https://optimization.cbe.cornell.edu/api.php?action=feedcontributions&user=Asa279&feedformat=atomCornell University Computational Optimization Open Textbook - Optimization Wiki - User contributions [en]2023-10-01T23:04:39ZUser contributionsMediaWiki 1.35.0https://optimization.cbe.cornell.edu/index.php?title=Weighted_sum_method&diff=6892Weighted sum method2022-11-10T20:16:51Z<p>Asa279: </p>
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<div>Authors: Maxwell Brown (mlb446), Nicole Tellado (nmt48), Sammy Kubesch(sk3246), Denise Lainez (dl2237), Abdulmohsen Albelushi (ama346)</div>Asa279https://optimization.cbe.cornell.edu/index.php?title=Branch_and_price&diff=6891Branch and price2022-11-10T20:16:14Z<p>Asa279: </p>
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<div>Authors: James Ramos (jr2336), Nathan Kendrick (nrk43), Daniel Lane (del226), Mike Chalawsky (mc2483)</div>Asa279https://optimization.cbe.cornell.edu/index.php?title=Ellipsoid_method&diff=6890Ellipsoid method2022-11-10T20:15:04Z<p>Asa279: </p>
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<div>Authors: Susan Long (scl227), Aidan Cronin (ac2425), Michael Truong (mt656), William McLaughlin (wdm66), Stephen Alexander (swa42)</div>Asa279https://optimization.cbe.cornell.edu/index.php?title=Model_predictive_control&diff=6889Model predictive control2022-11-10T20:14:44Z<p>Asa279: </p>
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<div>Authors: Tianqi Xiao (tx72)</div>Asa279https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization&diff=6888Quantum computing for optimization2022-11-10T20:14:16Z<p>Asa279: </p>
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<div>Authors: Luxin Xu (lx75), Yirun Mao (ym486), Haohao Chen (hc829), Yuxi Wei (yw2473)<br />
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== Introduction ==<br />
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Quantum computing (QC) is the next frontier in computation and has attracted a lot of attention from the scientific community in recent years. QC provides a novel approach to help solve some of the most complex optimization problems while offering an essential speed advantage over classical methods. <ref> M. A. Nielsen and I. L. Chuang, ''Quantum Computation and Quantum Information'' Cambridge University Press, 2010, p. 702.</ref> This is evident from QC techniques like Shor’s algorithm for integer factorization, <ref> P. W. Shor, "Algorithms for quantum computation: discrete logarithms and factoring," presented at the Proceedings 35th Annual Symposium on ''Foundations of Computer Science'', 1994. </ref> and Grover's search algorithm for unstructured databases. <ref> L. K. Grover, [https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.79.325 "Quantum Mechanics Helps in Searching for a Needle in a Haystack]," ''Physical Review Letters'', vol. 79, pp. 325-328, 1997. </ref> Quantum adiabatic algorithms too are efficient optimization strategies that quickly search over the solution space. Quantum computers perform computation by inducing quantum speedups whose scaling far exceeds the capability of the most powerful classical computers. QC’s major applications can be perceived in areas of optimization, machine learning, cryptography, and quantum chemistry. <ref> J. Preskill, [https://ui.adsabs.harvard.edu/abs/2018arXiv180100862P "Quantum Computing in the NISQ era and beyond"] </ref> Despite the contrasting views on QC’s viability and performance, there is no doubt that QC holds great promise to open up a new era of computing. <br />
<br />
[[Riemannian optimization]]<br />
[[Evolutionary algorithms]]<br />
[[Alternating direction method of multipliers]]<br />
[[Sequential linear programming]]<br />
[[Bayesian Optimization]]<br />
[[Monte Carlo methods]]<br />
[[Particle swarm optimization]]<br />
[[Support vector clustering]]<br />
[[Quantum computing for optimization]]<br />
[[Model predictive control]]<br />
[[Ellipsoid method]]<br />
[[Weighted sum method]]<br />
[[Weighted metric method]]<br />
[[Stochastic variance reduced gradient]]<br />
[[Branch and price]]<br />
[[Linear complementarity problem]]<br />
[[Parametric linear programming]]<br />
[[Convex optimization in classification problems]]<br />
[[Monte Carlo for machine learning applications]]<br />
<br />
<br />
== References ==<br />
<references /></div>Asa279https://optimization.cbe.cornell.edu/index.php?title=Support_vector_clustering&diff=6887Support vector clustering2022-11-10T20:13:12Z<p>Asa279: </p>
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<div>Authors: Miao Hu (mh2286), Hanjiang Gu (hg469), Jialin Liu(jl3625), Xiaochang Liu (xl836), Jintao Gu (jg2337)</div>Asa279https://optimization.cbe.cornell.edu/index.php?title=Weighted_metric_method&diff=6886Weighted metric method2022-11-10T20:12:49Z<p>Asa279: </p>
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<div>Authors: Ty McHugh (tjm328), Jaime Lugo-Castillo (jal543), Nazia Aktas (nta8), Malhon Godwin (mtg73), Zeeshan Bagban (zsb7)</div>Asa279https://optimization.cbe.cornell.edu/index.php?title=Particle_swarm_optimization&diff=6885Particle swarm optimization2022-11-10T20:12:16Z<p>Asa279: </p>
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<div>[[Jessie Jiang|Authors]]: Jessie Jiang (jj438), Jieyang Liu (jl4329), Yanming Huang (yh396)<br />
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==Introduction==<br />
Particle swarm optimization (PSO) is a heuristic approach to solve optimization problems. The original idea was proposed by Kennedy and Eberhart (1995) to simulate animals’ social interactions (e.g., a flock of birds searching for food). The intuition is to place a number of simple particles in the search space. Each of them evaluates the objective function at the current location. Based on each particle’s own and some other swarm members’ collective history of best locations, each particle will determine its movement to the next location and start the new iteration. Eventually the swarm as a whole is likely to move to an optimum of the objective function.<br />
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Compared to classic optimization methods such as gradient descent and quasi-newton methods, PSO does not use gradients of the problem and makes few or no assumptions about the problem being optimized. However, there is also no theoretical guarantee that PSO can find the global optimum. Indeed, it is challenging to understand swarm intelligence through theoretical analysis due to its apparent simplicity.<br />
<br />
==Canonical Forms==<br />
Each particle in the swarm has a set of D-dimensional vectors, where D is the dimensionality of the search space. The set comprises its current location <math>x_i</math>, the best location in its own history <math>p_i</math>, and its velocity to the next location <math>v_i</math>. Each location in the search space is evaluated as a problem solution, and the location with the lowest objective value is considered the ‘best’ location to be stored in <math>p_i</math>, if the objective function is minimized. The new location is chosen by simply adding the velocity vector to the current location, <math>v_i + x_i</math>. There are different ways to determine the velocity, which is the main source of the various forms. Through communication with other particles in its local neighborhood, a particle gets to know the neighborhood best location, <math>p_g</math>. The main idea is that each particle’s velocity is iteratively adjusted so that the particle stochastically oscillates around its own best location <math>p_i</math> and the collective best location <math>p_g </math>. Algorithm 1 presents the original form of PSO.</div>Asa279https://optimization.cbe.cornell.edu/index.php?title=Convex_optimization_in_classification_problems&diff=6884Convex optimization in classification problems2022-11-10T20:11:37Z<p>Asa279: </p>
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<div>Authors: Eddie Freedman (ebf45)</div>Asa279https://optimization.cbe.cornell.edu/index.php?title=Stochastic_variance_reduced_gradient&diff=6883Stochastic variance reduced gradient2022-11-10T20:11:12Z<p>Asa279: </p>
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<div>Authors: Rishi Kaashyap Balaji (rb849), Shreshtha Dhankar (sd728), Geet Chheda (gac222), Kalash Pai (krp57), Dhrumil Patel (djp265)</div>Asa279https://optimization.cbe.cornell.edu/index.php?title=Monte_Carlo_for_machine_learning_applications&diff=6882Monte Carlo for machine learning applications2022-11-10T20:10:50Z<p>Asa279: </p>
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<div>Authors:Alex Albertsson (aka85), Rong Chen (rc674), Ronaldo Li (jl3638), Connor Thomas (cpt37)</div>Asa279https://optimization.cbe.cornell.edu/index.php?title=Linear_complementarity_problem&diff=6881Linear complementarity problem2022-11-10T20:10:27Z<p>Asa279: </p>
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<div>Authors: Max Bodley (mjb559), Mavis Ofori-Brown (meo78), Preeti Uppuluri (pnu3), David Aitchison (dca64), Barrett Downs (bcd49)</div>Asa279https://optimization.cbe.cornell.edu/index.php?title=Sequential_linear_programming&diff=6880Sequential linear programming2022-11-10T20:09:51Z<p>Asa279: </p>
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<div>Authors: Nathan Preuus (nnp25)</div>Asa279https://optimization.cbe.cornell.edu/index.php?title=Alternating_direction_method_of_multipliers&diff=6879Alternating direction method of multipliers2022-11-10T20:09:29Z<p>Asa279: </p>
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<div>Authors: Kaleb Smith (ks885)</div>Asa279https://optimization.cbe.cornell.edu/index.php?title=Evolutionary_algorithms&diff=6878Evolutionary algorithms2022-11-10T20:08:55Z<p>Asa279: </p>
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<div>Authors :Tony Nugroho (ln255), Emily Yueh (ey84), Zirui Liu (zl398), Yanshu Li (yl2265), Ahmed Habib (amh362)</div>Asa279https://optimization.cbe.cornell.edu/index.php?title=Parametric_linear_programming&diff=6877Parametric linear programming2022-11-10T20:07:58Z<p>Asa279: </p>
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<div>Authors: Sandesh Sadawarte (sss286)</div>Asa279https://optimization.cbe.cornell.edu/index.php?title=2021_Cornell_Optimization_Open_Textbook_Feedback&diff=61662021 Cornell Optimization Open Textbook Feedback2021-12-18T21:35:57Z<p>Asa279: /* Optimization in game theory */</p>
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<div>== [[Lagrangean duality|Lagrangian duality]] ==<br />
* Author list, sections and TOC<br />
* An introduction of the topic<br />
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* Theory, methodology, and/or algorithmic discussions<br />
# 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.<br />
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* At least one numerical example<br />
# Please update the dual objective function and domain of dual variables accordingly.<br />
* A section to discuss and/or illustrate the applications<br />
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* A conclusion section<br />
* References<br />
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== [[Disjunctive inequalities|Disjunctive Inequalities]] ==<br />
* Author list<br />
* An introduction of the topic<br />
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* Theory, methodology, and/or algorithmic discussions<br />
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* At least one numerical example<br />
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* A section to discuss and/or illustrate the applications<br />
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* A conclusion section<br />
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* References<br />
==[[Stochastic programming|Stochastic Programming]]==<br />
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* An introduction of the topic<br />
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.<br />
* Theory, methodology, and/or algorithmic discussions<br />
** The symbol “xi” in the methodology subsection should be explained.<br />
** The inline notations (`x1`, `s1`) should also be typed using LaTex.<br />
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* A section to discuss and/or illustrate the applications;<br />
# I suggest eliminating citing the last name of the first author (i.e. Zhou et al.)<br />
==[[Exponential transformation|Exponential Transformation]]==<br />
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* Author list<br />
* An introduction of the topic<br />
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* Theory, methodology, and/or algorithmic discussions<br />
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* At least one numerical example<br />
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* A section to discuss and/or illustrate the applications<br />
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* A conclusion section<br />
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* References<br />
== [[Portfolio optimization|Portfolio Optimization]] ==<br />
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* Author list<br />
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* An introduction of the topic<br />
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* Theory, methodology, and/or algorithmic discussions<br />
# 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.”<br />
* At least one numerical example<br />
