain different approaches.
# Please add pros and cons explicitly as a list.
# Explain the physical meaning for examples of chance constraints along with all the notations used.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please remove this example as it is directly from this book. The example should be purely numerical without any background.
# Please use the equation editor for min, st., etc.
# Please use the mathematical editor for adding explanations in the text. Using “ x is a decision variable” is hard to read. Same for f(x) and others.
# Please change the table format so as not to confuse the reader.
# Multiple instances of [Chart to be added] are missing.
# Example is incomplete.
# Avoid pronouns such as “we”.
* A section to discuss and/or illustrate the applications
# Please connect several grammatical and spelling errors: “real life application”, Energy creation, particularly in renewable sources, have high variabilities”, and others
# “Zhao, Xue, Cao, and Zhang”. No need to list all authors within the article. Provide a reference is sufficient. If authors must be mentioned, (Zhao et al.) should be ok.
* A conclusion section
# Uniqueness and universality earlier are not clear to me. If they are not discussed earlier in the application, it would be better not to introduce new discussions in the conclusion.
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
* References
# References seem to vary in format. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Bayesian Optimization]] ==
* Section titles should not be "bold". Please double check using source editor on the section titles.
* Contents: Subheadings for EI and the algorithm should not be bolded, Random words should not be capitalized.
* Author list: Remove cornell ID, Please check names
* Introduction
# The introduction is too general and not substantial enough. For example, simply saying BayesOpt is useful when the objective function is unknown obscures exactly HOW it is useful (namely, computational efficiency in applications where ground truth sampling is expensive). Discussion on applications should be moved to a separate section.
# Machine learning rarely includes black-box functions to be optimized. Bayesian optimization is almost never used for optimizing ML loss functions but can instead be used for hyperparameter optimization. Please update such claims in this section.
* Theory, methodology, and/or algorithmic discussions
# Captions need reformatting.
# Consider italicizing keywords rather than bolding.
# Please add a citation to the first sentence.
# Discussion on acquisition functions should include comparisons, tradeoffs, and reasons to use one over the other. Should also note that expected improvement is the most widely used in practice, and explain.
# Avoid pronouns such as “we”.
# Please write equations in the Wiki instead of attaching images for equations.
# Acquisition function figure could be made larger and clearer to improve readability.
* At least one numerical example
# Any references to functions or methods in code ‘e.g. fmin’ should be properly formatted as code-stylized text.
# Please use the equation editor for min, st., etc.
# Avoid including a figure of the code for this example and explicitly describe the steps to the modeling and solution process instead.
# Avoid pronouns such as “our” and “we”.
* A section to discuss and/or illustrate the applications
* A conclusion section
# Please do not use brackets to enclose lists.
# Some claims here should be supported by references. Please cite each source after its sentence.
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Try to avoid references to “pop” machine learning blogs where anyone can be an author. (e.g. towardsdatascience)
# All references are URLs. Please cite publications and literature.
# A simple Google Scholar search would give you many references.

Notes on grammar: Needs some work. Several instances where colons are inappropriately inserted mid sentence or in subheadings. Explanations are not terse. Several instances of switching between personal and impersonal style of writing, which is distracting.

== [[Conjugate gradient methods]] ==

* Author list: Remove cornell ID
* Introduction
# All inline notations (e.g., `x`, `A`) should be typed using LaTex.
* Theory, methodology, and/or algorithmic discussions
# All equations need to be better formatted.
# Is Gauss-Newton no longer referenced?
# Theorems listed in the first section should be accompanied with high level explanation, not just a list of the theorems themselves. The page should read like an article, with proper flow.
# Please indent equation blocks.
# Please properly format pseudocode.
* At least one numerical example
# Steps should be accompanied with explanation, or reference to the corresponding step in the pseudocode.
# Please properly format in a more organized manner, aligning equations appropriately and demarcating steps appropriately.
* A section to discuss and/or illustrate the applications
# Consider including 2 additional examples of applications
* A conclusion section
# Consider adding future research directions
* References
# Reference primary sources rather than Wikipedia
# Too few references.
# More references should be added. A simple Google Scholar search would give you many references.

== [[Geometric programming|Geometric Programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Examples of applications in this section use the same reference. Please cite their individual sources.
* Theory, methodology, and/or algorithmic discussions
# The symbol denoting the domain in the definition of a monomial is unclear. Please clarify it or fix this if it is incorrect.
# Definition of posynomial refers to section 2.1 which is missing from the Wiki (sections are not numbered in the main text).
# In the generalized posynomial subsection, bullet points do not tell us why h(x) is posynomial. Either provide reasons or simply state that h(x) is posynomial. Also explain why h3 is a generalized posynomial.
# Additional theory on the feasibility analysis could be provided in this section.
* At least one numerical example
# In the transformation example, the last two constraints could also be simplified by applying a natural logarithm on both sides. Please update them as well.
* A section to discuss and/or illustrate the applications
# The figure in this section needs to be labeled.
# The figure needs to be resized and perhaps aligned to the center.
* A conclusion section:
# Please avoid vague language such as: “This makes”.
# Please avoid opinionated statements: “one of the best ways”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Adam]] ==

* Author list
* An introduction of the topic
# Some grammatical errors here, mostly related to the need for commas in certain places (e.g., “Before Adam..”).
# Some minor errors with parts of speech throughout the section, need to revisit phrases such as “which has broader scope in future for”, etc.
# Try splitting up some of the longer sentences in this section, a couple are hard to read.
# Avoid definitive statements about Adam being the best or always better solver, as this is simply not true (the choice of the “best” optimizer is setting-dependent). Use language such as “Research has shown that Adam has demonstrated superior experimental performance over..” and then cite academic references to back this claim.
# What does adam stand for? Introduction is insufficient. Please expand.
* Theory, methodology, and/or algorithmic discussions
# Revise grammar here, noticing some missing commas and uncapitalized word after period.
# Rephrase “second one is to update the old position with the updated position”.
# Use LaTex code or equation editor to display all equations and variables in this section, and actual subscripts instead of “m_t”, etc.
# Avoid inserting inline citations after words like “According to..” or “This article..” as it is a bit informal. This could be rephrased or changed to something like “According to author,^[2] …” with author name inserted.
# Remove white space before the period in RMSP discussion.
# Please provide a pseudocode.
# Please use list the two methods here “Adam is a combination of two gradient descent methods which are explained below”
# Please expand the theory section significantly. Theoretical convergence properties should be discussed, even if briefly.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
* A section to discuss and/or illustrate the applications
# Same comment as before, consider replacing inline citations after words like “According to..”.
* A conclusion section
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Try to avoid references to blogs and use peer-reviewed academic references instead.
# Too few references.
# More references should be added. A simple Google Scholar search would give you many references.

== [[A-star algorithm|a* algorithm]] ==

* Author list: Remove cornell ID
* Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.
* An introduction of the topic:
# Weird spacing between paragraphs. Please fix this issue.
# In the titles, please change the font from bold to normal to have consistent formatting in the site.
# Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.
# There are no citations in the introduction. Please cite every source.
* Theory, methodology, and/or algorithmic discussions
# Please add the mathematical description of the algorithm.
# Reference style varies in sentences. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please fix grammatical and spelling errors as (“from current position to the goal”, “There are a lot of discussions”, etc). Also, many hyphens are missing as “non playable”.
# In algorithms, it is a standard to add high-level description (i.e. pseudocode or flowchart). Please incorporate it.
# Use LaTex code or equation editor to display all equations and variables in this section (e.g., “f(n)...”, “h(n)..”, etc.). This goes for other sections as well.
* At least one numerical example
# The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.
# Instead of writing things like “The above image..”, label each figure and use the figure number to refer to it in text.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# No references in the applications. Please cite every source
# Preferably, add at least an additional application.
* A conclusion section
# Conclusion should summarize descriptions. Please modify it to provide a summary.
# Please pay attention to the length and structure of sentences here and in the full page. First sentence is hard to read.
* References
# References seem to vary in format and are not linked correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Incorrect reference style. Please follow the example and use the template.

== [[Job shop scheduling|Job-Shop Scheduling Problem]] ==

* An introduction of the topic
# The current introduction to the jobshop scheduling problem has only two sentences in addition to the parameter description. Introduction typically contains information about the problem, its importance in the real-world, and some information about the solution techniques and their types to solve the problem. Please add some information that covers the above.
* Theory, methodology, and/or algorithmic discussions
# It is unclear whether the assumptions stated in this section are required to apply the following solution techniques. Please clarify the same. Also use complete sentences to state them.
# The branch and bounds method described in this section only discusses the solution technique for problems with one machines. However, branch and bound is a general technique that can be applied to any MILP problems with varying scales. Please update the “methods” section to be as general as possible.
# Since this Wiki focuses on jobshop scheduling, at least two methods are expected. Branch and bound is a general MILP technique, so, it is recommended to add a tailored technique that can only solve specific jobshop scheduling problems. Solving the numerical example with this technique is not necessary.
# Reference to the branch and bound technique described in this section is a “youtube” video. Please add references in literature that describe this method in detail. The method used in this video is highly tailored for a single machine application. This is also an incorrect way to cite a reference. Please keep this section as general as possible.
# Use LaTex code or equation editor to display all equations and variables in this section and all other sections as well.
# Check grammar in this section. For example, phrases like “are as follows” need to be followed by a colon and not a period.
# Consider rewriting the assumptions as a list in this section.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# The example used in this section is exactly the same as the one in the youtube video. Please use a modification of this example or choose another example/method to demonstrate the solution technique.
# The figure in this section is not numbered when all others are. Relabel this figure for consistency and its number to refer to it in-text.
* A section to discuss and/or illustrate the applications
# This section should only focus on real-world applications of the jobshop scheduling problem. But currently, this section includes additional information on solution techniques/complexity that is appropriate for the Introduction section. Please discuss the applications of the problem in this section.
* A conclusion section
# The meaning of “Operations applications” is unclear. Please explain or update if necessary.
# The current conclusion section does not properly summarize the problem. Please refer to other Wiki examples for an idea to update the section accordingly.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please reference media sources like reference 5 appropriately.
# A simple Google Scholar search would give you many "formal" references.

== [[Optimization in game theory]] ==

* Author list: remove cornell IDs.
* An introduction of the topic
# References are not linked. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
* Theory, methodology, and/or algorithmic discussions
# Why only a subsection on "Nash Equilibrium" is included in "Theory" section? Please re-format.
# Please edit references.
# Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm.
# Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.
* At least one numerical example
# Please organize the last part in a more readable format. Questions may be in bold and numbered, answers are more direct, etc.
# Remember to cite all images and tables.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# Very good, link the reference and cite all sources.
* A conclusion section
# Please add more summarizing especially from theory sentences and avoid long sentences.
* References
# Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Reference primary sources rather than Wikipedia
# Incorrect reference style. Please correct.

== [[Trust-region methods]] ==

* Author list:
# Remove cornell IDs. Author is also spelled incorrectly.
# Add the course section.
* An introduction of the topic
# References are not linked. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Use LaTex code or equation editor to display all equations and variables (e.g., “xk”, “f`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “we”. This goes for all other sections as well.
* Theory, methodology, and/or algorithmic discussions
# Organization of ideas in this section needs work.
# You have not defined explicitly why the Cauchy point is important to compute beyond a vague allusion to performance improvements, which is also wrong (it is useful because of its guarantees for convergence, not performance) It is also misspelled.
# Each approach should have accompanying explanation and motivation for why it is being discussed. It is not enough to outline the algorithm.
# Please make sure symbols are properly subscripted and superscripted (e.g. “pk” should be “p_k”
# Please format the algorithm in proper algorithmic pseudocode format.
# Little to no discussion on global convergence guarantees
# Please include discussion about the advantages and disadvantages of the algorithm
# Fix typo “couchy point”.
* At least one numerical example
# Any code functions (uminfunc) should have proper text formatting.
# The graph needs a better caption explaining how the axes are labeled and what data points are being shown.
# Please increase the quality of the figure. It is hard to see the red line.
# Add citation to “The Rosenbrock function is a non-convex function, introduced by Howard H. Rosenbrock in 1960, which is often used as a performance test problem for optimization algorithms.”
* A section to discuss and/or illustrate the applications
# The content in this section as it is currently does NOT describe applications, but rather different approaches within the trust region methodology. Please provide specific applications (e.g. TRPO in reinforcement learning).
* A conclusion section
# Please add more summary, future research directions for example is a good start.
* References
# Incorrect reference style.
# Please consider having the references as this Wiki template, <nowiki>https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization</nowiki>
# More references should be added. A simple Google Scholar search would give you many references.

*There are numerous misspellings, grammatical errors, and incorrect claims. Please fix these.

== [[Momentum]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Apart from an explanation on momentum, it is necessary to briefly point out the limitations of SGD and why momentum could help with these limitations. Please update it accordingly.
# Remove bold on “Momentum”.
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
* Theory, methodology, and/or algorithmic discussions
# Equation formatting is very poor and should be formalized.
# It is important to use technical language for this Wiki. Although a layman’s explanation is appreciated, it would be better to skip using words like “zig zagging”. Try to explain all concepts in a technical language with few simplifications but NOT vice versa.
# The definition of the update rule for SGD with momentum looks incorrect, specifically the first expression. Please fix it and also explain all the parameters used.
# Use LaTex code or equation editor to display all equations and variables (e.g., “W”, “V`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “you”.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please try to label the plots that explains what each line color means.
* A section to discuss and/or illustrate the applications
# Please use correct terminology like “optimizing non-convex functions” and not “training non-convex models”.
# Adam, Adadelta, and RMSprop are variants of SGD that already use momentum. Please double check the writing and update if necessary.
* A conclusion section
# Please refrain from using words like “zig zag” effects.
* References
# Almost all references used are URLs. Please try to add journal/conference articles or books for references, instead of directly citing the URLs.

== [[Stochastic dynamic programming|Stochastic Dynamic programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Discussion on applications should be moved to a separate section.
* Theory, methodology, and/or algorithmic discussions
# Remove the grey box background of equations.
* At least one numerical example
* A section to discuss and/or illustrate the applications
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Outer-approximation (OA)|Outer-approximation]] ==

* An introduction of the topic
# See formatting guideline below
# Avoid opinionated statements such as “MINLP problems are usually the hardest to solve”.
# Rearrange the text such that the MINLP formulation is in the theory section and keep the introduction in words only.
* Theory, methodology, and/or algorithmic discussions
# Consider left aligning equations and optimization problem formulations by the “=”. See [[Stochastic programming|https://optimization.cbe.cornell.edu/index.php?title=Stochastic_programming]] for an example
# The sentence “The Outer-Approximation (OA) algorithm was first proposed by Duran and and Grossmann in 1986 to solve MINLP problems.” needs a reference.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# “Minimize” and “subject to” should be “min” and “s.t.” in MathType
* A section to discuss and/or illustrate the applications
# Does not explicitly point out why OA is applicable (and/or preferred) in these applications, rather than other MINLP approaches (show that the problem formulations are amenable to a solution approach through OA)
# The sentence “... an active research area and there exists a vast number of applications in fields such as engineering, computational chemistry, and finance.” needs references.
# Place GAMS code in a single code box or remove it.
# Consider reformatting to make steps more readable. Inserting spaces and breaking down steps would help.
* A conclusion section
# Too short. Consider discussion on future research direction and discussion on uncertainty
# Please review abbreviations throughout the page. Why is MINLP redefined here? “Outer-Approximation is a well known efficient approach for solving convex mixed-integer nonlinear programs (MINLP)”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove "Template:Reflist"

== [[Unit commitment problem]] ==

* Author list
* An introduction of the topic
# Please expand the introduction and avoid discussions of examples or specific applications in this section.
# The sentence “Nonlinear, Non-convex programming optimization problem.” doesn’t make sense by itself and Non-convex shouldn’t be capitalized.
* Theory, methodology, and/or algorithmic discussions
# Figure/image format should be revised to better display the content.
# Uppercase characters are used randomly (e.g., “non-convex transmission Constraints”) . Please follow correct language conventions for sentence structure.
# Avoid inserting inline citations after words like “written in matrix form as equation [3]..” or “presented in [3]...” as it is a bit informal when you don’t explicitly name the subject. Also these two sentences are grammatically incorrect and appear to be missing an ending period and comma, respectively.
# Don’t say “written in matrix form as equation..” and just cite the reference, actually write out the equation.
# Properly label the figure in this section with a figure number and improve visibility by making it larger.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Label the figures in this section properly with figure numbers.
# Fix typo “while minimize” to “while minimizing”.
# Avoid pronouns such as “we”.
# Use the equation editor when typing equations.
* A section to discuss and/or illustrate the applications:
# I suggest changing the order of the subtitles here. For example, Single-Period Unit Commitment.
* A conclusion section
* References

== [[Frank-Wolfe]] ==

* Author list:
* An introduction of the topic
# I suggest highlighting disadvantages along with advantages.
* Theory, methodology, and/or algorithmic discussions
# “[n x 1] matrix” please use the equation editor to express mathematical descriptions and symbols (p,b, etc)
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please show at least a few iterations. Even for smaller examples if needed. Report the final solution.
# Please use the LaTex code or equation editor for min and include s.t., etc.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps. For your example, please explicitly state that the derivative is taken etc.
* A section to discuss and/or illustrate the applications:
* A conclusion section
# Same as the introduction. Pros and cons should be evaluated together!
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Line search methods|Line Search Method]] ==

* Author list
* An introduction of the topic
# Expand the introduction and avoid discussion on some of the specific steps in the solution process.
# Provide references here.
* Theory, methodology, and/or algorithmic discussions
# The phrase “are as follows” in the steepest descent method discussion needs to be followed by a colon.
# Rephrase “has a nice convergence theory” and cite a reference for this claim.
# Avoid pronouns such as “we”.
# Add citation after “.. proposed by Phillip Wolfe in 1969.”
# Figure 1 is between two sections. Please fix this issue.
* At least one numerical example:
# Add some space between iterations or subsection break
* A section to discuss and/or illustrate the applications:
# Too few references in this section.
# Last paragraph makes some claims without references.
* A conclusion section
* References
# References should be properly formatted. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Piecewise linear approximation|Piecewise Linear Approximation]]==

* Author list
* An introduction of the topic
# The content of this section is good, but there are some issues with sentence clarity and some other grammatical errors. Please revisit this section and make changes accordingly.
* Theory, methodology, and/or algorithmic discussions
# Fix typo “to force the x’ values become associated with”.
* At least one numerical example
* A section to discuss and/or illustrate the applications
# Please aim for a maximum average sentence length of ~25 words. Some of these longer sentences are hard to read.
* A conclusion section
# Expand the conclusion section to be longer than one sentence. The conclusion section to include a brief summary of what was discussed above, an emphasis on it’s significance, and a brief discussion of future extensions and research direction if applicable.
* References
# Include hyperlinks to sources when possible.