# Fix misspelling “dolling decision variables”.<br />
* A section to discuss and/or illustrate the applications<br />
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* A conclusion section<br />
# Need some commas here (second sentence hard to read).<br />
* References<br />
# Remove white space between end of sentences and reference numbers.<br />
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== [[Chance-constraint method|Chance constraint method]] ==<br />
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* Author list: <br />
* An introduction of the topic<br />
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* Theory, methodology, and/or algorithmic discussions<br />
# Some normal text was expressed as equation.<br />
* At least one numerical example<br />
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* A section to discuss and/or illustrate the applications<br />
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* A conclusion section<br />
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* References<br />
== [[Bayesian Optimization]] ==<br />
* Introduction<br />
# Discussion on applications should be moved to a separate section.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Captions need reformatting.<br />
# Consider italicizing keywords rather than bolding.<br />
# Please add a citation to the first sentence. <br />
# Avoid pronouns such as “we”.<br />
# Acquisition function figure could be made larger and clearer to improve readability.<br />
* At least one numerical example<br />
# Any references to functions or methods in code ‘e.g. fmin’ should be properly formatted as code-stylized text.<br />
# Please use the equation editor for min, st., etc.<br />
# Avoid including a figure of the code for this example and explicitly describe the steps to the modeling and solution process instead. <br />
# Avoid pronouns such as “our” and “we”.<br />
* References<br />
# 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]]<br />
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== [[Conjugate gradient methods]] ==<br />
* Theory, methodology, and/or algorithmic discussions<br />
# All equations need to be better formatted.<br />
# Please indent equation blocks.<br />
# Please properly format pseudocode.<br />
* A conclusion section<br />
# Consider adding future research directions<br />
== [[Geometric programming|Geometric Programming]] ==<br />
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* Author list<br />
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* An introduction of the topic<br />
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* Theory, methodology, and/or algorithmic discussions<br />
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* At least one numerical example<br />
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* A section to discuss and/or illustrate the applications<br />
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* A conclusion section:<br />
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* References<br />
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== [[Adam]] ==<br />
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* Author list <br />
* An introduction of the topic<br />
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* Theory, methodology, and/or algorithmic discussions<br />
# 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.<br />
* At least one numerical example<br />
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* A section to discuss and/or illustrate the applications<br />
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* A conclusion section <br />
* References<br />
== [[A-star algorithm|a* algorithm]] ==<br />
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* Author list<br />
* An introduction of the topic:<br />
# Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.<br />
# There are no citations in the introduction. Please cite every source.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Please add the mathematical description of the algorithm. (Insufficient) <br />
# 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”.<br />
* At least one numerical example<br />
# The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.<br />
* A section to discuss and/or illustrate the applications<br />
* A conclusion section<br />
* References<br />
<br />
== [[Job shop scheduling|Job-Shop Scheduling Problem]] ==<br />
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* An introduction of the topic<br />
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* Theory, methodology, and/or algorithmic discussions<br />
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# 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.<br />
* At least one numerical example<br />
* A section to discuss and/or illustrate the applications<br />
* A conclusion section<br />
* References<br />
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== [[Optimization in game theory]] ==<br />
<br />
* Author list<br />
* An introduction of the topic<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm. <br />
# Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.<br />
# Formatting (incomplete). <br />
* At least one numerical example<br />
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* A section to discuss and/or illustrate the applications<br />
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* A conclusion section<br />
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* References<br />
# Incorrect reference style. <br />
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== [[Trust-region methods]] ==<br />
* An introduction of the topic<br />
** Avoid pronouns such as “we”. This goes for all other sections as well.<br />
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* Theory, methodology, and/or algorithmic discussions<br />
# Organization of ideas in this section needs work.<br />
# 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.<br />
# Please format the algorithm in proper algorithmic pseudocode format.<br />
* References<br />
# Incorrect reference style.<br />
<br />
*There are numerous misspellings, grammatical errors, and incorrect claims. Please fix these.<br />
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== [[Momentum]] ==<br />
* An introduction of the topic<br />
* Theory, methodology, and/or algorithmic discussions<br />
* At least one numerical example<br />
* A section to discuss and/or illustrate the applications<br />
* References<br />
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== [[Stochastic dynamic programming|Stochastic Dynamic programming]] ==<br />
<br />
* Author list<br />
# Remove cornell ID<br />
* An introduction of the topic<br />
# Discussion on applications should be moved to a separate section.<br />
* Theory, methodology, and/or algorithmic discussions <br />
# Remove the grey box background of equations.<br />
* At least one numerical example <br />
* A section to discuss and/or illustrate the applications <br />
* A conclusion section <br />
* References<br />
# 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]]<br />
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== [[Outer-approximation (OA)|Outer-approximation]] ==<br />
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* An introduction of the topic <br />
# See formatting guideline below<br />
# Avoid opinionated statements such as “MINLP problems are usually the hardest to solve”.<br />
# Rearrange the text such that the MINLP formulation is in the theory section and keep the introduction in words only. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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<br />
# The sentence “The Outer-Approximation (OA) algorithm was first proposed by Duran and and Grossmann in 1986 to solve MINLP problems.” needs a reference. <br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
# “Minimize” and “subject to” should be “min” and “s.t.” in MathType<br />
* A section to discuss and/or illustrate the applications<br />
# 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)<br />
# 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. <br />
# 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.<br />
# Consider reformatting to make steps more readable. Inserting spaces and breaking down steps would help. <br />
* A conclusion section<br />
# Too short. Consider discussion on future research direction and discussion on uncertainty<br />
# 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)”. <br />
* References<br />
# 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]]<br />
# Remove "Template:Reflist"<br />
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== [[Unit commitment problem]] ==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
# Please expand the introduction and avoid discussions of examples or specific applications in this section.<br />
# The sentence “Nonlinear, Non-convex programming optimization problem.” doesn’t make sense by itself and Non-convex shouldn’t be capitalized. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Figure/image format should be revised to better display the content.<br />
# Uppercase characters are used randomly (e.g., “non-convex transmission Constraints”) . Please follow correct language conventions for sentence structure.<br />
# 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. <br />
# Don’t say “written in matrix form as equation..” and just cite the reference, actually write out the equation. <br />
# Properly label the figure in this section with a figure number and improve visibility by making it larger. <br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
# Label the figures in this section properly with figure numbers.<br />
# Fix typo “while minimize” to “while minimizing”. <br />
# Avoid pronouns such as “we”. <br />
# Use the equation editor when typing equations. <br />
# 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.<br />
# 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).<br />
* A section to discuss and/or illustrate the applications:<br />
# I suggest changing the order of the subtitles here. For example, Single-Period Unit Commitment. <br />
* A conclusion section <br />
* References<br />
<br />
== [[Frank-Wolfe]] ==<br />
<br />
* Author list: <br />
* An introduction of the topic<br />
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* Theory, methodology, and/or algorithmic discussions<br />
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* At least one numerical example<br />
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* A section to discuss and/or illustrate the applications: <br />
* A conclusion section<br />
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* References<br />
== [[Line search methods|Line Search Method]] ==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
# Expand the introduction and avoid discussion on some of the specific steps in the solution process. <br />
# Provide references here. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# The phrase “are as follows” in the steepest descent method discussion needs to be followed by a colon. <br />
# Rephrase “has a nice convergence theory” and cite a reference for this claim.<br />
# Avoid pronouns such as “we”.<br />
# Add citation after “.. proposed by Phillip Wolfe in 1969.”<br />
# Figure 1 is between two sections. Please fix this issue. <br />
* At least one numerical example:<br />
# Add some space between iterations or subsection break<br />
* A section to discuss and/or illustrate the applications:<br />
# Too few references in this section. <br />
# Last paragraph makes some claims without references. <br />
* A conclusion section <br />
* References<br />
# 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]]<br />
# More references should be added. A simple Google Scholar search would give you many references.<br />
<br />
== [[Piecewise linear approximation|Piecewise Linear Approximation]]==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
# 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. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Fix typo “to force the x’ values become associated with”. <br />
* At least one numerical example <br />
* A section to discuss and/or illustrate the applications<br />
# Please aim for a maximum average sentence length of ~25 words. Some of these longer sentences are hard to read. <br />
* A conclusion section<br />
# 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.<br />
* References<br />
# Include hyperlinks to sources when possible.<br />
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== [[Mathematical programming with equilibrium constraints|Mathematical Programming with Equilibrium constraints]] ==<br />
<br />
* An introduction of the topic<br />
# 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.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# The meaning of parameter vector x is unclear. Please add more information or update if necessary.<br />
# 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.<br />
# Use equations instead of images to represent math programs and equations in the Implicit Descent and SQP subsection.<br />
# Apart from the steps for each solution technique, please also add a few sentences that describe each method.<br />
* At least one numerical example<br />
# Please define the terms like NCP, MP before abbreviating them. Also try not to unnecessarily abbreviate simple terms.<br />
# Equations should be typed by LaTex. Images for equations are unacceptable.<br />
# GAMS code is strongly discouraged. Please solve the problem "step-by-step".<br />
# 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.<br />
# Avoid using figures in the equations (subject to etc)<br />
* A section to discuss and/or illustrate the applications<br />
# Add references to “power management, highway pricing, chemical process engineering, and traffic planning.”<br />
* A conclusion section<br />
* References<br />
# 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]]<br />
# This Wiki contains very few references. Please check the list below and run a quick Google (Scholar) search to identify relevant literature.<br />
<br />
== [[Wing shape optimization|Wing shape Optimization]] ==<br />
<br />
* Author list: Remove cornell ID<br />
* 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.<br />
* An introduction of the topic<br />
# 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.)<br />
# Avoid discussion involving finer details of subject methods in this section. <br />
# In the titles, please change the font from bold to normal to have consistent formatting in the site. Same applies to box of content!<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Properly cite the CFD package, don’t just include a link. <br />
# Properly label the figure with a figure number.<br />
# Consider removing white space between isolated sentences to improve readability. <br />
* At least one numerical example<br />
# If you’ve already defined an abbreviation (CFD), there is no need to define it again. Just use the abbreviation.<br />
# Avoid pronouns such as “we” or “they”.<br />
# Phrases like “under the following” need to be followed by a colon.<br />
# 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.<br />
# “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. <br />
# Avoid inserting inline citations like “[4] introduces an..” as it is a bit informal when you don’t explicitly name the subject.<br />
# 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.<br />
# 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.<br />
# 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.<br />
# 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).<br />
* A section to discuss and/or illustrate the applications<br />
# Some characters are randomly capitalized in this section. <br />
* A conclusion section<br />
# 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. <br />
* References<br />
# 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]]<br />
<br />
== [[Interior-point method for NLP|Interior point method for NLP]] ==<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
** Need discussion about the concept of “central path” and the notion of self concordance<br />
** 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.<br />
** Fix typo “optimisation”.<br />
== [[AdaGrad|Adagrad]] ==<br />
* At least one numerical example<br />
# In the first sentence, “..take the following numerical example” should be followed by a colon. <br />
* A section to discuss and/or illustrate the applications<br />
# This section is too short; include specific applications in which input features are sparse and Adagrad excels.<br />
* <br />
* References <br />
<br />
# References not properly formatted<br />
<br />
== [[McCormick envelopes|McCormick Envelopes]] ==<br />
<br />
* Author list<br />
* Sections<br />
* An introduction of the topic<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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]]<br />
* At least one numerical example<br />
# Please add a few sentences to show the transition from problem to solution. <br />
# The solution technique should be clearly presented, and solved "step-by-step".<br />
* A section to discuss and/or illustrate the applications<br />
<br />
* A conclusion section: <br />
* References<br />
# Please follow the standard reference style - the current format is incorrect.<br />
<br />
== [[Branch and bound (BB) for MINLP|Branch and Bound for MINLP]] ==<br />
<br />
* Author list:<br />
** Remove NetIDS<br />
** Please remove abbreviations from the title (i.e. BB).<br />
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.<br />
* An introduction of the topic<br />
# 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]]<br />
# 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.<br />
# An illustration might be useful here. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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.<br />
# Use linked citations please as the Wiki template above. <br />
# 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.<br />
# Step 2 is missing yet it is referenced in the text multiple times. Please address this in addition to the above comment.<br />
# An illustration might be useful here as well. <br />
# Please explain what a Gomory Cut is. If the topic is available on optimization.cb.cornell.edu, you can link it. <br />
# The current equations seem to be simple text written in Italics. All mathematical symbols and equations should be formatted via LaTex.<br />
# Please format the math programs with equations and notations using formulations in lecture notes as templates.<br />
* At least one numerical example<br />
# Please add a few sentences to show the transition from problem to solution.<br />
# 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).<br />
# 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.<br />
# 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.<br />
# Make sure your example is not taken from a book as that is strictly disallowed. <br />
* A section to discuss and/or illustrate the applications<br />
# 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.<br />
# 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.<br />
* A conclusion section:<br />
# 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. <br />
# Please use summarizing sentences to describe earlier sections instead of introducing new concepts/discussion. <br />
* References<br />
# Too few references overall, you should aggregate information from multiple sources. A quick Google scholar search could provide relevant references.<br />
# 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]]<br />
# Please follow the standard reference style - the current format is incorrect.</div>Asa279https://optimization.cbe.cornell.edu/index.php?title=2021_Cornell_Optimization_Open_Textbook_Feedback&diff=61632021 Cornell Optimization Open Textbook Feedback2021-12-18T21:00:19Z<p>Asa279: /* McCormick Envelopes */</p>
<hr />
<div>== [[Lagrangean duality|Lagrangian duality]] ==<br />
* Author list, sections and TOC<br />
* An introduction of the topic<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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.<br />
<br />
* At least one numerical example<br />
# Please update the dual objective function and domain of dual variables accordingly.<br />
* A section to discuss and/or illustrate the applications<br />
<br />
* A conclusion section<br />
* References<br />
<br />
== [[Disjunctive inequalities|Disjunctive Inequalities]] ==<br />
* Author list<br />
* An introduction of the topic<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
<br />
* At least one numerical example<br />
<br />
* A section to discuss and/or illustrate the applications<br />
<br />
* A conclusion section<br />
<br />
* References<br />
==[[Stochastic programming|Stochastic Programming]]==<br />
<br />
* An introduction of the topic<br />
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.<br />
* Theory, methodology, and/or algorithmic discussions<br />
** The symbol “xi” in the methodology subsection should be explained.<br />
** The inline notations (`x1`, `s1`) should also be typed using LaTex.<br />
<br />
* A section to discuss and/or illustrate the applications;<br />
# I suggest eliminating citing the last name of the first author (i.e. Zhou et al.)<br />
==[[Exponential transformation|Exponential Transformation]]==<br />
<br />
* Author list<br />
* An introduction of the topic<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
<br />
* At least one numerical example<br />
<br />
* A section to discuss and/or illustrate the applications<br />
<br />
* A conclusion section<br />
<br />
* References<br />
== [[Portfolio optimization|Portfolio Optimization]] ==<br />
<br />
* Author list<br />
<br />
* An introduction of the topic<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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.”<br />
* At least one numerical example<br />
# Fix misspelling “dolling decision variables”.<br />
* A section to discuss and/or illustrate the applications<br />
<br />
* A conclusion section<br />
# Need some commas here (second sentence hard to read).<br />
* References<br />
# Remove white space between end of sentences and reference numbers.<br />
<br />
== [[Chance-constraint method|Chance constraint method]] ==<br />
<br />
* Author list: <br />
* An introduction of the topic<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Some normal text was expressed as equation.<br />
* At least one numerical example<br />
<br />
* A section to discuss and/or illustrate the applications<br />
<br />
* A conclusion section<br />
<br />
* References<br />
== [[Bayesian Optimization]] ==<br />
* Introduction<br />
# Discussion on applications should be moved to a separate section.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Captions need reformatting.<br />
# Consider italicizing keywords rather than bolding.<br />
# Please add a citation to the first sentence. <br />
# Avoid pronouns such as “we”.<br />
# Acquisition function figure could be made larger and clearer to improve readability.<br />
* At least one numerical example<br />
# Any references to functions or methods in code ‘e.g. fmin’ should be properly formatted as code-stylized text.<br />
# Please use the equation editor for min, st., etc.<br />
# Avoid including a figure of the code for this example and explicitly describe the steps to the modeling and solution process instead. <br />
# Avoid pronouns such as “our” and “we”.<br />
* References<br />
# 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]]<br />
<br />
== [[Conjugate gradient methods]] ==<br />
* Theory, methodology, and/or algorithmic discussions<br />
# All equations need to be better formatted.<br />
# Please indent equation blocks.<br />
# Please properly format pseudocode.<br />
* A conclusion section<br />
# Consider adding future research directions<br />
== [[Geometric programming|Geometric Programming]] ==<br />
<br />
* Author list<br />
<br />
* An introduction of the topic<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
<br />
* At least one numerical example<br />
<br />
* A section to discuss and/or illustrate the applications<br />
<br />
* A conclusion section:<br />
<br />
* References<br />
<br />
== [[Adam]] ==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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.<br />
* At least one numerical example<br />
<br />
* A section to discuss and/or illustrate the applications<br />
<br />
* A conclusion section <br />
* References<br />
== [[A-star algorithm|a* algorithm]] ==<br />
<br />
* Author list<br />
* An introduction of the topic:<br />
# Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.<br />
# There are no citations in the introduction. Please cite every source.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Please add the mathematical description of the algorithm. (Insufficient) <br />
# 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”.<br />
* At least one numerical example<br />
# The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.<br />
* A section to discuss and/or illustrate the applications<br />
* A conclusion section<br />
* References<br />
<br />
== [[Job shop scheduling|Job-Shop Scheduling Problem]] ==<br />
<br />
* An introduction of the topic<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
<br />
# 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.<br />
* At least one numerical example<br />
* A section to discuss and/or illustrate the applications<br />
* A conclusion section<br />
* References<br />
<br />
== [[Optimization in game theory]] ==<br />
<br />
* Author list<br />
* An introduction of the topic<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm. <br />
# Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.<br />
# Formatting (incomplete). <br />
* At least one numerical example<br />
<br />
* A section to discuss and/or illustrate the applications<br />
<br />
* A conclusion section<br />
# Please add more summarizing especially from theory sentences and avoid long sentences. <br />
* References<br />
# Incorrect reference style. <br />
<br />
== [[Trust-region methods]] ==<br />
* An introduction of the topic<br />
** Avoid pronouns such as “we”. This goes for all other sections as well.<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Organization of ideas in this section needs work.<br />
# 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.<br />
# Please format the algorithm in proper algorithmic pseudocode format.<br />
* References<br />