== [[Mathematical programming with equilibrium constraints|Mathematical Programming with Equilibrium constraints]] ==

* An introduction of the topic
# This section includes several terms like variational inequalities, constraint qualifications that were not discussed in the class. Please add a sentence to explain them before using them.
* Theory, methodology, and/or algorithmic discussions
# The meaning of parameter vector x is unclear. Please add more information or update if necessary.
# Equations and symbols in the PIPA subsection are not formatted correctly. Please use the same formatting for all equations, so they read as mathematical equations and not text. This goes for all other sections as well.
# Use equations instead of images to represent math programs and equations in the Implicit Descent and SQP subsection.
# Apart from the steps for each solution technique, please also add a few sentences that describe each method.
* At least one numerical example
# Please define the terms like NCP, MP before abbreviating them. Also try not to unnecessarily abbreviate simple terms.
# Equations should be typed by LaTex. Images for equations are unacceptable.
# GAMS code is strongly discouraged. Please solve the problem "step-by-step".
# The selected numerical example is fine but is directly solved with the MPEC solver in GAMS. Try to solve it manually like the homework/in-class problems step by step using the steps described in the previous section by choosing any of the methods.
# Avoid using figures in the equations (subject to etc)
* A section to discuss and/or illustrate the applications
# Add references to “power management, highway pricing, chemical process engineering, and traffic planning.”
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Wing shape optimization|Wing shape Optimization]] ==

* Author list: Remove cornell ID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# The introduction is missing several references (e.g., “software packages like computational fluid dynamics..”, sentences containing things that aren’t common knowledge, performance claims, etc.)
# Avoid discussion involving finer details of subject methods in this section.
# In the titles, please change the font from bold to normal to have consistent formatting in the site. Same applies to box of content!
* Theory, methodology, and/or algorithmic discussions
# Properly cite the CFD package, don’t just include a link.
# Properly label the figure with a figure number.
# Consider removing white space between isolated sentences to improve readability.
* At least one numerical example
# If you’ve already defined an abbreviation (CFD), there is no need to define it again. Just use the abbreviation.
# Avoid pronouns such as “we” or “they”.
# Phrases like “under the following” need to be followed by a colon.
# Properly label the figure with a figure number and consider making them larger to improve visibility. Call the reader's attention to the figures in text by referencing the figure number.
# “As seen in the video below” is stated yet there are only images present and it may be initially unclear to the reader which figure is being referenced here.
# Avoid inserting inline citations like “[4] introduces an..” as it is a bit informal when you don’t explicitly name the subject.
# Don’t just cite the reference when discussing the problem formulation, explicitly write the model formulation and solution process using LaTex or equation visual editor.
* A section to discuss and/or illustrate the applications
# Some characters are randomly capitalized in this section.
* A conclusion section
# These variables should be defined before the conclusion section, they are out of place here. Also, please use normal text when explaining variables except for the variable symbol.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Interior-point method for NLP|Interior point method for NLP]] ==

* An introduction of the topic:
* Theory, methodology, and/or algorithmic discussions
# Primal-Dual formulation and comparison to the Barrier Method is not discussed.
# Include brief discussion about big O convergence rates.
# Need discussion about the concept of “central path” and the notion of self concordance
# Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
# Graphs and images are incorrectly formatted to the page. Consider proper alignment with respect to the text body.
# Use explicitly typed Latex equations instead of images to represent math programs and equations.
# Fix typo “optimisation”.
# Use LaTex code or equation editor to display all equations and variables (e.g., “xi ”, “μ”, etc.).
* At least one numerical example:
# There are formatting issues with figures 2,3. Please make sure to embed them within their respective sections.
* A section to discuss and/or illustrate the applications
* A conclusion section
# Minor character code typos in the conclusion.
# Also, please add more discussion in this section. Future research directions is a good start.
# There is a box "􏰐"
* References

== [[AdaGrad|Adagrad]] ==

* An introduction of the topic:
* Theory, methodology, and/or algorithmic discussions
# Include discussion on its variants (most important is AdaDelta).
# Include disadvantages of Adagrad, since this provides motivation for the discussion on the variants and improvements of Adagrad
# Include comparisons to other popular optimizers (particularly important is comparisons to regular SGD and Adam)
# Different convergence rates are possible depending on the setting where Adagrad is used, but this is not mentioned on the page currently. As such the regret bound section should be more thoroughly explained.
* At least one numerical example
# In the first sentence, “..take the following numerical example” should be followed by a colon.
# Fix typo “trayectory”.
* A section to discuss and/or illustrate the applications
# This section is too short; include specific applications in which input features are sparse and Adagrad excels.
# Add reference to the claim “Mainly, it is a good choice for deep learning models with sparse input features”.
* A conclusion section
* References

# Too few references overall, you should aggregate information from multiple sources (even if the base algorithm itself comes from a singular paper)

== [[McCormick envelopes|McCormick Envelopes]] ==

* Author list: OK but I suggest removing NetID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# First sentence is hard to read. Please consider keeping sentences below 25-30 words.
# No references provided. Please cite all sources.
# Figure 1 is provided in the middle between two sections. Please include in the introduction section.
* Theory, methodology, and/or algorithmic discussions
# References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# When using mathematical expressions and symbols, please use the equation editor. (e.g., x*y, exy + y, sin (x+y) - x2)
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# For the sample GAMS code, please place it in a code box
* A section to discuss and/or illustrate the applications
# Having a list is not enough. Please explain at least three applications in a few sentences each.
# This section should be at least a paragraph to discuss relevant applications. Each application should be explicitly linked to the page topic. A few keywords do not meet the requirement at all.
* A conclusion section:
* References
# References are not expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please follow the standard reference style - the current format is incorrect.

2021 Cornell Optimization Open Textbook Feedback

2021-12-05T04:05:43Z

Asa273: /* Disjunctive Inequalities */

== [[Lagrangean duality|Lagrangian duality]] ==
* Author list, sections and TOC
# Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.
# Remove cornell ID from Author list
* An introduction of the topic
# This section includes sentences on constructing the dual problem and is referred to as Lagrangian relaxation (LR). This is incorrect, please fix the definition of LR.
# Definitions of LR and its relation to duality should be double checked and re-written.
# Only one reference is present in this section. Please add more relevant references by expanding this section.
# Consider merging the “introduction” and “history” sections.
# In the titles, please change the font from bold to normal to have consistent formatting in the site.
* Theory, methodology, and/or algorithmic discussions
# The Lagrangian variables associated with equality constraints h(x) are unbounded but the Lagrangian dual problem states them as non-negative. Please fix the same.
# Also to construct a dual, we do not change minimization to maximization directly. We observed such things in the examples in lecture notes due to simplification. The lagrangian dual problem would be minimize (,).
# Adding to the previous point, the Lagrangian is a lower bound on the original objective; the solution to the primal and dual or only equivalent if the duality gap is 0. You reference this in one section, but this is after your statement “Hence, solving the dual problem, which is a function of the Lagrangian multipliers (𝜆*) yields the same solution as the primal problem, which is a function of the original variables (x*). “. Please clarify the specific conditions that must hold for the solution of the dual to be equal to the primal’s.
# You refer to the “Complementary Slackness Theorem”, but don’t actually write the mathematical representation of complementary slackness. Please fix this. Also consider including the derivation of the complementary slackness condition, as it is both easy and short. Boyd is a good reference for this.
# Last step of the “process” subsection also needs updating according to the previous comments.
# The inline notations should also be typed using LaTex.
# Please use the LaTex code or equation editor for min, s.t., etc.
* At least one numerical example
# Only one dual variable is associated with each constraint. The numerical example uses two for the first and second constraint which is unnecessary. Please update it accordingly for both constraints. This particular example will only have two dual variables instead of the five dual variables used currently.
# All consecutive steps need to be updated since the dual variables would be updated.
# After substitution the nonlinear function should be further simplified. The current expression reads like a highly nonlinear function but can be easily simplified.
# Similar to the comments in the methodology section, inverting minimize to maximize is incorrect. Please update the dual objective function accordingly.
# Please use the LaTex code or equation editor for min, s.t., etc.
* A section to discuss and/or illustrate the applications
# Bullet points could be used to state the last four real-world examples that explain the physical meaning of the primal and dual problems.
# Add references for the last set of applications.
* A conclusion section
# This section contains a few typos. Please fix the same.
* References
# Some citations' hyperlinks are displaying.

== [[Disjunctive inequalities|Disjunctive Inequalities]] ==

* Author list
# Missing course section and semester
# Remove cornell ID
* An introduction of the topic
# No citations are present in this section.
# “mixed-integer programming (MIP)” should be used instead of “multiple integer programming (MIP)”. Please fix this error.
* Theory, methodology, and/or algorithmic discussions
# The abbreviation MILP is not previously defined. Please fix this issue.
# You consistently use the negative sign instead of the NOT operator for y (-y instead of ¬y).
# Some inconsistencies with the spacing of variables, constraints, etc., under the “General” section that need to be fixed.
# Typo in “This is shown below by M1, M2, y1, and y1:” where y1 needs to be changed to y2. Why use two different Big-M variables here? Elsewhere in the Wiki you only use one so this could lead to confusion with a general audience. Also if this was taken from the lecture notes then it needs to be cited.
* At least one numerical example
# Please reformulate and solve a complete numerical example rather than just reformulating a general example. Demonstrate the use of Big-M and Convex Hull formulation in an optimization problem that provides details such as individual steps in the problem solving process and final results.
# Add space between vee (V) operator and brackets in first line of Latex
# Please format variables correctly, for example, use <math>x_1</math> instead of x1.
* A section to discuss and/or illustrate the applications
# Please format the equations appropriately either by using latex code or the visual editor. These images are NOT acceptable!
* A conclusion section
# There is no conclusion presented in this section at all.
* References
# The included references have NOT been used anywhere in the Wiki. Add references for sentences that are not common knowledge and please link them appropriately with the text in Wiki. If the figures used here were not original works, you must also cite them.
# There are many papers on this topic. A simple Google (Scholar) search could provide you with sufficient references to cite.
# Many important references of this topic are missing.
# Please consider linking the references as demonstrated in the Wiki tutorial on Canvas and in this template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

==[[Stochastic programming|Stochastic Programming]] ==

* Author list: Remove cornell IDs
* An introduction of the topic
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
# This section only includes two sentences on Stochastic programming (SP), while the rest gives examples of uncertainty. Please discuss the need for SP in the presence of uncertainty. Also, discussion on robust optimization and its limitations should be removed since it is out of place.
* Theory, methodology, and/or algorithmic discussions
# Please avoid direct inline linkbacks to Wikipedia.
# The symbol “xi” in the methodology subsection should be explained.
* At least one numerical example
# Copying a numerical example "entirely" from a textbook is inappropriate. Your team should come up with a "numerical" case.
# No specific application context is needed for a numerical example.
# The inline notations (`x1`, `s1`) should also be typed using LaTex.
# Label all tables with a table number for better readability.
# Properly format the solution table with the label attached rather than the following sentence. The solution table looks different from the others, please fix this for consistency.
* A section to discuss and/or illustrate the applications;
# I suggest eliminating citing the last name of the first author (i.e. Zhou et al.)
* A conclusion section
* References
# URLs of some citations are not properly formatted (not showing the hyperlinks).

== [[Exponential transformation|Exponential Transformation]] ==

* Author list
# Missing course section
# Remove cornell ID
* An introduction of the topic
# Please expand the introduction.
# Please aim for a maximum average sentence length of ~25 words. Last sentence with 51 words is hard to read.
# Second Sentence: please change the word “they” as it could make the meaning ambiguous
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
# If you use abbreviations, please introduce them (e.g. NLP,MINLP)
* Theory, methodology, and/or algorithmic discussions
# Please explain the transformation in words along with equations
# Terms like posynomial should be described in detail.
# Please move the numerical example to the section below
# The “(eq 1)” is not needed here.
# Please expand this section.
* At least one numerical example
# In the third equation of the numerical example, it is confusing to have coefficients after numbers. Some readers may read it as an exponent.
# Last equation in this section after “further linearization” is incorrect. This equation cannot be further linearized, please fix this.
# Please explain the steps in the numerical examples in detail. The step-by-step solution should be provided.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# Missing part of text: “Proof of convexity of with positive definite test of Hessian…”
# Applications are not numerical examples. Please refer to this link for example of applications: [[Duality|https://optimization.cbe.cornell.edu/index.php?title=Duality]]
# Citation 7 is missing in current applications
# The section current applications is redundant
# Please use the LaTex code or equation editor for min, s.t., etc.
# Under current applications, do not just use a hyperlink to describe an application. Actually describe it. And properly inline citation style should be used instead of the hyperlink.
# The convexification application of MINLP can be further simplified for binary variables. Please refer to the lecture slides for more information.
* A conclusion section
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
* References
# Please consider linking the references by using this as Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Citation 7 is missing in current applications

== [[Sparse Reconstruction with Compressed Sensing|Sparse reconstruction with Compressed Sensing]] ==
This Wiki needs a significant rewrite. Please go through the comments for details.

* An introduction of the topic
# The introduction section should include information about the problem and its implications presented briefly. Please use full sentences to write this Wiki. You may use tools like Grammarly to check sentence formation and grammar.
# This section includes several typos like “sub modual”. Please fix them throughout the wiki and delete them if not required.
# Many abbreviations are used before previously defining them. Please define these abbreviations before using them in the text.
# This section is incomprehensible in its current form. Please rewrite with proper comprehension.
# Equations and math symbols need proper reformatting. The current version reads like text (along with equations) copy-pasted from a specific source.
# Try to place the figure at the top of the Wiki between the main text.
# Avoid pronouns such as “we”.
# I suggest the use of more formal abstract illustrations.
* Theory, methodology, and/or algorithmic discussions
# Equations and symbols need proper reformatting.
# Lemmas and theorems are not expected for this Wiki. Sparse reconstruction is a straightforward concept but is unnecessarily complicated here. Please refer to other Wiki examples to get an idea of what the Wiki should convey.
# All equations need to be better formatted.