# Incorrect reference style.<br />
<br />
*There are numerous misspellings, grammatical errors, and incorrect claims. Please fix these.<br />
<br />
== [[Momentum]] ==<br />
* An introduction of the topic<br />
# 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.<br />
# Remove bold on “Momentum”.<br />
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# <br />
# 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.<br />
# 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.<br />
# Avoid pronouns such as “you”.<br />
* At least one numerical example<br />
# 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.<br />
# Please try to label the plots that explains what each line color means.<br />
# Starting point for SGD with momentum is different in explanation and the table. Please fix the same.<br />
* A section to discuss and/or illustrate the applications<br />
# Please use correct terminology like “optimizing non-convex functions” and not “training non-convex models”.<br />
* References<br />
# 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.<br />
<br />
== [[Stochastic dynamic programming|Stochastic Dynamic programming]] ==<br />
<br />
* Author list<br />
# Remove cornell ID<br />
* An introduction of the topic<br />
# Discussion on applications should be moved to a separate section.<br />
* Theory, methodology, and/or algorithmic discussions <br />
# Remove the grey box background of equations.<br />
* At least one numerical example <br />
* A section to discuss and/or illustrate the applications <br />
* A conclusion section <br />
* References<br />
# 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]]<br />
<br />
== [[Outer-approximation (OA)|Outer-approximation]] ==<br />
<br />
* An introduction of the topic <br />
# See formatting guideline below<br />
# Avoid opinionated statements such as “MINLP problems are usually the hardest to solve”.<br />
# Rearrange the text such that the MINLP formulation is in the theory section and keep the introduction in words only. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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<br />
# The sentence “The Outer-Approximation (OA) algorithm was first proposed by Duran and and Grossmann in 1986 to solve MINLP problems.” needs a reference. <br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
# “Minimize” and “subject to” should be “min” and “s.t.” in MathType<br />
* A section to discuss and/or illustrate the applications<br />
# 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)<br />
# 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. <br />
# 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.<br />
# Consider reformatting to make steps more readable. Inserting spaces and breaking down steps would help. <br />
* A conclusion section<br />
# Too short. Consider discussion on future research direction and discussion on uncertainty<br />
# 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)”. <br />
* References<br />
# 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]]<br />
# Remove "Template:Reflist"<br />
<br />
== [[Unit commitment problem]] ==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
# Please expand the introduction and avoid discussions of examples or specific applications in this section.<br />
# The sentence “Nonlinear, Non-convex programming optimization problem.” doesn’t make sense by itself and Non-convex shouldn’t be capitalized. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Figure/image format should be revised to better display the content.<br />
# Uppercase characters are used randomly (e.g., “non-convex transmission Constraints”) . Please follow correct language conventions for sentence structure.<br />
# 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. <br />
# Don’t say “written in matrix form as equation..” and just cite the reference, actually write out the equation. <br />
# Properly label the figure in this section with a figure number and improve visibility by making it larger. <br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
# Label the figures in this section properly with figure numbers.<br />
# Fix typo “while minimize” to “while minimizing”. <br />
# Avoid pronouns such as “we”. <br />
# Use the equation editor when typing equations. <br />
# 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.<br />
# 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).<br />
* A section to discuss and/or illustrate the applications:<br />
# I suggest changing the order of the subtitles here. For example, Single-Period Unit Commitment. <br />
* A conclusion section <br />
* References<br />
<br />
== [[Frank-Wolfe]] ==<br />
<br />
* Author list: <br />
* An introduction of the topic<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
<br />
* At least one numerical example<br />
<br />
* A section to discuss and/or illustrate the applications: <br />
* A conclusion section<br />
<br />
* References<br />
== [[Line search methods|Line Search Method]] ==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
# Expand the introduction and avoid discussion on some of the specific steps in the solution process. <br />
# Provide references here. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# The phrase “are as follows” in the steepest descent method discussion needs to be followed by a colon. <br />
# Rephrase “has a nice convergence theory” and cite a reference for this claim.<br />
# Avoid pronouns such as “we”.<br />
# Add citation after “.. proposed by Phillip Wolfe in 1969.”<br />
# Figure 1 is between two sections. Please fix this issue. <br />
* At least one numerical example:<br />
# Add some space between iterations or subsection break<br />
* A section to discuss and/or illustrate the applications:<br />
# Too few references in this section. <br />
# Last paragraph makes some claims without references. <br />
* A conclusion section <br />
* References<br />
# 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]]<br />
# More references should be added. A simple Google Scholar search would give you many references.<br />
<br />
== [[Piecewise linear approximation|Piecewise Linear Approximation]]==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
# 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. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Fix typo “to force the x’ values become associated with”. <br />
* At least one numerical example <br />
* A section to discuss and/or illustrate the applications<br />
# Please aim for a maximum average sentence length of ~25 words. Some of these longer sentences are hard to read. <br />
* A conclusion section<br />
# 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.<br />
* References<br />
# Include hyperlinks to sources when possible.<br />
<br />
== [[Mathematical programming with equilibrium constraints|Mathematical Programming with Equilibrium constraints]] ==<br />
<br />
* An introduction of the topic<br />
# 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.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# The meaning of parameter vector x is unclear. Please add more information or update if necessary.<br />
# 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.<br />
# Use equations instead of images to represent math programs and equations in the Implicit Descent and SQP subsection.<br />
# Apart from the steps for each solution technique, please also add a few sentences that describe each method.<br />
* At least one numerical example<br />
# Please define the terms like NCP, MP before abbreviating them. Also try not to unnecessarily abbreviate simple terms.<br />
# Equations should be typed by LaTex. Images for equations are unacceptable.<br />
# GAMS code is strongly discouraged. Please solve the problem "step-by-step".<br />
# 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.<br />
# Avoid using figures in the equations (subject to etc)<br />
* A section to discuss and/or illustrate the applications<br />
# Add references to “power management, highway pricing, chemical process engineering, and traffic planning.”<br />
* A conclusion section<br />
* References<br />
# 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]]<br />
# This Wiki contains very few references. Please check the list below and run a quick Google (Scholar) search to identify relevant literature.<br />
<br />
== [[Wing shape optimization|Wing shape Optimization]] ==<br />
<br />
* Author list: Remove cornell ID<br />
* 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.<br />
* An introduction of the topic<br />
# 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.)<br />
# Avoid discussion involving finer details of subject methods in this section. <br />
# In the titles, please change the font from bold to normal to have consistent formatting in the site. Same applies to box of content!<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Properly cite the CFD package, don’t just include a link. <br />
# Properly label the figure with a figure number.<br />
# Consider removing white space between isolated sentences to improve readability. <br />
* At least one numerical example<br />
# If you’ve already defined an abbreviation (CFD), there is no need to define it again. Just use the abbreviation.<br />
# Avoid pronouns such as “we” or “they”.<br />
# Phrases like “under the following” need to be followed by a colon.<br />
# 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.<br />
# “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. <br />
# Avoid inserting inline citations like “[4] introduces an..” as it is a bit informal when you don’t explicitly name the subject.<br />
# 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.<br />
# 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.<br />
# 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.<br />
# 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).<br />
* A section to discuss and/or illustrate the applications<br />
# Some characters are randomly capitalized in this section. <br />
* A conclusion section<br />
# 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. <br />
* References<br />
# 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]]<br />
<br />
== [[Interior-point method for NLP|Interior point method for NLP]] ==<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
** Need discussion about the concept of “central path” and the notion of self concordance<br />
** 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.<br />
** Fix typo “optimisation”.<br />
== [[AdaGrad|Adagrad]] ==<br />
* At least one numerical example<br />
# In the first sentence, “..take the following numerical example” should be followed by a colon. <br />
* A section to discuss and/or illustrate the applications<br />
# This section is too short; include specific applications in which input features are sparse and Adagrad excels.<br />
* <br />
* References <br />
<br />
# References not properly formatted<br />
<br />
== [[McCormick envelopes|McCormick Envelopes]] ==<br />
<br />
* Author list<br />
* Sections<br />
* An introduction of the topic<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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]]<br />
* At least one numerical example<br />
# Please add a few sentences to show the transition from problem to solution. <br />
# The solution technique should be clearly presented, and solved "step-by-step".<br />
* A section to discuss and/or illustrate the applications<br />
<br />
* A conclusion section: <br />
* References<br />
# Please follow the standard reference style - the current format is incorrect.<br />
<br />
== [[Branch and bound (BB) for MINLP|Branch and Bound for MINLP]] ==<br />
<br />
* Author list:<br />
** Remove NetIDS<br />
** Please remove abbreviations from the title (i.e. BB).<br />
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.<br />
* An introduction of the topic<br />
# 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]]<br />
# 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.<br />
# An illustration might be useful here. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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.<br />
# Use linked citations please as the Wiki template above. <br />
# 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.<br />
# Step 2 is missing yet it is referenced in the text multiple times. Please address this in addition to the above comment.<br />
# An illustration might be useful here as well. <br />
# Please explain what a Gomory Cut is. If the topic is available on optimization.cb.cornell.edu, you can link it. <br />
# The current equations seem to be simple text written in Italics. All mathematical symbols and equations should be formatted via LaTex.<br />
# Please format the math programs with equations and notations using formulations in lecture notes as templates.<br />
* At least one numerical example<br />
# Please add a few sentences to show the transition from problem to solution.<br />
# 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).<br />
# 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.<br />
# 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.<br />
# Make sure your example is not taken from a book as that is strictly disallowed. <br />
* A section to discuss and/or illustrate the applications<br />
# 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.<br />
# 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.<br />
* A conclusion section:<br />
# 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. <br />
# Please use summarizing sentences to describe earlier sections instead of introducing new concepts/discussion. <br />
* References<br />
# Too few references overall, you should aggregate information from multiple sources. A quick Google scholar search could provide relevant references.<br />
# 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]]<br />
# Please follow the standard reference style - the current format is incorrect.</div>Asa279https://optimization.cbe.cornell.edu/index.php?title=2021_Cornell_Optimization_Open_Textbook_Feedback&diff=61602021 Cornell Optimization Open Textbook Feedback2021-12-18T20:55:45Z<p>Asa279: /* Frank-Wolfe */</p>
<hr />
<div>== [[Lagrangean duality|Lagrangian duality]] ==<br />
* Author list, sections and TOC<br />
* An introduction of the topic<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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.<br />
<br />
* At least one numerical example<br />
# Please update the dual objective function and domain of dual variables accordingly.<br />
* A section to discuss and/or illustrate the applications<br />
<br />
* A conclusion section<br />
* References<br />
<br />
== [[Disjunctive inequalities|Disjunctive Inequalities]] ==<br />
* Author list<br />
* An introduction of the topic<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
<br />
* At least one numerical example<br />
<br />
* A section to discuss and/or illustrate the applications<br />
<br />
* A conclusion section<br />
<br />
* References<br />
==[[Stochastic programming|Stochastic Programming]]==<br />
<br />
* An introduction of the topic<br />
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.<br />
* Theory, methodology, and/or algorithmic discussions<br />
** The symbol “xi” in the methodology subsection should be explained.<br />
** The inline notations (`x1`, `s1`) should also be typed using LaTex.<br />
<br />
* A section to discuss and/or illustrate the applications;<br />
# I suggest eliminating citing the last name of the first author (i.e. Zhou et al.)<br />
==[[Exponential transformation|Exponential Transformation]]==<br />
<br />
* Author list<br />
* An introduction of the topic<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
<br />
* At least one numerical example<br />
<br />
* A section to discuss and/or illustrate the applications<br />
<br />
* A conclusion section<br />
<br />
* References<br />
== [[Portfolio optimization|Portfolio Optimization]] ==<br />
<br />
* Author list<br />
<br />
* An introduction of the topic<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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.”<br />
* At least one numerical example<br />
# Fix misspelling “dolling decision variables”.<br />
* A section to discuss and/or illustrate the applications<br />
<br />
* A conclusion section<br />
# Need some commas here (second sentence hard to read).<br />
* References<br />
# Remove white space between end of sentences and reference numbers.<br />
<br />
== [[Chance-constraint method|Chance constraint method]] ==<br />
<br />
* Author list: <br />
* An introduction of the topic<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Some normal text was expressed as equation.<br />
* At least one numerical example<br />
<br />
* A section to discuss and/or illustrate the applications<br />
<br />
* A conclusion section<br />
<br />
* References<br />
== [[Bayesian Optimization]] ==<br />
* Introduction<br />
# Discussion on applications should be moved to a separate section.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Captions need reformatting.<br />
# Consider italicizing keywords rather than bolding.<br />
# Please add a citation to the first sentence. <br />
# Avoid pronouns such as “we”.<br />
# Acquisition function figure could be made larger and clearer to improve readability.<br />
* At least one numerical example<br />
# Any references to functions or methods in code ‘e.g. fmin’ should be properly formatted as code-stylized text.<br />
# Please use the equation editor for min, st., etc.<br />
# Avoid including a figure of the code for this example and explicitly describe the steps to the modeling and solution process instead. <br />
# Avoid pronouns such as “our” and “we”.<br />
* References<br />
# 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]]<br />
<br />
== [[Conjugate gradient methods]] ==<br />
* Theory, methodology, and/or algorithmic discussions<br />
# All equations need to be better formatted.<br />
# Please indent equation blocks.<br />
# Please properly format pseudocode.<br />
* A conclusion section<br />
# Consider adding future research directions<br />
== [[Geometric programming|Geometric Programming]] ==<br />
<br />
* Author list<br />
<br />
* An introduction of the topic<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
<br />
* At least one numerical example<br />
<br />
* A section to discuss and/or illustrate the applications<br />
<br />
* A conclusion section:<br />
<br />
* References<br />
<br />
== [[Adam]] ==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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.<br />
* At least one numerical example<br />
<br />
* A section to discuss and/or illustrate the applications<br />
<br />
* A conclusion section <br />
* References<br />
== [[A-star algorithm|a* algorithm]] ==<br />
<br />
* Author list<br />
* An introduction of the topic:<br />
# Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.<br />
# There are no citations in the introduction. Please cite every source.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Please add the mathematical description of the algorithm. (Insufficient) <br />
# 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”.<br />
* At least one numerical example<br />
# The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.<br />
* A section to discuss and/or illustrate the applications<br />
* A conclusion section<br />
* References<br />
<br />
== [[Job shop scheduling|Job-Shop Scheduling Problem]] ==<br />
<br />
* An introduction of the topic<br />
# 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.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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.<br />
# 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.<br />
# 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.<br />
# 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.<br />
# Use LaTex code or equation editor to display all equations and variables in this section and all other sections as well.<br />
# Check grammar in this section. For example, phrases like “are as follows” need to be followed by a colon and not a period. <br />
# Consider rewriting the assumptions as a list in this section. <br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
# 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.<br />
# 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.<br />
# A numerical example should be simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments).<br />
* A section to discuss and/or illustrate the applications<br />
# 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. <br />
* A conclusion section<br />
# The meaning of “Operations applications” is unclear. Please explain or update if necessary.<br />
# The current conclusion section does not properly summarize the problem. Please refer to other Wiki examples for an idea to update the section accordingly.<br />
* References<br />
# 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]] <br />
# Please reference media sources like reference 5 appropriately.<br />
# A simple Google Scholar search would give you many "formal" references.<br />
<br />
== [[Optimization in game theory]] ==<br />
<br />
* Author list<br />
* An introduction of the topic<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm. <br />
# Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.<br />
# Formatting (incomplete). <br />
* At least one numerical example<br />
<br />
* A section to discuss and/or illustrate the applications<br />
<br />
* A conclusion section<br />
# Please add more summarizing especially from theory sentences and avoid long sentences. <br />
* References<br />
# Incorrect reference style. <br />
<br />
== [[Trust-region methods]] ==<br />
* An introduction of the topic<br />
** Avoid pronouns such as “we”. This goes for all other sections as well.<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Organization of ideas in this section needs work.<br />
# 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.<br />
# Please format the algorithm in proper algorithmic pseudocode format.<br />
* References<br />
# Incorrect reference style.<br />
<br />
*There are numerous misspellings, grammatical errors, and incorrect claims. Please fix these.<br />
<br />
== [[Momentum]] ==<br />
* An introduction of the topic<br />
# 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.<br />
# Remove bold on “Momentum”.<br />
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# <br />
# 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.<br />
# 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.<br />
# Avoid pronouns such as “you”.<br />
* At least one numerical example<br />
# 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.<br />
# Please try to label the plots that explains what each line color means.<br />
# Starting point for SGD with momentum is different in explanation and the table. Please fix the same.<br />
* A section to discuss and/or illustrate the applications<br />
# Please use correct terminology like “optimizing non-convex functions” and not “training non-convex models”.<br />
* References<br />
# 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.<br />
<br />
== [[Stochastic dynamic programming|Stochastic Dynamic programming]] ==<br />
<br />
* Author list<br />
# Remove cornell ID<br />
* An introduction of the topic<br />
# Discussion on applications should be moved to a separate section.<br />
* Theory, methodology, and/or algorithmic discussions <br />
# Remove the grey box background of equations.<br />
* At least one numerical example <br />
* A section to discuss and/or illustrate the applications <br />
* A conclusion section <br />
* References<br />
# 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]]<br />
<br />
== [[Outer-approximation (OA)|Outer-approximation]] ==<br />
<br />
* An introduction of the topic <br />
# See formatting guideline below<br />
# Avoid opinionated statements such as “MINLP problems are usually the hardest to solve”.<br />
# Rearrange the text such that the MINLP formulation is in the theory section and keep the introduction in words only. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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<br />
# The sentence “The Outer-Approximation (OA) algorithm was first proposed by Duran and and Grossmann in 1986 to solve MINLP problems.” needs a reference. <br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
# “Minimize” and “subject to” should be “min” and “s.t.” in MathType<br />
* A section to discuss and/or illustrate the applications<br />
# 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)<br />
# 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. <br />
# 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.<br />
# Consider reformatting to make steps more readable. Inserting spaces and breaking down steps would help. <br />
* A conclusion section<br />
# Too short. Consider discussion on future research direction and discussion on uncertainty<br />
# 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)”. <br />
* References<br />
# 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]]<br />
# Remove "Template:Reflist"<br />
<br />
== [[Unit commitment problem]] ==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
# Please expand the introduction and avoid discussions of examples or specific applications in this section.<br />
# The sentence “Nonlinear, Non-convex programming optimization problem.” doesn’t make sense by itself and Non-convex shouldn’t be capitalized. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Figure/image format should be revised to better display the content.<br />
# Uppercase characters are used randomly (e.g., “non-convex transmission Constraints”) . Please follow correct language conventions for sentence structure.<br />
# 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. <br />
# Don’t say “written in matrix form as equation..” and just cite the reference, actually write out the equation. <br />
# Properly label the figure in this section with a figure number and improve visibility by making it larger. <br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
# Label the figures in this section properly with figure numbers.<br />
# Fix typo “while minimize” to “while minimizing”. <br />
# Avoid pronouns such as “we”. <br />
# Use the equation editor when typing equations. <br />
# 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.<br />
# 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).<br />
* A section to discuss and/or illustrate the applications:<br />