* At least one numerical example
# Numerical example is missing.
# Every iteration should be clearly presented, and solved "step-by-step".
* A section to discuss and/or illustrate the applications
# Having a list is not enough. Please explain at least three applications in a few sentences each.
* A conclusion section
# Conclusion section is missing.
* References
# The current reference list is not correctly formatted. References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Portfolio optimization|Portfolio Optimization]] ==

* Author list
# Remove cornell id
* An introduction of the topic
# The introductory sentence should be rephrased. The action of minimizing the risks does not inherently maximize the gains, rather PO aims to maximize gains whilst minimizing risks.
# Amount of whitespace can be reduced by changing the orientation of Figure 1 and the sentences in this section.
# Define terms such as risk, return, portfolio, etc., when you introduce them. Assume that the reader may not know much about finance. This goes for all other sections as well.
* Theory, methodology, and/or algorithmic discussions
# A brief mention of modern portfolio theory (i.e.. Markowitz) would be appropriate in this section.
# Several grammatical errors here involving sentence structure and clarity. Some questionable semantics (e.g., “The portfolio optimization mainly assumes two directions.”) and syntax (phrases such as “.. is as follows” should be followed by a colon). Misuse of commas and missing commas in this section. Two sentences introducing E(rp) and w should be combined into one.
# Use LaTex to distinguish variables written within a sentence, such as m and n.
# Rephrase “Cut the relevant information and conditions in the portfolio optimization, as well as the final requirements into the relevant variables, constraints and linear functions of the linear programming problem.”
# An explanation of a few common constraints would be helpful, rather than just including a table.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Solving the numerical example by GAMS is inappropriate. Please provide detailed step-by-step calculation results.
# All tables need to be labeled.
# Include figure number in label for consistency.
# Fix misspelling “dolling decision variables”.
# Use LaTex for all variables, equations, and constraints here.
# Example 2 table is hard to read, so making it bigger would help.
# Remove the “Using excel as the solver” part from the sentence before the solution discussion.
# Some grammatical errors here (phrases such as “.. is as follows” should be followed by a colon).
* A section to discuss and/or illustrate the applications
# Rephrase “Portfolio optimization can be used to screen investment projects that meet investors, rationally allocate investment amounts, etc.”
# Not sure “relevant” is the correct word choice here.
# You need more specific examples with the utility of portfolio optimization, this section is quite general as is. Some more detail and focus on real-world applications in the financial industry that relate to retirement planning, financial security, economic stability, etc., would be helpful.
* A conclusion section
# Need some commas here.
# The sentence “Linear programming has been around since the 1940’s and has such a wide base of applications” is not necessary.
* References
# Please consider linking the references as demonstrated in the Wiki tutorial on Canvas and in this template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove white space between end of sentences and reference numbers.

== [[Chance-constraint method|Chance constraint method]] ==

* Author list:
* An introduction of the topic
# Please consider correcting a few grammatical errors: “pre-planned for”, “god”, “certain levels of feasibility is guaranteed in what are”, and “Performance of a system”
# In “Chance-constraint”, it is capitalized randomly throughout the introduction. Please correct.
# Please use technical language to briefly introduce chance-constrained programming. Words like “acts of god”, “cost of doing business” are not appropriate for a technical Wiki.
* Theory, methodology, and/or algorithmic discussions
# Please add a citation to the first sentence.
# Xi is an uncertainty/randomness variable. It is better to use clear language.
# Please use the mathematical editor for adding explanations in the text. Using “ x is a decision variable” is hard to read. Same for f(x) and others.
# Theory is insufficient. Please expand and explain different approaches.
# Please add pros and cons explicitly as a list.
# Explain the physical meaning for examples of chance constraints along with all the notations used.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please remove this example as it is directly from this book. The example should be purely numerical without any background.
# Please use the equation editor for min, st., etc.
# Please use the mathematical editor for adding explanations in the text. Using “ x is a decision variable” is hard to read. Same for f(x) and others.
# Please change the table format so as not to confuse the reader.
# Multiple instances of [Chart to be added] are missing.
# Example is incomplete.
# Avoid pronouns such as “we”.
* A section to discuss and/or illustrate the applications
# Please connect several grammatical and spelling errors: “real life application”, Energy creation, particularly in renewable sources, have high variabilities”, and others
# “Zhao, Xue, Cao, and Zhang”. No need to list all authors within the article. Provide a reference is sufficient. If authors must be mentioned, (Zhao et al.) should be ok.
* A conclusion section
# Uniqueness and universality earlier are not clear to me. If they are not discussed earlier in the application, it would be better not to introduce new discussions in the conclusion.
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
* References
# References seem to vary in format. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Bayesian Optimization]] ==
* Section titles should not be "bold". Please double check using source editor on the section titles.
* Contents: Subheadings for EI and the algorithm should not be bolded, Random words should not be capitalized.
* Author list: Remove cornell ID, Please check names
* Introduction
# The introduction is too general and not substantial enough. For example, simply saying BayesOpt is useful when the objective function is unknown obscures exactly HOW it is useful (namely, computational efficiency in applications where ground truth sampling is expensive). Discussion on applications should be moved to a separate section.
# Machine learning rarely includes black-box functions to be optimized. Bayesian optimization is almost never used for optimizing ML loss functions but can instead be used for hyperparameter optimization. Please update such claims in this section.
* Theory, methodology, and/or algorithmic discussions
# Captions need reformatting.
# Consider italicizing keywords rather than bolding.
# Please add a citation to the first sentence.
# Discussion on acquisition functions should include comparisons, tradeoffs, and reasons to use one over the other. Should also note that expected improvement is the most widely used in practice, and explain.
# Avoid pronouns such as “we”.
# Please write equations in the Wiki instead of attaching images for equations.
# Acquisition function figure could be made larger and clearer to improve readability.
* At least one numerical example
# Any references to functions or methods in code ‘e.g. fmin’ should be properly formatted as code-stylized text.
# Please use the equation editor for min, st., etc.
# Avoid including a figure of the code for this example and explicitly describe the steps to the modeling and solution process instead.
# Avoid pronouns such as “our” and “we”.
* A section to discuss and/or illustrate the applications
* A conclusion section
# Please do not use brackets to enclose lists.
# Some claims here should be supported by references. Please cite each source after its sentence.
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Try to avoid references to “pop” machine learning blogs where anyone can be an author. (e.g. towardsdatascience)
# All references are URLs. Please cite publications and literature.
# A simple Google Scholar search would give you many references.

Notes on grammar: Needs some work. Several instances where colons are inappropriately inserted mid sentence or in subheadings. Explanations are not terse. Several instances of switching between personal and impersonal style of writing, which is distracting.

== [[Conjugate gradient methods]] ==

* Author list: Remove cornell ID
* Introduction
# All inline notations (e.g., `x`, `A`) should be typed using LaTex.
* Theory, methodology, and/or algorithmic discussions
# All equations need to be better formatted.
# Is Gauss-Newton no longer referenced?
# Theorems listed in the first section should be accompanied with high level explanation, not just a list of the theorems themselves. The page should read like an article, with proper flow.
# Please indent equation blocks.
# Please properly format pseudocode.
* At least one numerical example
# Steps should be accompanied with explanation, or reference to the corresponding step in the pseudocode.
# Please properly format in a more organized manner, aligning equations appropriately and demarcating steps appropriately.
* A section to discuss and/or illustrate the applications
# Consider including 2 additional examples of applications
* A conclusion section
# Consider adding future research directions
* References
# Reference primary sources rather than Wikipedia
# Too few references.
# More references should be added. A simple Google Scholar search would give you many references.

== [[Geometric programming|Geometric Programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Examples of applications in this section use the same reference. Please cite their individual sources.
* Theory, methodology, and/or algorithmic discussions
# The symbol denoting the domain in the definition of a monomial is unclear. Please clarify it or fix this if it is incorrect.
# Definition of posynomial refers to section 2.1 which is missing from the Wiki (sections are not numbered in the main text).
# In the generalized posynomial subsection, bullet points do not tell us why h(x) is posynomial. Either provide reasons or simply state that h(x) is posynomial. Also explain why h3 is a generalized posynomial.
# Additional theory on the feasibility analysis could be provided in this section.
* At least one numerical example
# In the transformation example, the last two constraints could also be simplified by applying a natural logarithm on both sides. Please update them as well.
* A section to discuss and/or illustrate the applications
# The figure in this section needs to be labeled.
# The figure needs to be resized and perhaps aligned to the center.
* A conclusion section:
# Please avoid vague language such as: “This makes”.
# Please avoid opinionated statements: “one of the best ways”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Adam]] ==

* Author list
* An introduction of the topic
# Some grammatical errors here, mostly related to the need for commas in certain places (e.g., “Before Adam..”).
# Some minor errors with parts of speech throughout the section, need to revisit phrases such as “which has broader scope in future for”, etc.
# Try splitting up some of the longer sentences in this section, a couple are hard to read.
# Avoid definitive statements about Adam being the best or always better solver, as this is simply not true (the choice of the “best” optimizer is setting-dependent). Use language such as “Research has shown that Adam has demonstrated superior experimental performance over..” and then cite academic references to back this claim.
# What does adam stand for? Introduction is insufficient. Please expand.
* Theory, methodology, and/or algorithmic discussions
# Revise grammar here, noticing some missing commas and uncapitalized word after period.
# Rephrase “second one is to update the old position with the updated position”.
# Use LaTex code or equation editor to display all equations and variables in this section, and actual subscripts instead of “m_t”, etc.
# Avoid inserting inline citations after words like “According to..” or “This article..” as it is a bit informal. This could be rephrased or changed to something like “According to author,^[2] …” with author name inserted.
# Remove white space before the period in RMSP discussion.
# Please provide a pseudocode.
# Please use list the two methods here “Adam is a combination of two gradient descent methods which are explained below”
# Please expand the theory section significantly. Theoretical convergence properties should be discussed, even if briefly.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
* A section to discuss and/or illustrate the applications
# Same comment as before, consider replacing inline citations after words like “According to..”.
* A conclusion section
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Try to avoid references to blogs and use peer-reviewed academic references instead.
# Too few references.
# More references should be added. A simple Google Scholar search would give you many references.

== [[A-star algorithm|a* algorithm]] ==

* Author list: Remove cornell ID
* Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.
* An introduction of the topic:
# Weird spacing between paragraphs. Please fix this issue.
# In the titles, please change the font from bold to normal to have consistent formatting in the site.
# Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.
# There are no citations in the introduction. Please cite every source.
* Theory, methodology, and/or algorithmic discussions
# Please add the mathematical description of the algorithm.
# Reference style varies in sentences. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please fix grammatical and spelling errors as (“from current position to the goal”, “There are a lot of discussions”, etc). Also, many hyphens are missing as “non playable”.
# In algorithms, it is a standard to add high-level description (i.e. pseudocode or flowchart). Please incorporate it.
# Use LaTex code or equation editor to display all equations and variables in this section (e.g., “f(n)...”, “h(n)..”, etc.). This goes for other sections as well.
* At least one numerical example
# The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.
# Instead of writing things like “The above image..”, label each figure and use the figure number to refer to it in text.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# No references in the applications. Please cite every source
# Preferably, add at least an additional application.
* A conclusion section
# Conclusion should summarize descriptions. Please modify it to provide a summary.
# Please pay attention to the length and structure of sentences here and in the full page. First sentence is hard to read.
* References
# References seem to vary in format and are not linked correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Incorrect reference style. Please follow the example and use the template.

== [[Job shop scheduling|Job-Shop Scheduling Problem]] ==

* An introduction of the topic
# The current introduction to the jobshop scheduling problem has only two sentences in addition to the parameter description. Introduction typically contains information about the problem, its importance in the real-world, and some information about the solution techniques and their types to solve the problem. Please add some information that covers the above.
* Theory, methodology, and/or algorithmic discussions
# It is unclear whether the assumptions stated in this section are required to apply the following solution techniques. Please clarify the same. Also use complete sentences to state them.
# The branch and bounds method described in this section only discusses the solution technique for problems with one machines. However, branch and bound is a general technique that can be applied to any MILP problems with varying scales. Please update the “methods” section to be as general as possible.
# Since this Wiki focuses on jobshop scheduling, at least two methods are expected. Branch and bound is a general MILP technique, so, it is recommended to add a tailored technique that can only solve specific jobshop scheduling problems. Solving the numerical example with this technique is not necessary.
# Reference to the branch and bound technique described in this section is a “youtube” video. Please add references in literature that describe this method in detail. The method used in this video is highly tailored for a single machine application. This is also an incorrect way to cite a reference. Please keep this section as general as possible.
# Use LaTex code or equation editor to display all equations and variables in this section and all other sections as well.
# Check grammar in this section. For example, phrases like “are as follows” need to be followed by a colon and not a period.
# Consider rewriting the assumptions as a list in this section.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# The example used in this section is exactly the same as the one in the youtube video. Please use a modification of this example or choose another example/method to demonstrate the solution technique.
# The figure in this section is not numbered when all others are. Relabel this figure for consistency and its number to refer to it in-text.
* A section to discuss and/or illustrate the applications
# This section should only focus on real-world applications of the jobshop scheduling problem. But currently, this section includes additional information on solution techniques/complexity that is appropriate for the Introduction section. Please discuss the applications of the problem in this section.
* A conclusion section
# The meaning of “Operations applications” is unclear. Please explain or update if necessary.
# The current conclusion section does not properly summarize the problem. Please refer to other Wiki examples for an idea to update the section accordingly.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please reference media sources like reference 5 appropriately.
# A simple Google Scholar search would give you many "formal" references.

== [[Optimization in game theory]] ==

* Author list: remove cornell IDs.
* An introduction of the topic
# References are not linked. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
* Theory, methodology, and/or algorithmic discussions
# Why only a subsection on "Nash Equilibrium" is included in "Theory" section? Please re-format.
# Please edit references.
# Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm.
# Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.
* At least one numerical example
# Please organize the last part in a more readable format. Questions may be in bold and numbered, answers are more direct, etc.
# Remember to cite all images and tables.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# Very good, link the reference and cite all sources.
* A conclusion section
# Please add more summarizing especially from theory sentences and avoid long sentences.
* References
# Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Reference primary sources rather than Wikipedia
# Incorrect reference style. Please correct.

== [[Trust-region methods]] ==

* Author list:
# Remove cornell IDs. Author is also spelled incorrectly.
# Add the course section.
* An introduction of the topic
# References are not linked. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Use LaTex code or equation editor to display all equations and variables (e.g., “xk”, “f`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “we”. This goes for all other sections as well.
* Theory, methodology, and/or algorithmic discussions
# Organization of ideas in this section needs work.
# You have not defined explicitly why the Cauchy point is important to compute beyond a vague allusion to performance improvements, which is also wrong (it is useful because of its guarantees for convergence, not performance) It is also misspelled.
# Each approach should have accompanying explanation and motivation for why it is being discussed. It is not enough to outline the algorithm.
# Please make sure symbols are properly subscripted and superscripted (e.g. “pk” should be “p_k”
# Please format the algorithm in proper algorithmic pseudocode format.
# Little to no discussion on global convergence guarantees
# Please include discussion about the advantages and disadvantages of the algorithm
# Fix typo “couchy point”.
* At least one numerical example
# Any code functions (uminfunc) should have proper text formatting.
# The graph needs a better caption explaining how the axes are labeled and what data points are being shown.
# Please increase the quality of the figure. It is hard to see the red line.
# Add citation to “The Rosenbrock function is a non-convex function, introduced by Howard H. Rosenbrock in 1960, which is often used as a performance test problem for optimization algorithms.”
* A section to discuss and/or illustrate the applications
# The content in this section as it is currently does NOT describe applications, but rather different approaches within the trust region methodology. Please provide specific applications (e.g. TRPO in reinforcement learning).
* A conclusion section
# Please add more summary, future research directions for example is a good start.
* References
# Incorrect reference style.
# Please consider having the references as this Wiki template, <nowiki>https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization</nowiki>
# More references should be added. A simple Google Scholar search would give you many references.

*There are numerous misspellings, grammatical errors, and incorrect claims. Please fix these.

== [[Momentum]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Apart from an explanation on momentum, it is necessary to briefly point out the limitations of SGD and why momentum could help with these limitations. Please update it accordingly.
# Remove bold on “Momentum”.
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
* Theory, methodology, and/or algorithmic discussions
# Equation formatting is very poor and should be formalized.
# It is important to use technical language for this Wiki. Although a layman’s explanation is appreciated, it would be better to skip using words like “zig zagging”. Try to explain all concepts in a technical language with few simplifications but NOT vice versa.
# The definition of the update rule for SGD with momentum looks incorrect, specifically the first expression. Please fix it and also explain all the parameters used.
# Use LaTex code or equation editor to display all equations and variables (e.g., “W”, “V`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “you”.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please try to label the plots that explains what each line color means.
* A section to discuss and/or illustrate the applications
# Please use correct terminology like “optimizing non-convex functions” and not “training non-convex models”.
# Adam, Adadelta, and RMSprop are variants of SGD that already use momentum. Please double check the writing and update if necessary.
* A conclusion section
# Please refrain from using words like “zig zag” effects.
* References
# Almost all references used are URLs. Please try to add journal/conference articles or books for references, instead of directly citing the URLs.

== [[Stochastic dynamic programming|Stochastic Dynamic programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Discussion on applications should be moved to a separate section.
* Theory, methodology, and/or algorithmic discussions
# Remove the grey box background of equations.
* At least one numerical example
* A section to discuss and/or illustrate the applications
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Outer-approximation (OA)|Outer-approximation]] ==

* An introduction of the topic
# See formatting guideline below
# Avoid opinionated statements such as “MINLP problems are usually the hardest to solve”.
# Rearrange the text such that the MINLP formulation is in the theory section and keep the introduction in words only.
* Theory, methodology, and/or algorithmic discussions
# Consider left aligning equations and optimization problem formulations by the “=”. See [[Stochastic programming|https://optimization.cbe.cornell.edu/index.php?title=Stochastic_programming]] for an example
# The sentence “The Outer-Approximation (OA) algorithm was first proposed by Duran and and Grossmann in 1986 to solve MINLP problems.” needs a reference.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# “Minimize” and “subject to” should be “min” and “s.t.” in MathType
* A section to discuss and/or illustrate the applications
# Does not explicitly point out why OA is applicable (and/or preferred) in these applications, rather than other MINLP approaches (show that the problem formulations are amenable to a solution approach through OA)
# The sentence “... an active research area and there exists a vast number of applications in fields such as engineering, computational chemistry, and finance.” needs references.
# Place GAMS code in a single code box or remove it.
# Consider reformatting to make steps more readable. Inserting spaces and breaking down steps would help.
* A conclusion section
# Too short. Consider discussion on future research direction and discussion on uncertainty
# Please review abbreviations throughout the page. Why is MINLP redefined here? “Outer-Approximation is a well known efficient approach for solving convex mixed-integer nonlinear programs (MINLP)”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove "Template:Reflist"

== [[Unit commitment problem]] ==

* Author list
* An introduction of the topic
# Please expand the introduction and avoid discussions of examples or specific applications in this section.
# The sentence “Nonlinear, Non-convex programming optimization problem.” doesn’t make sense by itself and Non-convex shouldn’t be capitalized.
* Theory, methodology, and/or algorithmic discussions
# Figure/image format should be revised to better display the content.
# Uppercase characters are used randomly (e.g., “non-convex transmission Constraints”) . Please follow correct language conventions for sentence structure.
# Avoid inserting inline citations after words like “written in matrix form as equation [3]..” or “presented in [3]...” as it is a bit informal when you don’t explicitly name the subject. Also these two sentences are grammatically incorrect and appear to be missing an ending period and comma, respectively.
# Don’t say “written in matrix form as equation..” and just cite the reference, actually write out the equation.
# Properly label the figure in this section with a figure number and improve visibility by making it larger.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Label the figures in this section properly with figure numbers.
# Fix typo “while minimize” to “while minimizing”.
# Avoid pronouns such as “we”.
# Use the equation editor when typing equations.
* A section to discuss and/or illustrate the applications:
# I suggest changing the order of the subtitles here. For example, Single-Period Unit Commitment.
* A conclusion section
* References

== [[Frank-Wolfe]] ==

* Author list:
* An introduction of the topic
# I suggest highlighting disadvantages along with advantages.
* Theory, methodology, and/or algorithmic discussions
# “[n x 1] matrix” please use the equation editor to express mathematical descriptions and symbols (p,b, etc)
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please show at least a few iterations. Even for smaller examples if needed. Report the final solution.
# Please use the LaTex code or equation editor for min and include s.t., etc.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps. For your example, please explicitly state that the derivative is taken etc.
* A section to discuss and/or illustrate the applications:
* A conclusion section
# Same as the introduction. Pros and cons should be evaluated together!
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Line search methods|Line Search Method]] ==

* Author list
* An introduction of the topic
# Expand the introduction and avoid discussion on some of the specific steps in the solution process.
# Provide references here.
* Theory, methodology, and/or algorithmic discussions
# The phrase “are as follows” in the steepest descent method discussion needs to be followed by a colon.
# Rephrase “has a nice convergence theory” and cite a reference for this claim.
# Avoid pronouns such as “we”.
# Add citation after “.. proposed by Phillip Wolfe in 1969.”
# Figure 1 is between two sections. Please fix this issue.
* At least one numerical example:
# Add some space between iterations or subsection break
* A section to discuss and/or illustrate the applications:
# Too few references in this section.
# Last paragraph makes some claims without references.
* A conclusion section
* References
# References should be properly formatted. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Piecewise linear approximation|Piecewise Linear Approximation]]==

* Author list
* An introduction of the topic
# The content of this section is good, but there are some issues with sentence clarity and some other grammatical errors. Please revisit this section and make changes accordingly.
* Theory, methodology, and/or algorithmic discussions
# Fix typo “to force the x’ values become associated with”.
* At least one numerical example
* A section to discuss and/or illustrate the applications
# Please aim for a maximum average sentence length of ~25 words. Some of these longer sentences are hard to read.
* A conclusion section
# Expand the conclusion section to be longer than one sentence. The conclusion section to include a brief summary of what was discussed above, an emphasis on it’s significance, and a brief discussion of future extensions and research direction if applicable.
* References
# Include hyperlinks to sources when possible.

== [[Mathematical programming with equilibrium constraints|Mathematical Programming with Equilibrium constraints]] ==

* An introduction of the topic
# This section includes several terms like variational inequalities, constraint qualifications that were not discussed in the class. Please add a sentence to explain them before using them.
* Theory, methodology, and/or algorithmic discussions
# The meaning of parameter vector x is unclear. Please add more information or update if necessary.
# Equations and symbols in the PIPA subsection are not formatted correctly. Please use the same formatting for all equations, so they read as mathematical equations and not text. This goes for all other sections as well.
# Use equations instead of images to represent math programs and equations in the Implicit Descent and SQP subsection.
# Apart from the steps for each solution technique, please also add a few sentences that describe each method.
* At least one numerical example
# Please define the terms like NCP, MP before abbreviating them. Also try not to unnecessarily abbreviate simple terms.
# Equations should be typed by LaTex. Images for equations are unacceptable.
# GAMS code is strongly discouraged. Please solve the problem "step-by-step".
# The selected numerical example is fine but is directly solved with the MPEC solver in GAMS. Try to solve it manually like the homework/in-class problems step by step using the steps described in the previous section by choosing any of the methods.
# Avoid using figures in the equations (subject to etc)
* A section to discuss and/or illustrate the applications
# Add references to “power management, highway pricing, chemical process engineering, and traffic planning.”
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Wing shape optimization|Wing shape Optimization]] ==

* Author list: Remove cornell ID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# The introduction is missing several references (e.g., “software packages like computational fluid dynamics..”, sentences containing things that aren’t common knowledge, performance claims, etc.)
# Avoid discussion involving finer details of subject methods in this section.
# In the titles, please change the font from bold to normal to have consistent formatting in the site. Same applies to box of content!
* Theory, methodology, and/or algorithmic discussions
# Properly cite the CFD package, don’t just include a link.
# Properly label the figure with a figure number.
# Consider removing white space between isolated sentences to improve readability.
* At least one numerical example
# If you’ve already defined an abbreviation (CFD), there is no need to define it again. Just use the abbreviation.
# Avoid pronouns such as “we” or “they”.
# Phrases like “under the following” need to be followed by a colon.
# Properly label the figure with a figure number and consider making them larger to improve visibility. Call the reader's attention to the figures in text by referencing the figure number.
# “As seen in the video below” is stated yet there are only images present and it may be initially unclear to the reader which figure is being referenced here.
# Avoid inserting inline citations like “[4] introduces an..” as it is a bit informal when you don’t explicitly name the subject.
# Don’t just cite the reference when discussing the problem formulation, explicitly write the model formulation and solution process using LaTex or equation visual editor.
* A section to discuss and/or illustrate the applications
# Some characters are randomly capitalized in this section.
* A conclusion section
# These variables should be defined before the conclusion section, they are out of place here. Also, please use normal text when explaining variables except for the variable symbol.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Interior-point method for NLP|Interior point method for NLP]] ==

* An introduction of the topic:
* Theory, methodology, and/or algorithmic discussions
# Primal-Dual formulation and comparison to the Barrier Method is not discussed.
# Include brief discussion about big O convergence rates.
# Need discussion about the concept of “central path” and the notion of self concordance
# Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
# Graphs and images are incorrectly formatted to the page. Consider proper alignment with respect to the text body.
# Use explicitly typed Latex equations instead of images to represent math programs and equations.
# Fix typo “optimisation”.
# Use LaTex code or equation editor to display all equations and variables (e.g., “xi ”, “μ”, etc.).
* At least one numerical example:
# There are formatting issues with figures 2,3. Please make sure to embed them within their respective sections.
* A section to discuss and/or illustrate the applications
* A conclusion section
# Minor character code typos in the conclusion.
# Also, please add more discussion in this section. Future research directions is a good start.
# There is a box "􏰐"
* References

== [[AdaGrad|Adagrad]] ==

* An introduction of the topic:
* Theory, methodology, and/or algorithmic discussions
# Include discussion on its variants (most important is AdaDelta).
# Include disadvantages of Adagrad, since this provides motivation for the discussion on the variants and improvements of Adagrad
# Include comparisons to other popular optimizers (particularly important is comparisons to regular SGD and Adam)
# Different convergence rates are possible depending on the setting where Adagrad is used, but this is not mentioned on the page currently. As such the regret bound section should be more thoroughly explained.
* At least one numerical example
# In the first sentence, “..take the following numerical example” should be followed by a colon.
# Fix typo “trayectory”.
* A section to discuss and/or illustrate the applications
# This section is too short; include specific applications in which input features are sparse and Adagrad excels.
# Add reference to the claim “Mainly, it is a good choice for deep learning models with sparse input features”.
* A conclusion section
* References

# Too few references overall, you should aggregate information from multiple sources (even if the base algorithm itself comes from a singular paper)

== [[McCormick envelopes|McCormick Envelopes]] ==

* Author list: OK but I suggest removing NetID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# First sentence is hard to read. Please consider keeping sentences below 25-30 words.
# No references provided. Please cite all sources.
# Figure 1 is provided in the middle between two sections. Please include in the introduction section.
* Theory, methodology, and/or algorithmic discussions
# References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# When using mathematical expressions and symbols, please use the equation editor. (e.g., x*y, exy + y, sin (x+y) - x2)
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# For the sample GAMS code, please place it in a code box
* A section to discuss and/or illustrate the applications
# Having a list is not enough. Please explain at least three applications in a few sentences each.
# This section should be at least a paragraph to discuss relevant applications. Each application should be explicitly linked to the page topic. A few keywords do not meet the requirement at all.
* A conclusion section:
* References
# References are not expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please follow the standard reference style - the current format is incorrect.

2021 Cornell Optimization Open Textbook Feedback

2021-12-05T01:09:08Z

Asa273: /* McCormick Envelopes */

== [[Lagrangean duality|Lagrangian duality]] ==
* Author list, sections and TOC
# Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.
# Remove cornell ID from Author list
* An introduction of the topic
# This section includes sentences on constructing the dual problem and is referred to as Lagrangian relaxation (LR). This is incorrect, please fix the definition of LR.
# Definitions of LR and its relation to duality should be double checked and re-written.
# Only one reference is present in this section. Please add more relevant references by expanding this section.
# Consider merging the “introduction” and “history” sections.
# In the titles, please change the font from bold to normal to have consistent formatting in the site.
* Theory, methodology, and/or algorithmic discussions
# The Lagrangian variables associated with equality constraints h(x) are unbounded but the Lagrangian dual problem states them as non-negative. Please fix the same.
# Also to construct a dual, we do not change minimization to maximization directly. We observed such things in the examples in lecture notes due to simplification. The lagrangian dual problem would be minimize (,).
# Adding to the previous point, the Lagrangian is a lower bound on the original objective; the solution to the primal and dual or only equivalent if the duality gap is 0. You reference this in one section, but this is after your statement “Hence, solving the dual problem, which is a function of the Lagrangian multipliers (𝜆*) yields the same solution as the primal problem, which is a function of the original variables (x*). “. Please clarify the specific conditions that must hold for the solution of the dual to be equal to the primal’s.
# You refer to the “Complementary Slackness Theorem”, but don’t actually write the mathematical representation of complementary slackness. Please fix this. Also consider including the derivation of the complementary slackness condition, as it is both easy and short. Boyd is a good reference for this.
# Last step of the “process” subsection also needs updating according to the previous comments.
# The inline notations should also be typed using LaTex.
# Please use the LaTex code or equation editor for min, s.t., etc.
* At least one numerical example
# Only one dual variable is associated with each constraint. The numerical example uses two for the first and second constraint which is unnecessary. Please update it accordingly for both constraints. This particular example will only have two dual variables instead of the five dual variables used currently.
# All consecutive steps need to be updated since the dual variables would be updated.
# After substitution the nonlinear function should be further simplified. The current expression reads like a highly nonlinear function but can be easily simplified.
# Similar to the comments in the methodology section, inverting minimize to maximize is incorrect. Please update the dual objective function accordingly.
# Please use the LaTex code or equation editor for min, s.t., etc.
* A section to discuss and/or illustrate the applications
# Bullet points could be used to state the last four real-world examples that explain the physical meaning of the primal and dual problems.
# Add references for the last set of applications.
* A conclusion section
# This section contains a few typos. Please fix the same.
* References
# Some citations' hyperlinks are displaying.

== [[Disjunctive inequalities|Disjunctive Inequalities]] ==

* Author list
# Missing course section and semester
# Remove cornell ID
* An introduction of the topic
# No citations are present in this section.
# “mixed-integer programming (MIP)” should be used instead of “multiple integer programming (MIP)”. Please fix this error.
* Theory, methodology, and/or algorithmic discussions
# The abbreviation MILP is not previously defined. Please fix this issue.
# You consistently use the negative sign instead of the NOT operator for y (-y instead of ¬y).
# Some inconsistencies with the spacing of variables, constraints, etc., under the “General” section that need to be fixed.
# Typo in “This is shown below by M1, M2, y1, and y1:” where y1 needs to be changed to y2. Why use two different Big-M variables here? Elsewhere in the Wiki you only use one so this could lead to confusion with a general audience. Also if this was taken from the lecture notes then it needs to be cited.
* At least one numerical example
# Please reformulate and solve a complete numerical example rather than just reformulating a general example. Demonstrate the use of Big-M and Convex Hull formulation in an optimization problem that provides details such as individual steps in the problem solving process and final results.
# Add space between vee (V) operator and brackets in first line of Latex
# Please format variables correctly, for example, use x1 instead of x1.
* A section to discuss and/or illustrate the applications
# Please format the equations appropriately either by using latex code or the visual editor. These images are NOT acceptable!
* A conclusion section
# There is no conclusion presented in this section at all.
* References
# The included references have NOT been used anywhere in the Wiki. Add references for sentences that are not common knowledge and please link them appropriately with the text in Wiki. If the figures used here were not original works, you must also cite them.
# There are many papers on this topic. A simple Google (Scholar) search could provide you with sufficient references to cite.
# Many important references of this topic are missing.
# Please consider linking the references as demonstrated in the Wiki tutorial on Canvas and in this template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

==[[Stochastic programming|Stochastic Programming]] ==

* Author list: Remove cornell IDs
* An introduction of the topic
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
# This section only includes two sentences on Stochastic programming (SP), while the rest gives examples of uncertainty. Please discuss the need for SP in the presence of uncertainty. Also, discussion on robust optimization and its limitations should be removed since it is out of place.
* Theory, methodology, and/or algorithmic discussions
# Please avoid direct inline linkbacks to Wikipedia.
# The symbol “xi” in the methodology subsection should be explained.
* At least one numerical example
# Copying a numerical example "entirely" from a textbook is inappropriate. Your team should come up with a "numerical" case.
# No specific application context is needed for a numerical example.
# The inline notations (`x1`, `s1`) should also be typed using LaTex.
# Label all tables with a table number for better readability.
# Properly format the solution table with the label attached rather than the following sentence. The solution table looks different from the others, please fix this for consistency.
* A section to discuss and/or illustrate the applications;
# I suggest eliminating citing the last name of the first author (i.e. Zhou et al.)
* A conclusion section
* References
# URLs of some citations are not properly formatted (not showing the hyperlinks).