# I suggest changing the order of the subtitles here. For example, Single-Period Unit Commitment. <br />
* A conclusion section <br />
* References<br />
<br />
== [[Frank-Wolfe]] ==<br />
<br />
* Author list: <br />
* An introduction of the topic<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
<br />
* At least one numerical example<br />
<br />
* A section to discuss and/or illustrate the applications: <br />
* A conclusion section<br />
<br />
* References<br />
== [[Line search methods|Line Search Method]] ==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
# Expand the introduction and avoid discussion on some of the specific steps in the solution process. <br />
# Provide references here. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# The phrase “are as follows” in the steepest descent method discussion needs to be followed by a colon. <br />
# Rephrase “has a nice convergence theory” and cite a reference for this claim.<br />
# Avoid pronouns such as “we”.<br />
# Add citation after “.. proposed by Phillip Wolfe in 1969.”<br />
# Figure 1 is between two sections. Please fix this issue. <br />
* At least one numerical example:<br />
# Add some space between iterations or subsection break<br />
* A section to discuss and/or illustrate the applications:<br />
# Too few references in this section. <br />
# Last paragraph makes some claims without references. <br />
* A conclusion section <br />
* References<br />
# 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]]<br />
# More references should be added. A simple Google Scholar search would give you many references.<br />
<br />
== [[Piecewise linear approximation|Piecewise Linear Approximation]]==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
# 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. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Fix typo “to force the x’ values become associated with”. <br />
* At least one numerical example <br />
* A section to discuss and/or illustrate the applications<br />
# Please aim for a maximum average sentence length of ~25 words. Some of these longer sentences are hard to read. <br />
* A conclusion section<br />
# 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.<br />
* References<br />
# Include hyperlinks to sources when possible.<br />
<br />
== [[Mathematical programming with equilibrium constraints|Mathematical Programming with Equilibrium constraints]] ==<br />
<br />
* An introduction of the topic<br />
# 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.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# The meaning of parameter vector x is unclear. Please add more information or update if necessary.<br />
# 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.<br />
# Use equations instead of images to represent math programs and equations in the Implicit Descent and SQP subsection.<br />
# Apart from the steps for each solution technique, please also add a few sentences that describe each method.<br />
* At least one numerical example<br />
# Please define the terms like NCP, MP before abbreviating them. Also try not to unnecessarily abbreviate simple terms.<br />
# Equations should be typed by LaTex. Images for equations are unacceptable.<br />
# GAMS code is strongly discouraged. Please solve the problem "step-by-step".<br />
# 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.<br />
# Avoid using figures in the equations (subject to etc)<br />
* A section to discuss and/or illustrate the applications<br />
# Add references to “power management, highway pricing, chemical process engineering, and traffic planning.”<br />
* A conclusion section<br />
* References<br />
# 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]]<br />
# This Wiki contains very few references. Please check the list below and run a quick Google (Scholar) search to identify relevant literature.<br />
<br />
== [[Wing shape optimization|Wing shape Optimization]] ==<br />
<br />
* Author list: Remove cornell ID<br />
* 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.<br />
* An introduction of the topic<br />
# 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.)<br />
# Avoid discussion involving finer details of subject methods in this section. <br />
# In the titles, please change the font from bold to normal to have consistent formatting in the site. Same applies to box of content!<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Properly cite the CFD package, don’t just include a link. <br />
# Properly label the figure with a figure number.<br />
# Consider removing white space between isolated sentences to improve readability. <br />
* At least one numerical example<br />
# If you’ve already defined an abbreviation (CFD), there is no need to define it again. Just use the abbreviation.<br />
# Avoid pronouns such as “we” or “they”.<br />
# Phrases like “under the following” need to be followed by a colon.<br />
# 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.<br />
# “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. <br />
# Avoid inserting inline citations like “[4] introduces an..” as it is a bit informal when you don’t explicitly name the subject.<br />
# 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.<br />
# 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.<br />
# 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.<br />
# 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).<br />
* A section to discuss and/or illustrate the applications<br />
# Some characters are randomly capitalized in this section. <br />
* A conclusion section<br />
# 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. <br />
* References<br />
# 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]]<br />
<br />
== [[Interior-point method for NLP|Interior point method for NLP]] ==<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
** Need discussion about the concept of “central path” and the notion of self concordance<br />
** 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.<br />
** Fix typo “optimisation”.<br />
== [[AdaGrad|Adagrad]] ==<br />
* At least one numerical example<br />
# In the first sentence, “..take the following numerical example” should be followed by a colon. <br />
* A section to discuss and/or illustrate the applications<br />
# This section is too short; include specific applications in which input features are sparse and Adagrad excels.<br />
* <br />
* References <br />
<br />
# References not properly formatted<br />
<br />
== [[McCormick envelopes|McCormick Envelopes]] ==<br />
<br />
* Author list: OK but I suggest removing NetID<br />
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.<br />
* An introduction of the topic<br />
# First sentence is hard to read. Please consider keeping sentences below 25-30 words. <br />
# No references provided. Please cite all sources. <br />
# Figure 1 is provided in the middle between two sections. Please include in the introduction section. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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]]<br />
# When using mathematical expressions and symbols, please use the equation editor. (e.g., x*y, exy + y, sin (x+y) - x2)<br />
* At least one numerical example<br />
# Please add a few sentences to show the transition from problem to solution. <br />
# The solution technique should be clearly presented, and solved "step-by-step".<br />
# GAMS code is unnecessary. Please provide detailed step-by-step calculation results.<br />
* A section to discuss and/or illustrate the applications<br />
# Having a list is not enough. Please explain at least three applications in a few sentences each. <br />
# 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.<br />
* A conclusion section: <br />
* References<br />
# 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]]<br />
# Please follow the standard reference style - the current format is incorrect.<br />
<br />
== [[Branch and bound (BB) for MINLP|Branch and Bound for MINLP]] ==<br />
<br />
* Author list:<br />
** Remove NetIDS<br />
** Please remove abbreviations from the title (i.e. BB).<br />
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.<br />
* An introduction of the topic<br />
# 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]]<br />
# 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.<br />
# An illustration might be useful here. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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.<br />
# Use linked citations please as the Wiki template above. <br />
# 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.<br />
# Step 2 is missing yet it is referenced in the text multiple times. Please address this in addition to the above comment.<br />
# An illustration might be useful here as well. <br />
# Please explain what a Gomory Cut is. If the topic is available on optimization.cb.cornell.edu, you can link it. <br />
# The current equations seem to be simple text written in Italics. All mathematical symbols and equations should be formatted via LaTex.<br />
# Please format the math programs with equations and notations using formulations in lecture notes as templates.<br />
* At least one numerical example<br />
# Please add a few sentences to show the transition from problem to solution.<br />
# 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).<br />
# 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.<br />
# 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.<br />
# Make sure your example is not taken from a book as that is strictly disallowed. <br />
* A section to discuss and/or illustrate the applications<br />
# 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.<br />
# 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.<br />
* A conclusion section:<br />
# 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. <br />
# Please use summarizing sentences to describe earlier sections instead of introducing new concepts/discussion. <br />
* References<br />
# Too few references overall, you should aggregate information from multiple sources. A quick Google scholar search could provide relevant references.<br />
# 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]]<br />
# Please follow the standard reference style - the current format is incorrect.</div>Asa279https://optimization.cbe.cornell.edu/index.php?title=2021_Cornell_Optimization_Open_Textbook_Feedback&diff=61572021 Cornell Optimization Open Textbook Feedback2021-12-18T20:48:49Z<p>Asa279: /* Optimization in game theory */</p>
<hr />
<div>== [[Lagrangean duality|Lagrangian duality]] ==<br />
* Author list, sections and TOC<br />
* An introduction of the topic<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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.<br />
<br />
* At least one numerical example<br />
# Please update the dual objective function and domain of dual variables accordingly.<br />
* A section to discuss and/or illustrate the applications<br />
<br />
* A conclusion section<br />
* References<br />
<br />
== [[Disjunctive inequalities|Disjunctive Inequalities]] ==<br />
* Author list<br />
* An introduction of the topic<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
<br />
* At least one numerical example<br />
<br />
* A section to discuss and/or illustrate the applications<br />
<br />
* A conclusion section<br />
<br />
* References<br />
==[[Stochastic programming|Stochastic Programming]]==<br />
<br />
* An introduction of the topic<br />
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.<br />
* Theory, methodology, and/or algorithmic discussions<br />
** The symbol “xi” in the methodology subsection should be explained.<br />
** The inline notations (`x1`, `s1`) should also be typed using LaTex.<br />
<br />
* A section to discuss and/or illustrate the applications;<br />
# I suggest eliminating citing the last name of the first author (i.e. Zhou et al.)<br />
==[[Exponential transformation|Exponential Transformation]]==<br />
<br />
* Author list<br />
* An introduction of the topic<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
<br />
* At least one numerical example<br />
<br />
* A section to discuss and/or illustrate the applications<br />
<br />
* A conclusion section<br />
<br />
* References<br />
== [[Portfolio optimization|Portfolio Optimization]] ==<br />
<br />
* Author list<br />
<br />
* An introduction of the topic<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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.”<br />
* At least one numerical example<br />
# Fix misspelling “dolling decision variables”.<br />
* A section to discuss and/or illustrate the applications<br />
<br />
* A conclusion section<br />
# Need some commas here (second sentence hard to read).<br />
* References<br />
# Remove white space between end of sentences and reference numbers.<br />
<br />
== [[Chance-constraint method|Chance constraint method]] ==<br />
<br />
* Author list: <br />
* An introduction of the topic<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Some normal text was expressed as equation.<br />
* At least one numerical example<br />
<br />
* A section to discuss and/or illustrate the applications<br />
<br />
* A conclusion section<br />
<br />
* References<br />
== [[Bayesian Optimization]] ==<br />
* Introduction<br />