== [[Exponential transformation|Exponential Transformation]] ==

* Author list
# Missing course section
# Remove cornell ID
* An introduction of the topic
# Please expand the introduction.
# Please aim for a maximum average sentence length of ~25 words. Last sentence with 51 words is hard to read.
# Second Sentence: please change the word “they” as it could make the meaning ambiguous
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
# If you use abbreviations, please introduce them (e.g. NLP,MINLP)
* Theory, methodology, and/or algorithmic discussions
# Please explain the transformation in words along with equations
# Terms like posynomial should be described in detail.
# Please move the numerical example to the section below
# The “(eq 1)” is not needed here.
# Please expand this section.
* At least one numerical example
# In the third equation of the numerical example, it is confusing to have coefficients after numbers. Some readers may read it as an exponent.
# Last equation in this section after “further linearization” is incorrect. This equation cannot be further linearized, please fix this.
* A section to discuss and/or illustrate the applications
# Missing part of text: “Proof of convexity of with positive definite test of Hessian…”
# Applications are not numerical examples. Please refer to this link for example of applications: [[Duality|https://optimization.cbe.cornell.edu/index.php?title=Duality]]
# Citation 7 is missing in current applications
# The section current applications is redundant
# Please use the LaTex code or equation editor for min, s.t., etc.
# Under current applications, do not just use a hyperlink to describe an application. Actually describe it. And properly inline citation style should be used instead of the hyperlink.
# The convexification application of MINLP can be further simplified for binary variables. Please refer to the lecture slides for more information.
* A conclusion section
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
* References
# Please consider linking the references by using this as Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Citation 7 is missing in current applications

== [[Sparse Reconstruction with Compressed Sensing|Sparse reconstruction with Compressed Sensing]] ==
This Wiki needs a significant rewrite. Please go through the comments for details.

* An introduction of the topic
# The introduction section should include information about the problem and its implications presented briefly. Please use full sentences to write this Wiki. You may use tools like Grammarly to check sentence formation and grammar.
# This section includes several typos like “sub modual”. Please fix them throughout the wiki and delete them if not required.
# Many abbreviations are used before previously defining them. Please define these abbreviations before using them in the text.
# This section is incomprehensible in its current form. Please rewrite with proper comprehension.
# Equations and math symbols need proper reformatting. The current version reads like text (along with equations) copy-pasted from a specific source.
# Try to place the figure at the top of the Wiki between the main text.
# Avoid pronouns such as “we”.
# I suggest the use of more formal abstract illustrations.
* Theory, methodology, and/or algorithmic discussions
# Equations and symbols need proper reformatting.
# Lemmas and theorems are not expected for this Wiki. Sparse reconstruction is a straightforward concept but is unnecessarily complicated here. Please refer to other Wiki examples to get an idea of what the Wiki should convey.
* At least one numerical example
# Numerical example is missing.
* A section to discuss and/or illustrate the applications
# Having a list is not enough. Please explain at least three applications in a few sentences each.
* A conclusion section
# Conclusion section is missing.
* References
# The current reference list is not correctly formatted. References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Portfolio optimization|Portfolio Optimization]] ==

* Author list
# Remove cornell id
* An introduction of the topic
# The introductory sentence should be rephrased. The action of minimizing the risks does not inherently maximize the gains, rather PO aims to maximize gains whilst minimizing risks.
# Amount of whitespace can be reduced by changing the orientation of Figure 1 and the sentences in this section.
# Define terms such as risk, return, portfolio, etc., when you introduce them. Assume that the reader may not know much about finance. This goes for all other sections as well.
* Theory, methodology, and/or algorithmic discussions
# A brief mention of modern portfolio theory (i.e.. Markowitz) would be appropriate in this section.
# Several grammatical errors here involving sentence structure and clarity. Some questionable semantics (e.g., “The portfolio optimization mainly assumes two directions.”) and syntax (phrases such as “.. is as follows” should be followed by a colon). Misuse of commas and missing commas in this section. Two sentences introducing E(rp) and w should be combined into one.
# Use LaTex to distinguish variables written within a sentence, such as m and n.
# Rephrase “Cut the relevant information and conditions in the portfolio optimization, as well as the final requirements into the relevant variables, constraints and linear functions of the linear programming problem.”
# An explanation of a few common constraints would be helpful, rather than just including a table.
* At least one numerical example
# All tables need to be labeled.
# Include figure number in label for consistency.
# Fix misspelling “dolling decision variables”.
# Use LaTex for all variables, equations, and constraints here.
# Example 2 table is hard to read, so making it bigger would help.
# Remove the “Using excel as the solver” part from the sentence before the solution discussion.
# Some grammatical errors here (phrases such as “.. is as follows” should be followed by a colon).
* A section to discuss and/or illustrate the applications
# Rephrase “Portfolio optimization can be used to screen investment projects that meet investors, rationally allocate investment amounts, etc.”
# Not sure “relevant” is the correct word choice here.
# You need more specific examples with the utility of portfolio optimization, this section is quite general as is. Some more detail and focus on real-world applications in the financial industry that relate to retirement planning, financial security, economic stability, etc., would be helpful.
* A conclusion section
# Need some commas here.
# The sentence “Linear programming has been around since the 1940’s and has such a wide base of applications” is not necessary.
* References
# Please consider linking the references as demonstrated in the Wiki tutorial on Canvas and in this template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove white space between end of sentences and reference numbers.

== [[Chance-constraint method|Chance constraint method]] ==

* Author list:
* An introduction of the topic
# Please consider correcting a few grammatical errors: “pre-planned for”, “god”, “certain levels of feasibility is guaranteed in what are”, and “Performance of a system”
# In “Chance-constraint”, it is capitalized randomly throughout the introduction. Please correct.
# Please use technical language to briefly introduce chance-constrained programming. Words like “acts of god”, “cost of doing business” are not appropriate for a technical Wiki.
* Theory, methodology, and/or algorithmic discussions
# Please add a citation to the first sentence.
# Xi is an uncertainty/randomness variable. It is better to use clear language.
# Please use the mathematical editor for adding explanations in the text. Using “ x is a decision variable” is hard to read. Same for f(x) and others.
# Theory is insufficient. Please expand and explain different approaches.
# Please add pros and cons explicitly as a list.
# Explain the physical meaning for examples of chance constraints along with all the notations used.
* At least one numerical example
# Please use the equation editor for min, st., etc.
# Please use the mathematical editor for adding explanations in the text. Using “ x is a decision variable” is hard to read. Same for f(x) and others.
# Please change the table format so as not to confuse the reader.
# Multiple instances of [Chart to be added] are missing.
# Example is incomplete.
# Avoid pronouns such as “we”.
* A section to discuss and/or illustrate the applications
# Please connect several grammatical and spelling errors: “real life application”, Energy creation, particularly in renewable sources, have high variabilities”, and others
# “Zhao, Xue, Cao, and Zhang”. No need to list all authors within the article. Provide a reference is sufficient. If authors must be mentioned, (Zhao et al.) should be ok.
* A conclusion section
# Uniqueness and universality earlier are not clear to me. If they are not discussed earlier in the application, it would be better not to introduce new discussions in the conclusion.
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
* References
# References seem to vary in format. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Bayesian Optimization | Bayesian Optimization]] ==

* Contents: Subheadings for EI and the algorithm should not be bolded, Random words should not be capitalized.
* Author list: Remove cornell ID, Please check names
* Introduction
# The introduction is too general and not substantial enough. For example, simply saying BayesOpt is useful when the objective function is unknown obscures exactly HOW it is useful (namely, computational efficiency in applications where ground truth sampling is expensive). Discussion on applications should be moved to a separate section.
# Machine learning rarely includes black-box functions to be optimized. Bayesian optimization is almost never used for optimizing ML loss functions but can instead be used for hyperparameter optimization. Please update such claims in this section.
* Theory, methodology, and/or algorithmic discussions
# Captions need reformatting.
# Consider italicizing keywords rather than bolding.
# Please add a citation to the first sentence.
# Discussion on acquisition functions should include comparisons, tradeoffs, and reasons to use one over the other. Should also note that expected improvement is the most widely used in practice, and explain.
# Avoid pronouns such as “we”.
# Please write equations in the Wiki instead of attaching images for equations.
# Acquisition function figure could be made larger and clearer to improve readability.
* At least one numerical example
# Any references to functions or methods in code ‘e.g. fmin’ should be properly formatted as code-stylized text.
# Please use the equation editor for min, st., etc.
# Avoid including a figure of the code for this example and explicitly describe the steps to the modeling and solution process instead.
# Avoid pronouns such as “our” and “we”.
* A section to discuss and/or illustrate the applications
* A conclusion section
# Please do not use brackets to enclose lists.
# Some claims here should be supported by references. Please cite each source after its sentence.
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Try to avoid references to “pop” machine learning blogs where anyone can be an author. (e.g. towardsdatascience)

Notes on grammar: Needs some work. Several instances where colons are inappropriately inserted mid sentence or in subheadings. Explanations are not terse. Several instances of switching between personal and impersonal style of writing, which is distracting.

== [[Conjugate gradient methods|Conjugate gradient methods ]] ==

* Author list: Remove cornell ID
* Introduction
# All inline notations (e.g., `x`, `A`) should be typed using LaTex.
* Theory, methodology, and/or algorithmic discussions
# Is Gauss-Newton no longer referenced?
# Theorems listed in the first section should be accompanied with high level explanation, not just a list of the theorems themselves. The page should read like an article, with proper flow.
# Please indent equation blocks.
# Please properly format pseudocode.
* At least one numerical example
# Steps should be accompanied with explanation, or reference to the corresponding step in the pseudocode.
* A section to discuss and/or illustrate the applications
# Consider including 2 additional examples of applications
* A conclusion section
# Consider adding future research directions
* References
# Reference primary sources rather than Wikipedia
# Too few references.

== [[Geometric programming|Geometric Programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Examples of applications in this section use the same reference. Please cite their individual sources.
* Theory, methodology, and/or algorithmic discussions
# The symbol denoting the domain in the definition of a monomial is unclear. Please clarify it or fix this if it is incorrect.
# Definition of posynomial refers to section 2.1 which is missing from the Wiki (sections are not numbered in the main text).
# In the generalized posynomial subsection, bullet points do not tell us why h(x) is posynomial. Either provide reasons or simply state that h(x) is posynomial. Also explain why h3 is a generalized posynomial.
# Additional theory on the feasibility analysis could be provided in this section.
* At least one numerical example
# In the transformation example, the last two constraints could also be simplified by applying a natural logarithm on both sides. Please update them as well.
* A section to discuss and/or illustrate the applications
# The figure in this section needs to be labeled.
# The figure needs to be resized and perhaps aligned to the center.
* A conclusion section:
# Please avoid vague language such as: “This makes”.
# Please avoid opinionated statements: “one of the best ways”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Adam|Adam]] ==

* Author list
* An introduction of the topic
# Some grammatical errors here, mostly related to the need for commas in certain places (e.g., “Before Adam..”).
# Some minor errors with parts of speech throughout the section, need to revisit phrases such as “which has broader scope in future for”, etc.
# Try splitting up some of the longer sentences in this section, a couple are hard to read.
# Avoid definitive statements about Adam being the best or always better solver, as this is simply not true (the choice of the “best” optimizer is setting-dependent). Use language such as “Research has shown that Adam has demonstrated superior experimental performance over..” and then cite academic references to back this claim.
# What does adam stand for? Introduction is insufficient. Please expand.
* Theory, methodology, and/or algorithmic discussions
# Revise grammar here, noticing some missing commas and uncapitalized word after period.
# Rephrase “second one is to update the old position with the updated position”.
# Use LaTex code or equation editor to display all equations and variables in this section, and actual subscripts instead of “m_t”, etc.
# Avoid inserting inline citations after words like “According to..” or “This article..” as it is a bit informal. This could be rephrased or changed to something like “According to author,^[2] …” with author name inserted.
# Remove white space before the period in RMSP discussion.
# Please provide a pseudocode.
# Please use list the two methods here “Adam is a combination of two gradient descent methods which are explained below”
# Please expand the theory section significantly. Theoretical convergence properties should be discussed, even if briefly.
* At least one numerical example
* A section to discuss and/or illustrate the applications
# Same comment as before, consider replacing inline citations after words like “According to..”.
* A conclusion section
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Try to avoid references to blogs and use peer-reviewed academic references instead.
# Too few references.

== [[A-star algorithm|a* algorithm]] ==

* Author list:
# Remove cornell ID
* An introduction of the topic:
# In the titles, please change the font from bold to normal to have consistent formatting in the site.
# Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.
# There are no citations in the introduction. Please cite every source.
* Theory, methodology, and/or algorithmic discussions
# Please add the mathematical description of the algorithm.
# Reference style varies in sentences. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please fix grammatical and spelling errors as (“from current position to the goal”, “There are a lot of discussions”, etc). Also, many hyphens are missing as “non playable”.
# In algorithms, it is a standard to add high-level description (i.e. pseudocode or flowchart). Please incorporate it.
# Use LaTex code or equation editor to display all equations and variables in this section (e.g., “f(n)...”, “h(n)..”, etc.). This goes for other sections as well.
* At least one numerical example
# The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.
# Instead of writing things like “The above image..”, label each figure and use the figure number to refer to it in text.
* A section to discuss and/or illustrate the applications
# No references in the applications. Please cite every source
# Preferably, add at least an additional application.
* A conclusion section
# Conclusion should summarize descriptions. Please modify it to provide a summary.
# Please pay attention to the length and structure of sentences here and in the full page. First sentence is hard to read.
* References
# References seem to vary in format and are not linked correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Job shop scheduling|Job-Shop Scheduling Problem]] ==

* An introduction of the topic
# The current introduction to the jobshop scheduling problem has only two sentences in addition to the parameter description. Introduction typically contains information about the problem, its importance in the real-world, and some information about the solution techniques and their types to solve the problem. Please add some information that covers the above.
* Theory, methodology, and/or algorithmic discussions
# It is unclear whether the assumptions stated in this section are required to apply the following solution techniques. Please clarify the same. Also use complete sentences to state them.
# The branch and bounds method described in this section only discusses the solution technique for problems with one machines. However, branch and bound is a general technique that can be applied to any MILP problems with varying scales. Please update the “methods” section to be as general as possible.
# Since this Wiki focuses on jobshop scheduling, at least two methods are expected. Branch and bound is a general MILP technique, so, it is recommended to add a tailored technique that can only solve specific jobshop scheduling problems. Solving the numerical example with this technique is not necessary.
# Reference to the branch and bound technique described in this section is a “youtube” video. Please add references in literature that describe this method in detail. The method used in this video is highly tailored for a single machine application. This is also an incorrect way to cite a reference. Please keep this section as general as possible.
# Use LaTex code or equation editor to display all equations and variables in this section and all other sections as well.
# Check grammar in this section. For example, phrases like “are as follows” need to be followed by a colon and not a period.
# Consider rewriting the assumptions as a list in this section.
* At least one numerical example
# The example used in this section is exactly the same as the one in the youtube video. Please use a modification of this example or choose another example/method to demonstrate the solution technique.
# The figure in this section is not numbered when all others are. Relabel this figure for consistency and its number to refer to it in-text.
* A section to discuss and/or illustrate the applications
# This section should only focus on real-world applications of the jobshop scheduling problem. But currently, this section includes additional information on solution techniques/complexity that is appropriate for the Introduction section. Please discuss the applications of the problem in this section.
* A conclusion section
# The meaning of “Operations applications” is unclear. Please explain or update if necessary.
# The current conclusion section does not properly summarize the problem. Please refer to other Wiki examples for an idea to update the section accordingly.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please reference media sources like reference 5 appropriately.