# Discussion on applications should be moved to a separate section.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Captions need reformatting.<br />
# Consider italicizing keywords rather than bolding.<br />
# Please add a citation to the first sentence. <br />
# Avoid pronouns such as “we”.<br />
# Acquisition function figure could be made larger and clearer to improve readability.<br />
* At least one numerical example<br />
# Any references to functions or methods in code ‘e.g. fmin’ should be properly formatted as code-stylized text.<br />
# Please use the equation editor for min, st., etc.<br />
# Avoid including a figure of the code for this example and explicitly describe the steps to the modeling and solution process instead. <br />
# Avoid pronouns such as “our” and “we”.<br />
* References<br />
# 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]]<br />
<br />
== [[Conjugate gradient methods]] ==<br />
* Theory, methodology, and/or algorithmic discussions<br />
# All equations need to be better formatted.<br />
# Please indent equation blocks.<br />
# Please properly format pseudocode.<br />
* A conclusion section<br />
# Consider adding future research directions<br />
== [[Geometric programming|Geometric Programming]] ==<br />
<br />
* Author list<br />
# Remove cornell ID<br />
* An introduction of the topic<br />
# Examples of applications in this section use the same reference. Please cite their individual sources.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# The symbol denoting the domain in the definition of a monomial is unclear. Please clarify it or fix this if it is incorrect.<br />
# Definition of posynomial refers to section 2.1 which is missing from the Wiki (sections are not numbered in the main text).<br />
# 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.<br />
# Additional theory on the feasibility analysis could be provided in this section.<br />
* At least one numerical example<br />
# In the transformation example, the last two constraints could also be simplified. Please update them as well.<br />
* A section to discuss and/or illustrate the applications<br />
# The figure in this section needs to be labeled. <br />
# The figure needs to be resized and perhaps aligned to the center. <br />
* A conclusion section:<br />
# Please avoid vague language such as: “This makes”.<br />
# Please avoid opinionated statements: “one of the best ways”.<br />
* References<br />
# 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]]<br />
# This Wiki has very few references. A quick Google Scholar search may provide relevant references.<br />
<br />
== [[Adam]] ==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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.<br />
* At least one numerical example<br />
<br />
* A section to discuss and/or illustrate the applications<br />
<br />
* A conclusion section <br />
* References<br />
== [[A-star algorithm|a* algorithm]] ==<br />
<br />
* Author list<br />
* An introduction of the topic:<br />
# Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.<br />
# There are no citations in the introduction. Please cite every source.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Please add the mathematical description of the algorithm. (Insufficient) <br />
# 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”.<br />
* At least one numerical example<br />
# The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.<br />
* A section to discuss and/or illustrate the applications<br />
* A conclusion section<br />
* References<br />
<br />
== [[Job shop scheduling|Job-Shop Scheduling Problem]] ==<br />
<br />
* An introduction of the topic<br />
# 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.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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.<br />
# 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.<br />
# 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.<br />
# 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.<br />
# Use LaTex code or equation editor to display all equations and variables in this section and all other sections as well.<br />
# Check grammar in this section. For example, phrases like “are as follows” need to be followed by a colon and not a period. <br />
# Consider rewriting the assumptions as a list in this section. <br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
# 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.<br />
# 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.<br />
# A numerical example should be simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments).<br />
* A section to discuss and/or illustrate the applications<br />
# 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. <br />
* A conclusion section<br />
# The meaning of “Operations applications” is unclear. Please explain or update if necessary.<br />
# The current conclusion section does not properly summarize the problem. Please refer to other Wiki examples for an idea to update the section accordingly.<br />
* References<br />
# 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]] <br />
# Please reference media sources like reference 5 appropriately.<br />
# A simple Google Scholar search would give you many "formal" references.<br />
<br />
== [[Optimization in game theory]] ==<br />
<br />
* Author list<br />
* An introduction of the topic<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm. <br />
# Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.<br />
# Formatting (incomplete). <br />
* At least one numerical example<br />
<br />
* A section to discuss and/or illustrate the applications<br />
<br />
* A conclusion section<br />
# Please add more summarizing especially from theory sentences and avoid long sentences. <br />
* References<br />
# Incorrect reference style. <br />
<br />
== [[Trust-region methods]] ==<br />
* An introduction of the topic<br />
** Avoid pronouns such as “we”. This goes for all other sections as well.<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Organization of ideas in this section needs work.<br />
# 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.<br />
# Please format the algorithm in proper algorithmic pseudocode format.<br />
* References<br />
# Incorrect reference style.<br />
<br />
*There are numerous misspellings, grammatical errors, and incorrect claims. Please fix these.<br />
<br />
== [[Momentum]] ==<br />
* An introduction of the topic<br />
# 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.<br />
# Remove bold on “Momentum”.<br />
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# <br />
# 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.<br />
# 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.<br />
# Avoid pronouns such as “you”.<br />
* At least one numerical example<br />
# 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.<br />
# Please try to label the plots that explains what each line color means.<br />
# Starting point for SGD with momentum is different in explanation and the table. Please fix the same.<br />
* A section to discuss and/or illustrate the applications<br />
# Please use correct terminology like “optimizing non-convex functions” and not “training non-convex models”.<br />
* References<br />
# 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.<br />
<br />
== [[Stochastic dynamic programming|Stochastic Dynamic programming]] ==<br />
<br />
* Author list<br />
# Remove cornell ID<br />
* An introduction of the topic<br />
# Discussion on applications should be moved to a separate section.<br />
* Theory, methodology, and/or algorithmic discussions <br />
# Remove the grey box background of equations.<br />
* At least one numerical example <br />
* A section to discuss and/or illustrate the applications <br />
* A conclusion section <br />
* References<br />
# 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]]<br />
<br />
== [[Outer-approximation (OA)|Outer-approximation]] ==<br />
<br />
* An introduction of the topic <br />
# See formatting guideline below<br />
# Avoid opinionated statements such as “MINLP problems are usually the hardest to solve”.<br />
# Rearrange the text such that the MINLP formulation is in the theory section and keep the introduction in words only. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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<br />
# The sentence “The Outer-Approximation (OA) algorithm was first proposed by Duran and and Grossmann in 1986 to solve MINLP problems.” needs a reference. <br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
# “Minimize” and “subject to” should be “min” and “s.t.” in MathType<br />
* A section to discuss and/or illustrate the applications<br />
# 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)<br />
# 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. <br />
# 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.<br />
# Consider reformatting to make steps more readable. Inserting spaces and breaking down steps would help. <br />
* A conclusion section<br />
# Too short. Consider discussion on future research direction and discussion on uncertainty<br />
# 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)”. <br />
* References<br />
# 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]]<br />
# Remove "Template:Reflist"<br />
<br />
== [[Unit commitment problem]] ==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
# Please expand the introduction and avoid discussions of examples or specific applications in this section.<br />
# The sentence “Nonlinear, Non-convex programming optimization problem.” doesn’t make sense by itself and Non-convex shouldn’t be capitalized. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Figure/image format should be revised to better display the content.<br />
# Uppercase characters are used randomly (e.g., “non-convex transmission Constraints”) . Please follow correct language conventions for sentence structure.<br />
# 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. <br />
# Don’t say “written in matrix form as equation..” and just cite the reference, actually write out the equation. <br />
# Properly label the figure in this section with a figure number and improve visibility by making it larger. <br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
# Label the figures in this section properly with figure numbers.<br />
# Fix typo “while minimize” to “while minimizing”. <br />
# Avoid pronouns such as “we”. <br />
# Use the equation editor when typing equations. <br />
# 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.<br />
# 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).<br />
* A section to discuss and/or illustrate the applications:<br />
# I suggest changing the order of the subtitles here. For example, Single-Period Unit Commitment. <br />
* A conclusion section <br />
* References<br />
<br />
== [[Frank-Wolfe]] ==<br />
<br />
* Author list: <br />
* An introduction of the topic<br />
# I suggest highlighting disadvantages along with advantages. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# “[n x 1] matrix” please use the equation editor to express mathematical descriptions and symbols (p,b, etc)<br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
# Please show at least a few iterations. Even for smaller examples if needed. Report the final solution. <br />
# Please use the LaTex code or equation editor for min and include s.t., etc.<br />
# 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.<br />
* A section to discuss and/or illustrate the applications: <br />
* A conclusion section<br />
# Same as the introduction. Pros and cons should be evaluated together!<br />
* References<br />
# 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]]<br />
<br />
== [[Line search methods|Line Search Method]] ==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
# Expand the introduction and avoid discussion on some of the specific steps in the solution process. <br />
# Provide references here. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# The phrase “are as follows” in the steepest descent method discussion needs to be followed by a colon. <br />
# Rephrase “has a nice convergence theory” and cite a reference for this claim.<br />
# Avoid pronouns such as “we”.<br />
# Add citation after “.. proposed by Phillip Wolfe in 1969.”<br />
# Figure 1 is between two sections. Please fix this issue. <br />
* At least one numerical example:<br />
# Add some space between iterations or subsection break<br />
* A section to discuss and/or illustrate the applications:<br />
# Too few references in this section. <br />
# Last paragraph makes some claims without references. <br />
* A conclusion section <br />
* References<br />
# 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]]<br />
# More references should be added. A simple Google Scholar search would give you many references.<br />
<br />
== [[Piecewise linear approximation|Piecewise Linear Approximation]]==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
# 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. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Fix typo “to force the x’ values become associated with”. <br />
* At least one numerical example <br />
* A section to discuss and/or illustrate the applications<br />
# Please aim for a maximum average sentence length of ~25 words. Some of these longer sentences are hard to read. <br />
* A conclusion section<br />