== [[Optimization in game theory|Optimization in game theory]] ==

* Author list: remove cornell IDs.
* An introduction of the topic
# References are not linked. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
* Theory, methodology, and/or algorithmic discussions
# Please edit references.
# Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm.
# Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.
* At least one numerical example
# Please organize the last part in a more readable format. Questions may be in bold and numbered, answers are more direct, etc.
# Remember to cite all images and tables.
* A section to discuss and/or illustrate the applications
# Very good, link the reference and cite all sources.
* A conclusion section
# Please add more summarizing especially from theory sentences and avoid long sentences.
* References
# Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Reference primary sources rather than Wikipedia

== [[Trust-region methods|Trust-region methods]] ==

* Author list:
# Remove cornell IDs. Author is also spelled incorrectly.
# Add the course section.
* An introduction of the topic
# References are not linked. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Use LaTex code or equation editor to display all equations and variables (e.g., “xk”, “f`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “we”. This goes for all other sections as well.
* Theory, methodology, and/or algorithmic discussions
# Organization of ideas in this section needs work.
# You have not defined explicitly why the Cauchy point is important to compute beyond a vague allusion to performance improvements, which is also wrong (it is useful because of its guarantees for convergence, not performance) It is also misspelled.
# Each approach should have accompanying explanation and motivation for why it is being discussed. It is not enough to outline the algorithm.
# Please make sure symbols are properly subscripted and superscripted (e.g. “pk” should be “p_k”
# Please format the algorithm in proper algorithmic pseudocode format.
# Little to no discussion on global convergence guarantees
# Please include discussion about the advantages and disadvantages of the algorithm
# Fix typo “couchy point”.
* At least one numerical example
# Any code functions (uminfunc) should have proper text formatting.
# The graph needs a better caption explaining how the axes are labeled and what data points are being shown.
# Please increase the quality of the figure. It is hard to see the red line.
# Add citation to “The Rosenbrock function is a non-convex function, introduced by Howard H. Rosenbrock in 1960, which is often used as a performance test problem for optimization algorithms.”
* A section to discuss and/or illustrate the applications
# The content in this section as it is currently does NOT describe applications, but rather different approaches within the trust region methodology. Please provide specific applications (e.g. TRPO in reinforcement learning).
* A conclusion section
# Please add more summary, future research directions for example is a good start.
* References
# Please consider having the references as this Wiki template, <nowiki>https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization</nowiki>

There are numerous misspellings, grammatical errors, and incorrect claims. Please fix these.

== [[Momentum|Momentum]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Apart from an explanation on momentum, it is necessary to briefly point out the limitations of SGD and why momentum could help with these limitations. Please update it accordingly.
# Remove bold on “Momentum”.
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
* Theory, methodology, and/or algorithmic discussions
# It is important to use technical language for this Wiki. Although a layman’s explanation is appreciated, it would be better to skip using words like “zig zagging”. Try to explain all concepts in a technical language with few simplifications but NOT vice versa.
# The definition of the update rule for SGD with momentum looks incorrect, specifically the first expression. Please fix it and also explain all the parameters used.
# Use LaTex code or equation editor to display all equations and variables (e.g., “W”, “V`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “you”.
* At least one numerical example
# Please try to label the plots that explains what each line color means.
* A section to discuss and/or illustrate the applications
# Please use correct terminology like “optimizing non-convex functions” and not “training non-convex models”.
# Adam, Adadelta, and RMSprop are variants of SGD that already use momentum. Please double check the writing and update if necessary.
* A conclusion section
# Please refrain from using words like “zig zag” effects.
* References
# Almost all references used are URLs. Please try to add journal/conference articles or books for references, instead of directly citing the URLs.

== [[Stochastic dynamic programming|Stochastic Dynamic programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Discussion on applications should be moved to a separate section.
* Theory, methodology, and/or algorithmic discussions
# Remove the grey box background of equations.
* At least one numerical example
* A section to discuss and/or illustrate the applications
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Outer-approximation (OA)|Outer-approximation]] ==

* An introduction of the topic
# See formatting guideline below
# Avoid opinionated statements such as “MINLP problems are usually the hardest to solve”.
# Rearrange the text such that the MINLP formulation is in the theory section and keep the introduction in words only.
* Theory, methodology, and/or algorithmic discussions
# Consider left aligning equations and optimization problem formulations by the “=”. See [[Stochastic programming|https://optimization.cbe.cornell.edu/index.php?title=Stochastic_programming]] for an example
# The sentence “The Outer-Approximation (OA) algorithm was first proposed by Duran and and Grossmann in 1986 to solve MINLP problems.” needs a reference.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# “Minimize” and “subject to” should be “min” and “s.t.” in MathType
* A section to discuss and/or illustrate the applications
# Does not explicitly point out why OA is applicable (and/or preferred) in these applications, rather than other MINLP approaches (show that the problem formulations are amenable to a solution approach through OA)
# The sentence “... an active research area and there exists a vast number of applications in fields such as engineering, computational chemistry, and finance.” needs references.
# Place GAMS code in a single code box or remove it.
# Consider reformatting to make steps more readable. Inserting spaces and breaking down steps would help.
* A conclusion section
# Too short. Consider discussion on future research direction and discussion on uncertainty
# Please review abbreviations throughout the page. Why is MINLP redefined here? “Outer-Approximation is a well known efficient approach for solving convex mixed-integer nonlinear programs (MINLP)”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove "Template:Reflist"

== [[Unit commitment problem|Unit commitment problem]] ==

* Author list
* An introduction of the topic
# Please expand the introduction and avoid discussions of examples or specific applications in this section.
# The sentence “Nonlinear, Non-convex programming optimization problem.” doesn’t make sense by itself and Non-convex shouldn’t be capitalized.
* Theory, methodology, and/or algorithmic discussions
# Figure/image format should be revised to better display the content.
# Uppercase characters are used randomly (e.g., “non-convex transmission Constraints”) . Please follow correct language conventions for sentence structure.
# Avoid inserting inline citations after words like “written in matrix form as equation [3]..” or “presented in [3]...” as it is a bit informal when you don’t explicitly name the subject. Also these two sentences are grammatically incorrect and appear to be missing an ending period and comma, respectively.
# Don’t say “written in matrix form as equation..” and just cite the reference, actually write out the equation.
# Properly label the figure in this section with a figure number and improve visibility by making it larger.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Label the figures in this section properly with figure numbers.
# Fix typo “while minimize” to “while minimizing”.
# Avoid pronouns such as “we”.
# Use the equation editor when typing equations.
* A section to discuss and/or illustrate the applications:
# I suggest changing the order of the subtitles here. For example, Single-Period Unit Commitment.
* A conclusion section
* References

== [[Frank-Wolfe|Frank-Wolfe]] ==

* Author list:
* An introduction of the topic
# I suggest highlighting disadvantages along with advantages.
* Theory, methodology, and/or algorithmic discussions
# “[n x 1] matrix” please use the equation editor to express mathematical descriptions and symbols (p,b, etc)
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please show at least a few iterations. Even for smaller examples if needed. Report the final solution.
# Please use the LaTex code or equation editor for min and include s.t., etc.
* A section to discuss and/or illustrate the applications:
* A conclusion section
# Same as the introduction. Pros and cons should be evaluated together!
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Line search methods|Line Search Method]] ==

* Author list
* An introduction of the topic
# Expand the introduction and avoid discussion on some of the specific steps in the solution process.
# Provide references here.
* Theory, methodology, and/or algorithmic discussions
# The phrase “are as follows” in the steepest descent method discussion needs to be followed by a colon.
# Rephrase “has a nice convergence theory” and cite a reference for this claim.
# Avoid pronouns such as “we”.
# Add citation after “.. proposed by Phillip Wolfe in 1969.”
# Figure 1 is between two sections. Please fix this issue.
* At least one numerical example:
# Add some space between iterations or subsection break
* A section to discuss and/or illustrate the applications:
# Too few references in this section.
# Last paragraph makes some claims without references.
* A conclusion section
* References
# References should be properly formatted. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Piecewise linear approximation|Piecewise Linear Approximation]]==

* Author list
* An introduction of the topic
# The content of this section is good, but there are some issues with sentence clarity and some other grammatical errors. Please revisit this section and make changes accordingly.
* Theory, methodology, and/or algorithmic discussions
# Fix typo “to force the x’ values become associated with”.
* At least one numerical example
* A section to discuss and/or illustrate the applications
# Please aim for a maximum average sentence length of ~25 words. Some of these longer sentences are hard to read.
* A conclusion section
# Expand the conclusion section to be longer than one sentence. The conclusion section to include a brief summary of what was discussed above, an emphasis on it’s significance, and a brief discussion of future extensions and research direction if applicable.
* References
# Include hyperlinks to sources when possible.

== [[Mathematical programming with equilibrium constraints|Mathematical Programming with Equilibrium constraints]] ==

* An introduction of the topic
# This section includes several terms like variational inequalities, constraint qualifications that were not discussed in the class. Please add a sentence to explain them before using them.
* Theory, methodology, and/or algorithmic discussions
# The meaning of parameter vector x is unclear. Please add more information or update if necessary.
# Equations and symbols in the PIPA subsection are not formatted correctly. Please use the same formatting for all equations, so they read as mathematical equations and not text. This goes for all other sections as well.
# Use equations instead of images to represent math programs and equations in the Implicit Descent and SQP subsection.
# Apart from the steps for each solution technique, please also add a few sentences that describe each method.
* At least one numerical example
# Please define the terms like NCP, MP before abbreviating them. Also try not to unnecessarily abbreviate simple terms.
# Equations should be typed by LaTex. Images for equations are unacceptable.
# GAMS code is strongly discouraged. Please solve the problem "step-by-step".
# The selected numerical example is fine but is directly solved with the MPEC solver in GAMS. Try to solve it manually like the homework/in-class problems step by step using the steps described in the previous section by choosing any of the methods.
# Avoid using figures in the equations (subject to etc)
* A section to discuss and/or illustrate the applications
# Add references to “power management, highway pricing, chemical process engineering, and traffic planning.”
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Wing shape optimization|Wing shape Optimization]] ==

* Author list: Remove cornell ID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# The introduction is missing several references (e.g., “software packages like computational fluid dynamics..”, sentences containing things that aren’t common knowledge, performance claims, etc.)
# Avoid discussion involving finer details of subject methods in this section.
# In the titles, please change the font from bold to normal to have consistent formatting in the site. Same applies to box of content!
* Theory, methodology, and/or algorithmic discussions
# Properly cite the CFD package, don’t just include a link.
# Properly label the figure with a figure number.
# Consider removing white space between isolated sentences to improve readability.
* At least one numerical example
# If you’ve already defined an abbreviation (CFD), there is no need to define it again. Just use the abbreviation.
# Avoid pronouns such as “we” or “they”.
# Phrases like “under the following” need to be followed by a colon.
# Properly label the figure with a figure number and consider making them larger to improve visibility. Call the reader's attention to the figures in text by referencing the figure number.
# “As seen in the video below” is stated yet there are only images present and it may be initially unclear to the reader which figure is being referenced here.
# Avoid inserting inline citations like “[4] introduces an..” as it is a bit informal when you don’t explicitly name the subject.
# Don’t just cite the reference when discussing the problem formulation, explicitly write the model formulation and solution process using LaTex or equation visual editor.
* A section to discuss and/or illustrate the applications
# Some characters are randomly capitalized in this section.
* A conclusion section
# These variables should be defined before the conclusion section, they are out of place here. Also, please use normal text when explaining variables except for the variable symbol.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Interior-point method for NLP|Interior point method for NLP]] ==

* An introduction of the topic:
* Theory, methodology, and/or algorithmic discussions
# Primal-Dual formulation and comparison to the Barrier Method is not discussed.
# Include brief discussion about big O convergence rates.
# Need discussion about the concept of “central path” and the notion of self concordance
# Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
# Graphs and images are incorrectly formatted to the page. Consider proper alignment with respect to the text body.
# Use explicitly typed Latex equations instead of images to represent math programs and equations.
# Fix typo “optimisation”.
# Use LaTex code or equation editor to display all equations and variables (e.g., “xi ”, “μ”, etc.).
* At least one numerical example:
# There are formatting issues with figures 2,3. Please make sure to embed them within their respective sections.
* A section to discuss and/or illustrate the applications
* A conclusion section
# Minor character code typos in the conclusion.
# Also, please add more discussion in this section. Future research directions is a good start.
# There is a box "􏰐"
* References

== [[AdaGrad|Adagrad]] ==

* An introduction of the topic:
* Theory, methodology, and/or algorithmic discussions
# Include discussion on its variants (most important is AdaDelta).
# Include disadvantages of Adagrad, since this provides motivation for the discussion on the variants and improvements of Adagrad
# Include comparisons to other popular optimizers (particularly important is comparisons to regular SGD and Adam)
# Different convergence rates are possible depending on the setting where Adagrad is used, but this is not mentioned on the page currently. As such the regret bound section should be more thoroughly explained.
* At least one numerical example
# In the first sentence, “..take the following numerical example” should be followed by a colon.
# Fix typo “trayectory”.
* A section to discuss and/or illustrate the applications
# This section is too short; include specific applications in which input features are sparse and Adagrad excels.
# Add reference to the claim “Mainly, it is a good choice for deep learning models with sparse input features”.
* A conclusion section
* References

# Too few references overall, you should aggregate information from multiple sources (even if the base algorithm itself comes from a singular paper)

== [[McCormick envelopes|McCormick Envelopes]] ==

* Author list: OK but I suggest removing NetID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# First sentence is hard to read. Please consider keeping sentences below 25-30 words.
# No references provided. Please cite all sources.
# Figure 1 is provided in the middle between two sections. Please include in the introduction section.
* Theory, methodology, and/or algorithmic discussions
# References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# When using mathematical expressions and symbols, please use the equation editor. (e.g., x*y, exy + y, sin (x+y) - x2)
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# For the sample GAMS code, please place it in a code box
* A section to discuss and/or illustrate the applications
# Having a list is not enough. Please explain at least three applications in a few sentences each.
# This section should be at least a paragraph to discuss relevant applications. Each application should be explicitly linked to the page topic. A few keywords do not meet the requirement at all.
* A conclusion section:
* References
# References are not expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please follow the standard reference style - the current format is incorrect.

2021 Cornell Optimization Open Textbook Feedback

2021-12-05T01:07:52Z

Asa273: /* Adagrad */

== [[Lagrangean duality|Lagrangian duality]] ==
* Author list, sections and TOC
# Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.
# Remove cornell ID from Author list
* An introduction of the topic
# This section includes sentences on constructing the dual problem and is referred to as Lagrangian relaxation (LR). This is incorrect, please fix the definition of LR.
# Definitions of LR and its relation to duality should be double checked and re-written.
# Only one reference is present in this section. Please add more relevant references by expanding this section.
# Consider merging the “introduction” and “history” sections.
# In the titles, please change the font from bold to normal to have consistent formatting in the site.
* Theory, methodology, and/or algorithmic discussions
# The Lagrangian variables associated with equality constraints h(x) are unbounded but the Lagrangian dual problem states them as non-negative. Please fix the same.
# Also to construct a dual, we do not change minimization to maximization directly. We observed such things in the examples in lecture notes due to simplification. The lagrangian dual problem would be minimize (,).
# Adding to the previous point, the Lagrangian is a lower bound on the original objective; the solution to the primal and dual or only equivalent if the duality gap is 0. You reference this in one section, but this is after your statement “Hence, solving the dual problem, which is a function of the Lagrangian multipliers (𝜆*) yields the same solution as the primal problem, which is a function of the original variables (x*). “. Please clarify the specific conditions that must hold for the solution of the dual to be equal to the primal’s.
# You refer to the “Complementary Slackness Theorem”, but don’t actually write the mathematical representation of complementary slackness. Please fix this. Also consider including the derivation of the complementary slackness condition, as it is both easy and short. Boyd is a good reference for this.
# Last step of the “process” subsection also needs updating according to the previous comments.
# The inline notations should also be typed using LaTex.
# Please use the LaTex code or equation editor for min, s.t., etc.
* At least one numerical example
# Only one dual variable is associated with each constraint. The numerical example uses two for the first and second constraint which is unnecessary. Please update it accordingly for both constraints. This particular example will only have two dual variables instead of the five dual variables used currently.
# All consecutive steps need to be updated since the dual variables would be updated.
# After substitution the nonlinear function should be further simplified. The current expression reads like a highly nonlinear function but can be easily simplified.
# Similar to the comments in the methodology section, inverting minimize to maximize is incorrect. Please update the dual objective function accordingly.
# Please use the LaTex code or equation editor for min, s.t., etc.
* A section to discuss and/or illustrate the applications
# Bullet points could be used to state the last four real-world examples that explain the physical meaning of the primal and dual problems.
# Add references for the last set of applications.
* A conclusion section
# This section contains a few typos. Please fix the same.
* References
# Some citations' hyperlinks are displaying.

== [[Disjunctive inequalities|Disjunctive Inequalities]] ==

* Author list
# Missing course section and semester
# Remove cornell ID
* An introduction of the topic
# No citations are present in this section.
# “mixed-integer programming (MIP)” should be used instead of “multiple integer programming (MIP)”. Please fix this error.
* Theory, methodology, and/or algorithmic discussions
# The abbreviation MILP is not previously defined. Please fix this issue.
# You consistently use the negative sign instead of the NOT operator for y (-y instead of ¬y).
# Some inconsistencies with the spacing of variables, constraints, etc., under the “General” section that need to be fixed.
# Typo in “This is shown below by M1, M2, y1, and y1:” where y1 needs to be changed to y2. Why use two different Big-M variables here? Elsewhere in the Wiki you only use one so this could lead to confusion with a general audience. Also if this was taken from the lecture notes then it needs to be cited.
* At least one numerical example
# Please reformulate and solve a complete numerical example rather than just reformulating a general example. Demonstrate the use of Big-M and Convex Hull formulation in an optimization problem that provides details such as individual steps in the problem solving process and final results.
# Add space between vee (V) operator and brackets in first line of Latex
# Please format variables correctly, for example, use x1 instead of x1.
* A section to discuss and/or illustrate the applications
# Please format the equations appropriately either by using latex code or the visual editor. These images are NOT acceptable!
* A conclusion section
# There is no conclusion presented in this section at all.
* References
# The included references have NOT been used anywhere in the Wiki. Add references for sentences that are not common knowledge and please link them appropriately with the text in Wiki. If the figures used here were not original works, you must also cite them.
# There are many papers on this topic. A simple Google (Scholar) search could provide you with sufficient references to cite.
# Many important references of this topic are missing.
# Please consider linking the references as demonstrated in the Wiki tutorial on Canvas and in this template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

==[[Stochastic programming|Stochastic Programming]] ==

* Author list: Remove cornell IDs
* An introduction of the topic
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
# This section only includes two sentences on Stochastic programming (SP), while the rest gives examples of uncertainty. Please discuss the need for SP in the presence of uncertainty. Also, discussion on robust optimization and its limitations should be removed since it is out of place.
* Theory, methodology, and/or algorithmic discussions
# Please avoid direct inline linkbacks to Wikipedia.
# The symbol “xi” in the methodology subsection should be explained.
* At least one numerical example
# Copying a numerical example "entirely" from a textbook is inappropriate. Your team should come up with a "numerical" case.
# No specific application context is needed for a numerical example.
# The inline notations (`x1`, `s1`) should also be typed using LaTex.
# Label all tables with a table number for better readability.
# Properly format the solution table with the label attached rather than the following sentence. The solution table looks different from the others, please fix this for consistency.
* A section to discuss and/or illustrate the applications;
# I suggest eliminating citing the last name of the first author (i.e. Zhou et al.)
* A conclusion section
* References
# URLs of some citations are not properly formatted (not showing the hyperlinks).

== [[Exponential transformation|Exponential Transformation]] ==

* Author list
# Missing course section
# Remove cornell ID
* An introduction of the topic
# Please expand the introduction.
# Please aim for a maximum average sentence length of ~25 words. Last sentence with 51 words is hard to read.
# Second Sentence: please change the word “they” as it could make the meaning ambiguous
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
# If you use abbreviations, please introduce them (e.g. NLP,MINLP)
* Theory, methodology, and/or algorithmic discussions
# Please explain the transformation in words along with equations
# Terms like posynomial should be described in detail.
# Please move the numerical example to the section below
# The “(eq 1)” is not needed here.
# Please expand this section.
* At least one numerical example
# In the third equation of the numerical example, it is confusing to have coefficients after numbers. Some readers may read it as an exponent.
# Last equation in this section after “further linearization” is incorrect. This equation cannot be further linearized, please fix this.
* A section to discuss and/or illustrate the applications
# Missing part of text: “Proof of convexity of with positive definite test of Hessian…”
# Applications are not numerical examples. Please refer to this link for example of applications: [[Duality|https://optimization.cbe.cornell.edu/index.php?title=Duality]]
# Citation 7 is missing in current applications
# The section current applications is redundant
# Please use the LaTex code or equation editor for min, s.t., etc.
# Under current applications, do not just use a hyperlink to describe an application. Actually describe it. And properly inline citation style should be used instead of the hyperlink.
# The convexification application of MINLP can be further simplified for binary variables. Please refer to the lecture slides for more information.
* A conclusion section
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
* References
# Please consider linking the references by using this as Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Citation 7 is missing in current applications

== [[Sparse Reconstruction with Compressed Sensing|Sparse reconstruction with Compressed Sensing]] ==
This Wiki needs a significant rewrite. Please go through the comments for details.

* An introduction of the topic
# The introduction section should include information about the problem and its implications presented briefly. Please use full sentences to write this Wiki. You may use tools like Grammarly to check sentence formation and grammar.
# This section includes several typos like “sub modual”. Please fix them throughout the wiki and delete them if not required.
# Many abbreviations are used before previously defining them. Please define these abbreviations before using them in the text.
# This section is incomprehensible in its current form. Please rewrite with proper comprehension.
# Equations and math symbols need proper reformatting. The current version reads like text (along with equations) copy-pasted from a specific source.
# Try to place the figure at the top of the Wiki between the main text.
# Avoid pronouns such as “we”.
# I suggest the use of more formal abstract illustrations.
* Theory, methodology, and/or algorithmic discussions
# Equations and symbols need proper reformatting.
# Lemmas and theorems are not expected for this Wiki. Sparse reconstruction is a straightforward concept but is unnecessarily complicated here. Please refer to other Wiki examples to get an idea of what the Wiki should convey.
* At least one numerical example
# Numerical example is missing.
* A section to discuss and/or illustrate the applications
# Having a list is not enough. Please explain at least three applications in a few sentences each.
* A conclusion section
# Conclusion section is missing.
* References
# The current reference list is not correctly formatted. References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Portfolio optimization|Portfolio Optimization]] ==

* Author list
# Remove cornell id
* An introduction of the topic
# The introductory sentence should be rephrased. The action of minimizing the risks does not inherently maximize the gains, rather PO aims to maximize gains whilst minimizing risks.
# Amount of whitespace can be reduced by changing the orientation of Figure 1 and the sentences in this section.
# Define terms such as risk, return, portfolio, etc., when you introduce them. Assume that the reader may not know much about finance. This goes for all other sections as well.
* Theory, methodology, and/or algorithmic discussions
# A brief mention of modern portfolio theory (i.e.. Markowitz) would be appropriate in this section.
# Several grammatical errors here involving sentence structure and clarity. Some questionable semantics (e.g., “The portfolio optimization mainly assumes two directions.”) and syntax (phrases such as “.. is as follows” should be followed by a colon). Misuse of commas and missing commas in this section. Two sentences introducing E(rp) and w should be combined into one.
# Use LaTex to distinguish variables written within a sentence, such as m and n.
# Rephrase “Cut the relevant information and conditions in the portfolio optimization, as well as the final requirements into the relevant variables, constraints and linear functions of the linear programming problem.”
# An explanation of a few common constraints would be helpful, rather than just including a table.
* At least one numerical example
# All tables need to be labeled.
# Include figure number in label for consistency.
# Fix misspelling “dolling decision variables”.
# Use LaTex for all variables, equations, and constraints here.
# Example 2 table is hard to read, so making it bigger would help.
# Remove the “Using excel as the solver” part from the sentence before the solution discussion.
# Some grammatical errors here (phrases such as “.. is as follows” should be followed by a colon).
* A section to discuss and/or illustrate the applications
# Rephrase “Portfolio optimization can be used to screen investment projects that meet investors, rationally allocate investment amounts, etc.”
# Not sure “relevant” is the correct word choice here.
# You need more specific examples with the utility of portfolio optimization, this section is quite general as is. Some more detail and focus on real-world applications in the financial industry that relate to retirement planning, financial security, economic stability, etc., would be helpful.
* A conclusion section
# Need some commas here.
# The sentence “Linear programming has been around since the 1940’s and has such a wide base of applications” is not necessary.
* References
# Please consider linking the references as demonstrated in the Wiki tutorial on Canvas and in this template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove white space between end of sentences and reference numbers.

== [[Chance-constraint method|Chance constraint method]] ==

* Author list:
* An introduction of the topic
# Please consider correcting a few grammatical errors: “pre-planned for”, “god”, “certain levels of feasibility is guaranteed in what are”, and “Performance of a system”
# In “Chance-constraint”, it is capitalized randomly throughout the introduction. Please correct.
# Please use technical language to briefly introduce chance-constrained programming. Words like “acts of god”, “cost of doing business” are not appropriate for a technical Wiki.
* Theory, methodology, and/or algorithmic discussions
# Please add a citation to the first sentence.
# Xi is an uncertainty/randomness variable. It is better to use clear language.
# Please use the mathematical editor for adding explanations in the text. Using “ x is a decision variable” is hard to read. Same for f(x) and others.
# Theory is insufficient. Please expand and explain different approaches.
# Please add pros and cons explicitly as a list.
# Explain the physical meaning for examples of chance constraints along with all the notations used.
* At least one numerical example
# Please use the equation editor for min, st., etc.
# Please use the mathematical editor for adding explanations in the text. Using “ x is a decision variable” is hard to read. Same for f(x) and others.
# Please change the table format so as not to confuse the reader.
# Multiple instances of [Chart to be added] are missing.
# Example is incomplete.
# Avoid pronouns such as “we”.
* A section to discuss and/or illustrate the applications
# Please connect several grammatical and spelling errors: “real life application”, Energy creation, particularly in renewable sources, have high variabilities”, and others
# “Zhao, Xue, Cao, and Zhang”. No need to list all authors within the article. Provide a reference is sufficient. If authors must be mentioned, (Zhao et al.) should be ok.
* A conclusion section
# Uniqueness and universality earlier are not clear to me. If they are not discussed earlier in the application, it would be better not to introduce new discussions in the conclusion.
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
* References
# References seem to vary in format. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Bayesian Optimization | Bayesian Optimization]] ==

* Contents: Subheadings for EI and the algorithm should not be bolded, Random words should not be capitalized.
* Author list: Remove cornell ID, Please check names
* Introduction
# The introduction is too general and not substantial enough. For example, simply saying BayesOpt is useful when the objective function is unknown obscures exactly HOW it is useful (namely, computational efficiency in applications where ground truth sampling is expensive). Discussion on applications should be moved to a separate section.
# Machine learning rarely includes black-box functions to be optimized. Bayesian optimization is almost never used for optimizing ML loss functions but can instead be used for hyperparameter optimization. Please update such claims in this section.
* Theory, methodology, and/or algorithmic discussions
# Captions need reformatting.
# Consider italicizing keywords rather than bolding.
# Please add a citation to the first sentence.
# Discussion on acquisition functions should include comparisons, tradeoffs, and reasons to use one over the other. Should also note that expected improvement is the most widely used in practice, and explain.
# Avoid pronouns such as “we”.
# Please write equations in the Wiki instead of attaching images for equations.
# Acquisition function figure could be made larger and clearer to improve readability.
* At least one numerical example
# Any references to functions or methods in code ‘e.g. fmin’ should be properly formatted as code-stylized text.
# Please use the equation editor for min, st., etc.
# Avoid including a figure of the code for this example and explicitly describe the steps to the modeling and solution process instead.
# Avoid pronouns such as “our” and “we”.
* A section to discuss and/or illustrate the applications
* A conclusion section
# Please do not use brackets to enclose lists.
# Some claims here should be supported by references. Please cite each source after its sentence.
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Try to avoid references to “pop” machine learning blogs where anyone can be an author. (e.g. towardsdatascience)

Notes on grammar: Needs some work. Several instances where colons are inappropriately inserted mid sentence or in subheadings. Explanations are not terse. Several instances of switching between personal and impersonal style of writing, which is distracting.

== [[Conjugate gradient methods|Conjugate gradient methods ]] ==

* Author list: Remove cornell ID
* Introduction
# All inline notations (e.g., `x`, `A`) should be typed using LaTex.
* Theory, methodology, and/or algorithmic discussions
# Is Gauss-Newton no longer referenced?
# Theorems listed in the first section should be accompanied with high level explanation, not just a list of the theorems themselves. The page should read like an article, with proper flow.
# Please indent equation blocks.
# Please properly format pseudocode.
* At least one numerical example
# Steps should be accompanied with explanation, or reference to the corresponding step in the pseudocode.
* A section to discuss and/or illustrate the applications
# Consider including 2 additional examples of applications
* A conclusion section
# Consider adding future research directions
* References
# Reference primary sources rather than Wikipedia
# Too few references.

== [[Geometric programming|Geometric Programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Examples of applications in this section use the same reference. Please cite their individual sources.
* Theory, methodology, and/or algorithmic discussions
# The symbol denoting the domain in the definition of a monomial is unclear. Please clarify it or fix this if it is incorrect.
# Definition of posynomial refers to section 2.1 which is missing from the Wiki (sections are not numbered in the main text).
# In the generalized posynomial subsection, bullet points do not tell us why h(x) is posynomial. Either provide reasons or simply state that h(x) is posynomial. Also explain why h3 is a generalized posynomial.
# Additional theory on the feasibility analysis could be provided in this section.
* At least one numerical example
# In the transformation example, the last two constraints could also be simplified by applying a natural logarithm on both sides. Please update them as well.
* A section to discuss and/or illustrate the applications
# The figure in this section needs to be labeled.
# The figure needs to be resized and perhaps aligned to the center.
* A conclusion section:
# Please avoid vague language such as: “This makes”.
# Please avoid opinionated statements: “one of the best ways”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Adam|Adam]] ==

* Author list
* An introduction of the topic
# Some grammatical errors here, mostly related to the need for commas in certain places (e.g., “Before Adam..”).
# Some minor errors with parts of speech throughout the section, need to revisit phrases such as “which has broader scope in future for”, etc.
# Try splitting up some of the longer sentences in this section, a couple are hard to read.
# Avoid definitive statements about Adam being the best or always better solver, as this is simply not true (the choice of the “best” optimizer is setting-dependent). Use language such as “Research has shown that Adam has demonstrated superior experimental performance over..” and then cite academic references to back this claim.
# What does adam stand for? Introduction is insufficient. Please expand.
* Theory, methodology, and/or algorithmic discussions
# Revise grammar here, noticing some missing commas and uncapitalized word after period.
# Rephrase “second one is to update the old position with the updated position”.
# Use LaTex code or equation editor to display all equations and variables in this section, and actual subscripts instead of “m_t”, etc.
# Avoid inserting inline citations after words like “According to..” or “This article..” as it is a bit informal. This could be rephrased or changed to something like “According to author,^[2] …” with author name inserted.
# Remove white space before the period in RMSP discussion.
# Please provide a pseudocode.
# Please use list the two methods here “Adam is a combination of two gradient descent methods which are explained below”
# Please expand the theory section significantly. Theoretical convergence properties should be discussed, even if briefly.
* At least one numerical example
* A section to discuss and/or illustrate the applications
# Same comment as before, consider replacing inline citations after words like “According to..”.
* A conclusion section
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Try to avoid references to blogs and use peer-reviewed academic references instead.
# Too few references.

== [[A-star algorithm|a* algorithm]] ==

* Author list:
# Remove cornell ID
* An introduction of the topic:
# In the titles, please change the font from bold to normal to have consistent formatting in the site.
# Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.
# There are no citations in the introduction. Please cite every source.
* Theory, methodology, and/or algorithmic discussions
# Please add the mathematical description of the algorithm.
# Reference style varies in sentences. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please fix grammatical and spelling errors as (“from current position to the goal”, “There are a lot of discussions”, etc). Also, many hyphens are missing as “non playable”.
# In algorithms, it is a standard to add high-level description (i.e. pseudocode or flowchart). Please incorporate it.
# Use LaTex code or equation editor to display all equations and variables in this section (e.g., “f(n)...”, “h(n)..”, etc.). This goes for other sections as well.
* At least one numerical example
# The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.
# Instead of writing things like “The above image..”, label each figure and use the figure number to refer to it in text.
* A section to discuss and/or illustrate the applications
# No references in the applications. Please cite every source
# Preferably, add at least an additional application.
* A conclusion section
# Conclusion should summarize descriptions. Please modify it to provide a summary.
# Please pay attention to the length and structure of sentences here and in the full page. First sentence is hard to read.
* References
# References seem to vary in format and are not linked correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Job shop scheduling|Job-Shop Scheduling Problem]] ==

* An introduction of the topic
# The current introduction to the jobshop scheduling problem has only two sentences in addition to the parameter description. Introduction typically contains information about the problem, its importance in the real-world, and some information about the solution techniques and their types to solve the problem. Please add some information that covers the above.
* Theory, methodology, and/or algorithmic discussions
# It is unclear whether the assumptions stated in this section are required to apply the following solution techniques. Please clarify the same. Also use complete sentences to state them.
# The branch and bounds method described in this section only discusses the solution technique for problems with one machines. However, branch and bound is a general technique that can be applied to any MILP problems with varying scales. Please update the “methods” section to be as general as possible.
# Since this Wiki focuses on jobshop scheduling, at least two methods are expected. Branch and bound is a general MILP technique, so, it is recommended to add a tailored technique that can only solve specific jobshop scheduling problems. Solving the numerical example with this technique is not necessary.
# Reference to the branch and bound technique described in this section is a “youtube” video. Please add references in literature that describe this method in detail. The method used in this video is highly tailored for a single machine application. This is also an incorrect way to cite a reference. Please keep this section as general as possible.
# Use LaTex code or equation editor to display all equations and variables in this section and all other sections as well.
# Check grammar in this section. For example, phrases like “are as follows” need to be followed by a colon and not a period.
# Consider rewriting the assumptions as a list in this section.
* At least one numerical example
# The example used in this section is exactly the same as the one in the youtube video. Please use a modification of this example or choose another example/method to demonstrate the solution technique.
# The figure in this section is not numbered when all others are. Relabel this figure for consistency and its number to refer to it in-text.
* A section to discuss and/or illustrate the applications
# This section should only focus on real-world applications of the jobshop scheduling problem. But currently, this section includes additional information on solution techniques/complexity that is appropriate for the Introduction section. Please discuss the applications of the problem in this section.
* A conclusion section
# The meaning of “Operations applications” is unclear. Please explain or update if necessary.
# The current conclusion section does not properly summarize the problem. Please refer to other Wiki examples for an idea to update the section accordingly.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please reference media sources like reference 5 appropriately.

== [[Optimization in game theory|Optimization in game theory]] ==

* Author list: remove cornell IDs.
* An introduction of the topic
# References are not linked. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
* Theory, methodology, and/or algorithmic discussions
# Please edit references.
# Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm.
# Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.
* At least one numerical example
# Please organize the last part in a more readable format. Questions may be in bold and numbered, answers are more direct, etc.
# Remember to cite all images and tables.
* A section to discuss and/or illustrate the applications
# Very good, link the reference and cite all sources.
* A conclusion section
# Please add more summarizing especially from theory sentences and avoid long sentences.
* References
# Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Reference primary sources rather than Wikipedia

== [[Trust-region methods|Trust-region methods]] ==

* Author list:
# Remove cornell IDs. Author is also spelled incorrectly.
# Add the course section.
* An introduction of the topic
# References are not linked. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Use LaTex code or equation editor to display all equations and variables (e.g., “xk”, “f`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “we”. This goes for all other sections as well.
* Theory, methodology, and/or algorithmic discussions
# Organization of ideas in this section needs work.
# You have not defined explicitly why the Cauchy point is important to compute beyond a vague allusion to performance improvements, which is also wrong (it is useful because of its guarantees for convergence, not performance) It is also misspelled.
# Each approach should have accompanying explanation and motivation for why it is being discussed. It is not enough to outline the algorithm.
# Please make sure symbols are properly subscripted and superscripted (e.g. “pk” should be “p_k”
# Please format the algorithm in proper algorithmic pseudocode format.
# Little to no discussion on global convergence guarantees
# Please include discussion about the advantages and disadvantages of the algorithm
# Fix typo “couchy point”.
* At least one numerical example
# Any code functions (uminfunc) should have proper text formatting.
# The graph needs a better caption explaining how the axes are labeled and what data points are being shown.
# Please increase the quality of the figure. It is hard to see the red line.
# Add citation to “The Rosenbrock function is a non-convex function, introduced by Howard H. Rosenbrock in 1960, which is often used as a performance test problem for optimization algorithms.”
* A section to discuss and/or illustrate the applications
# The content in this section as it is currently does NOT describe applications, but rather different approaches within the trust region methodology. Please provide specific applications (e.g. TRPO in reinforcement learning).
* A conclusion section
# Please add more summary, future research directions for example is a good start.
* References
# Please consider having the references as this Wiki template, <nowiki>https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization</nowiki>

There are numerous misspellings, grammatical errors, and incorrect claims. Please fix these.

== [[Momentum|Momentum]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Apart from an explanation on momentum, it is necessary to briefly point out the limitations of SGD and why momentum could help with these limitations. Please update it accordingly.
# Remove bold on “Momentum”.
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
* Theory, methodology, and/or algorithmic discussions
# It is important to use technical language for this Wiki. Although a layman’s explanation is appreciated, it would be better to skip using words like “zig zagging”. Try to explain all concepts in a technical language with few simplifications but NOT vice versa.
# The definition of the update rule for SGD with momentum looks incorrect, specifically the first expression. Please fix it and also explain all the parameters used.
# Use LaTex code or equation editor to display all equations and variables (e.g., “W”, “V`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “you”.
* At least one numerical example
# Please try to label the plots that explains what each line color means.
* A section to discuss and/or illustrate the applications
# Please use correct terminology like “optimizing non-convex functions” and not “training non-convex models”.
# Adam, Adadelta, and RMSprop are variants of SGD that already use momentum. Please double check the writing and update if necessary.
* A conclusion section
# Please refrain from using words like “zig zag” effects.
* References
# Almost all references used are URLs. Please try to add journal/conference articles or books for references, instead of directly citing the URLs.

== [[Stochastic dynamic programming|Stochastic Dynamic programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Discussion on applications should be moved to a separate section.
* Theory, methodology, and/or algorithmic discussions
# Remove the grey box background of equations.
* At least one numerical example
* A section to discuss and/or illustrate the applications
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Outer-approximation (OA)|Outer-approximation]] ==

* An introduction of the topic
# See formatting guideline below
# Avoid opinionated statements such as “MINLP problems are usually the hardest to solve”.
# Rearrange the text such that the MINLP formulation is in the theory section and keep the introduction in words only.
* Theory, methodology, and/or algorithmic discussions
# Consider left aligning equations and optimization problem formulations by the “=”. See [[Stochastic programming|https://optimization.cbe.cornell.edu/index.php?title=Stochastic_programming]] for an example
# The sentence “The Outer-Approximation (OA) algorithm was first proposed by Duran and and Grossmann in 1986 to solve MINLP problems.” needs a reference.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# “Minimize” and “subject to” should be “min” and “s.t.” in MathType
* A section to discuss and/or illustrate the applications
# Does not explicitly point out why OA is applicable (and/or preferred) in these applications, rather than other MINLP approaches (show that the problem formulations are amenable to a solution approach through OA)
# The sentence “... an active research area and there exists a vast number of applications in fields such as engineering, computational chemistry, and finance.” needs references.
# Place GAMS code in a single code box or remove it.
# Consider reformatting to make steps more readable. Inserting spaces and breaking down steps would help.
* A conclusion section
# Too short. Consider discussion on future research direction and discussion on uncertainty
# Please review abbreviations throughout the page. Why is MINLP redefined here? “Outer-Approximation is a well known efficient approach for solving convex mixed-integer nonlinear programs (MINLP)”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove "Template:Reflist"

== [[Unit commitment problem|Unit commitment problem]] ==

* Author list
* An introduction of the topic
# Please expand the introduction and avoid discussions of examples or specific applications in this section.
# The sentence “Nonlinear, Non-convex programming optimization problem.” doesn’t make sense by itself and Non-convex shouldn’t be capitalized.
* Theory, methodology, and/or algorithmic discussions
# Figure/image format should be revised to better display the content.
# Uppercase characters are used randomly (e.g., “non-convex transmission Constraints”) . Please follow correct language conventions for sentence structure.
# Avoid inserting inline citations after words like “written in matrix form as equation [3]..” or “presented in [3]...” as it is a bit informal when you don’t explicitly name the subject. Also these two sentences are grammatically incorrect and appear to be missing an ending period and comma, respectively.
# Don’t say “written in matrix form as equation..” and just cite the reference, actually write out the equation.
# Properly label the figure in this section with a figure number and improve visibility by making it larger.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Label the figures in this section properly with figure numbers.
# Fix typo “while minimize” to “while minimizing”.
# Avoid pronouns such as “we”.
# Use the equation editor when typing equations.
* A section to discuss and/or illustrate the applications:
# I suggest changing the order of the subtitles here. For example, Single-Period Unit Commitment.
* A conclusion section
* References

== [[Frank-Wolfe|Frank-Wolfe]] ==

* Author list:
* An introduction of the topic
# I suggest highlighting disadvantages along with advantages.
* Theory, methodology, and/or algorithmic discussions
# “[n x 1] matrix” please use the equation editor to express mathematical descriptions and symbols (p,b, etc)
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please show at least a few iterations. Even for smaller examples if needed. Report the final solution.
# Please use the LaTex code or equation editor for min and include s.t., etc.
* A section to discuss and/or illustrate the applications:
* A conclusion section
# Same as the introduction. Pros and cons should be evaluated together!
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Line search methods|Line Search Method]] ==

* Author list
* An introduction of the topic
# Expand the introduction and avoid discussion on some of the specific steps in the solution process.
# Provide references here.
* Theory, methodology, and/or algorithmic discussions
# The phrase “are as follows” in the steepest descent method discussion needs to be followed by a colon.
# Rephrase “has a nice convergence theory” and cite a reference for this claim.
# Avoid pronouns such as “we”.
# Add citation after “.. proposed by Phillip Wolfe in 1969.”
# Figure 1 is between two sections. Please fix this issue.
* At least one numerical example:
# Add some space between iterations or subsection break
* A section to discuss and/or illustrate the applications:
# Too few references in this section.
# Last paragraph makes some claims without references.
* A conclusion section
* References
# References should be properly formatted. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Piecewise linear approximation|Piecewise Linear Approximation]]==

* Author list
* An introduction of the topic
# The content of this section is good, but there are some issues with sentence clarity and some other grammatical errors. Please revisit this section and make changes accordingly.
* Theory, methodology, and/or algorithmic discussions
# Fix typo “to force the x’ values become associated with”.
* At least one numerical example
* A section to discuss and/or illustrate the applications
# Please aim for a maximum average sentence length of ~25 words. Some of these longer sentences are hard to read.
* A conclusion section
# Expand the conclusion section to be longer than one sentence. The conclusion section to include a brief summary of what was discussed above, an emphasis on it’s significance, and a brief discussion of future extensions and research direction if applicable.
* References
# Include hyperlinks to sources when possible.

== [[Mathematical programming with equilibrium constraints|Mathematical Programming with Equilibrium constraints]] ==

* An introduction of the topic
# This section includes several terms like variational inequalities, constraint qualifications that were not discussed in the class. Please add a sentence to explain them before using them.
* Theory, methodology, and/or algorithmic discussions
# The meaning of parameter vector x is unclear. Please add more information or update if necessary.
# Equations and symbols in the PIPA subsection are not formatted correctly. Please use the same formatting for all equations, so they read as mathematical equations and not text. This goes for all other sections as well.
# Use equations instead of images to represent math programs and equations in the Implicit Descent and SQP subsection.
# Apart from the steps for each solution technique, please also add a few sentences that describe each method.
* At least one numerical example
# Please define the terms like NCP, MP before abbreviating them. Also try not to unnecessarily abbreviate simple terms.
# Equations should be typed by LaTex. Images for equations are unacceptable.
# GAMS code is strongly discouraged. Please solve the problem "step-by-step".
# The selected numerical example is fine but is directly solved with the MPEC solver in GAMS. Try to solve it manually like the homework/in-class problems step by step using the steps described in the previous section by choosing any of the methods.
# Avoid using figures in the equations (subject to etc)
* A section to discuss and/or illustrate the applications
# Add references to “power management, highway pricing, chemical process engineering, and traffic planning.”
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Wing shape optimization|Wing shape Optimization]] ==

* Author list: Remove cornell ID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# The introduction is missing several references (e.g., “software packages like computational fluid dynamics..”, sentences containing things that aren’t common knowledge, performance claims, etc.)
# Avoid discussion involving finer details of subject methods in this section.
# In the titles, please change the font from bold to normal to have consistent formatting in the site. Same applies to box of content!
* Theory, methodology, and/or algorithmic discussions
# Properly cite the CFD package, don’t just include a link.
# Properly label the figure with a figure number.
# Consider removing white space between isolated sentences to improve readability.
* At least one numerical example
# If you’ve already defined an abbreviation (CFD), there is no need to define it again. Just use the abbreviation.
# Avoid pronouns such as “we” or “they”.
# Phrases like “under the following” need to be followed by a colon.
# Properly label the figure with a figure number and consider making them larger to improve visibility. Call the reader's attention to the figures in text by referencing the figure number.
# “As seen in the video below” is stated yet there are only images present and it may be initially unclear to the reader which figure is being referenced here.
# Avoid inserting inline citations like “[4] introduces an..” as it is a bit informal when you don’t explicitly name the subject.
# Don’t just cite the reference when discussing the problem formulation, explicitly write the model formulation and solution process using LaTex or equation visual editor.
* A section to discuss and/or illustrate the applications
# Some characters are randomly capitalized in this section.
* A conclusion section
# These variables should be defined before the conclusion section, they are out of place here. Also, please use normal text when explaining variables except for the variable symbol.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Interior-point method for NLP|Interior point method for NLP]] ==

* An introduction of the topic:
* Theory, methodology, and/or algorithmic discussions
# Primal-Dual formulation and comparison to the Barrier Method is not discussed.
# Include brief discussion about big O convergence rates.
# Need discussion about the concept of “central path” and the notion of self concordance
# Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
# Graphs and images are incorrectly formatted to the page. Consider proper alignment with respect to the text body.
# Use explicitly typed Latex equations instead of images to represent math programs and equations.
# Fix typo “optimisation”.
# Use LaTex code or equation editor to display all equations and variables (e.g., “xi ”, “μ”, etc.).
* At least one numerical example:
# There are formatting issues with figures 2,3. Please make sure to embed them within their respective sections.
* A section to discuss and/or illustrate the applications
* A conclusion section
# Minor character code typos in the conclusion.
# Also, please add more discussion in this section. Future research directions is a good start.
# There is a box "􏰐"
* References

== [[AdaGrad|Adagrad]] ==

* An introduction of the topic:
* Theory, methodology, and/or algorithmic discussions
# Include discussion on its variants (most important is AdaDelta).
# Include disadvantages of Adagrad, since this provides motivation for the discussion on the variants and improvements of Adagrad
# Include comparisons to other popular optimizers (particularly important is comparisons to regular SGD and Adam)
# Different convergence rates are possible depending on the setting where Adagrad is used, but this is not mentioned on the page currently. As such the regret bound section should be more thoroughly explained.
* At least one numerical example
# In the first sentence, “..take the following numerical example” should be followed by a colon.
# Fix typo “trayectory”.
* A section to discuss and/or illustrate the applications
# This section is too short; include specific applications in which input features are sparse and Adagrad excels.
# Add reference to the claim “Mainly, it is a good choice for deep learning models with sparse input features”.
* A conclusion section
* References

# Too few references overall, you should aggregate information from multiple sources (even if the base algorithm itself comes from a singular paper)

== [[McCormick envelopes|McCormick Envelopes]] ==

* Author list: OK but I suggest removing NetID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
*# First sentence is hard to read. Please consider keeping sentences below 25-30 words.
*# No references provided. Please cite all sources.
*# Figure 1 is provided in the middle between two sections. Please include in the introduction section.
* Theory, methodology, and/or algorithmic discussions
*# References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
*# When using mathematical expressions and symbols, please use the equation editor. (e.g., x*y, exy + y, sin (x+y) - x2)
* At least one numerical example
*# Please add a few sentences to show the transition from problem to solution.
*# For the sample GAMS code, please place it in a code box
* A section to discuss and/or illustrate the applications
*# Having a list is not enough. Please explain at least three applications in a few sentences each.
*# This section should be at least a paragraph to discuss relevant applications. Each application should be explicitly linked to the page topic. A few keywords do not meet the requirement at all.
* A conclusion section:
* References
*# References are not expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
*# Please follow the standard reference style - the current format is incorrect.