# 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.<br />
* References<br />
# Include hyperlinks to sources when possible.<br />
<br />
== [[Mathematical programming with equilibrium constraints|Mathematical Programming with Equilibrium constraints]] ==<br />
<br />
* An introduction of the topic<br />
# 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.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# The meaning of parameter vector x is unclear. Please add more information or update if necessary.<br />
# 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.<br />
# Use equations instead of images to represent math programs and equations in the Implicit Descent and SQP subsection.<br />
# Apart from the steps for each solution technique, please also add a few sentences that describe each method.<br />
* At least one numerical example<br />
# Please define the terms like NCP, MP before abbreviating them. Also try not to unnecessarily abbreviate simple terms.<br />
# Equations should be typed by LaTex. Images for equations are unacceptable.<br />
# GAMS code is strongly discouraged. Please solve the problem "step-by-step".<br />
# 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.<br />
# Avoid using figures in the equations (subject to etc)<br />
* A section to discuss and/or illustrate the applications<br />
# Add references to “power management, highway pricing, chemical process engineering, and traffic planning.”<br />
* A conclusion section<br />
* References<br />
# 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]]<br />
# This Wiki contains very few references. Please check the list below and run a quick Google (Scholar) search to identify relevant literature.<br />
<br />
== [[Wing shape optimization|Wing shape Optimization]] ==<br />
<br />
* Author list: Remove cornell ID<br />
* 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.<br />
* An introduction of the topic<br />
# 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.)<br />
# Avoid discussion involving finer details of subject methods in this section. <br />
# In the titles, please change the font from bold to normal to have consistent formatting in the site. Same applies to box of content!<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Properly cite the CFD package, don’t just include a link. <br />
# Properly label the figure with a figure number.<br />
# Consider removing white space between isolated sentences to improve readability. <br />
* At least one numerical example<br />
# If you’ve already defined an abbreviation (CFD), there is no need to define it again. Just use the abbreviation.<br />
# Avoid pronouns such as “we” or “they”.<br />
# Phrases like “under the following” need to be followed by a colon.<br />
# 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.<br />
# “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. <br />
# Avoid inserting inline citations like “[4] introduces an..” as it is a bit informal when you don’t explicitly name the subject.<br />
# 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.<br />
# 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.<br />
# 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.<br />
# 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).<br />
* A section to discuss and/or illustrate the applications<br />
# Some characters are randomly capitalized in this section. <br />
* A conclusion section<br />
# 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. <br />
* References<br />
# 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]]<br />
<br />
== [[Interior-point method for NLP|Interior point method for NLP]] ==<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
** Need discussion about the concept of “central path” and the notion of self concordance<br />
** 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.<br />
** Fix typo “optimisation”.<br />
== [[AdaGrad|Adagrad]] ==<br />
* At least one numerical example<br />
# In the first sentence, “..take the following numerical example” should be followed by a colon. <br />
* A section to discuss and/or illustrate the applications<br />
# This section is too short; include specific applications in which input features are sparse and Adagrad excels.<br />
* <br />
* References <br />
<br />
# References not properly formatted<br />
<br />
== [[McCormick envelopes|McCormick Envelopes]] ==<br />
<br />
* Author list: OK but I suggest removing NetID<br />
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.<br />
* An introduction of the topic<br />
# First sentence is hard to read. Please consider keeping sentences below 25-30 words. <br />
# No references provided. Please cite all sources. <br />
# Figure 1 is provided in the middle between two sections. Please include in the introduction section. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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]]<br />
# When using mathematical expressions and symbols, please use the equation editor. (e.g., x*y, exy + y, sin (x+y) - x2)<br />
* At least one numerical example<br />
# Please add a few sentences to show the transition from problem to solution. <br />
# The solution technique should be clearly presented, and solved "step-by-step".<br />
# GAMS code is unnecessary. Please provide detailed step-by-step calculation results.<br />
* A section to discuss and/or illustrate the applications<br />
# Having a list is not enough. Please explain at least three applications in a few sentences each. <br />
# 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.<br />
* A conclusion section: <br />
* References<br />
# 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]]<br />
# Please follow the standard reference style - the current format is incorrect.<br />
<br />
== [[Branch and bound (BB) for MINLP|Branch and Bound for MINLP]] ==<br />
<br />
* Author list:<br />
** Remove NetIDS<br />
** Please remove abbreviations from the title (i.e. BB).<br />
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.<br />
* An introduction of the topic<br />
# 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]]<br />
# 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.<br />
# An illustration might be useful here. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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.<br />
# Use linked citations please as the Wiki template above. <br />
# 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.<br />
# Step 2 is missing yet it is referenced in the text multiple times. Please address this in addition to the above comment.<br />
# An illustration might be useful here as well. <br />
# Please explain what a Gomory Cut is. If the topic is available on optimization.cb.cornell.edu, you can link it. <br />
# The current equations seem to be simple text written in Italics. All mathematical symbols and equations should be formatted via LaTex.<br />
# Please format the math programs with equations and notations using formulations in lecture notes as templates.<br />
* At least one numerical example<br />
# Please add a few sentences to show the transition from problem to solution.<br />
# 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).<br />
# 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.<br />
# 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.<br />
# Make sure your example is not taken from a book as that is strictly disallowed. <br />
* A section to discuss and/or illustrate the applications<br />
# 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.<br />
# 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.<br />
* A conclusion section:<br />
# 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. <br />
# Please use summarizing sentences to describe earlier sections instead of introducing new concepts/discussion. <br />
* References<br />
# Too few references overall, you should aggregate information from multiple sources. A quick Google scholar search could provide relevant references.<br />
# 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]]<br />
# Please follow the standard reference style - the current format is incorrect.</div>Asa279https://optimization.cbe.cornell.edu/index.php?title=2021_Cornell_Optimization_Open_Textbook_Feedback&diff=61552021 Cornell Optimization Open Textbook Feedback2021-12-18T20:11:21Z<p>Asa279: /* a* algorithm */</p>
<hr />
<div>== [[Lagrangean duality|Lagrangian duality]] ==<br />
* Author list, sections and TOC<br />
# Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.<br />
# Remove cornell ID from Author list<br />
* An introduction of the topic<br />
# 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.<br />
# Definitions of LR and its relation to duality should be double checked and re-written.<br />
# Only one reference is present in this section. Please add more relevant references by expanding this section.<br />
# Consider merging the “introduction” and “history” sections.<br />
# In the titles, please change the font from bold to normal to have consistent formatting in the site.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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.<br />
# 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 (,).<br />
# 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.<br />
# 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.<br />
# Last step of the “process” subsection also needs updating according to the previous comments.<br />
# The inline notations should also be typed using LaTex.<br />
# Please use the LaTex code or equation editor for min, s.t., etc.<br />
* At least one numerical example<br />
# 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.<br />
# All consecutive steps need to be updated since the dual variables would be updated.<br />
# After substitution the nonlinear function should be further simplified. The current expression reads like a highly nonlinear function but can be easily simplified.<br />
# 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.<br />
# Please use the LaTex code or equation editor for min, s.t., etc.<br />
* A section to discuss and/or illustrate the applications<br />
# Bullet points could be used to state the last four real-world examples that explain the physical meaning of the primal and dual problems.<br />
# Add references for the last set of applications. <br />
* A conclusion section<br />
# This section contains a few typos. Please fix the same.<br />
* References<br />
# Some citations' hyperlinks are displaying.<br />
<br />
== [[Disjunctive inequalities|Disjunctive Inequalities]] ==<br />
* Author list<br />
* An introduction of the topic<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
<br />
* At least one numerical example<br />
<br />
* A section to discuss and/or illustrate the applications<br />
<br />
* A conclusion section<br />
<br />
* References<br />
==[[Stochastic programming|Stochastic Programming]]==<br />
<br />
* An introduction of the topic<br />
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.<br />
* Theory, methodology, and/or algorithmic discussions<br />
** The symbol “xi” in the methodology subsection should be explained.<br />
** The inline notations (`x1`, `s1`) should also be typed using LaTex.<br />
<br />
* A section to discuss and/or illustrate the applications;<br />
# I suggest eliminating citing the last name of the first author (i.e. Zhou et al.)<br />
==[[Exponential transformation|Exponential Transformation]]==<br />
<br />
* Author list<br />
* An introduction of the topic<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
<br />
* At least one numerical example<br />
<br />
* A section to discuss and/or illustrate the applications<br />
<br />
* A conclusion section<br />
<br />
* References<br />
== [[Portfolio optimization|Portfolio Optimization]] ==<br />
<br />
* Author list<br />
<br />
* An introduction of the topic<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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.”<br />
* At least one numerical example<br />
# Fix misspelling “dolling decision variables”.<br />
* A section to discuss and/or illustrate the applications<br />
<br />
* A conclusion section<br />
# Need some commas here (second sentence hard to read).<br />
* References<br />
# Remove white space between end of sentences and reference numbers.<br />
<br />
== [[Chance-constraint method|Chance constraint method]] ==<br />
<br />
* Author list: <br />
* An introduction of the topic<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Some normal text was expressed as equation.<br />
* At least one numerical example<br />
<br />
* A section to discuss and/or illustrate the applications<br />
<br />
* A conclusion section<br />
<br />
* References<br />
== [[Bayesian Optimization]] ==<br />
* Introduction<br />
# Discussion on applications should be moved to a separate section.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Captions need reformatting.<br />
# Consider italicizing keywords rather than bolding.<br />
# Please add a citation to the first sentence. <br />
# Avoid pronouns such as “we”.<br />
# Acquisition function figure could be made larger and clearer to improve readability.<br />
* At least one numerical example<br />
# Any references to functions or methods in code ‘e.g. fmin’ should be properly formatted as code-stylized text.<br />
# Please use the equation editor for min, st., etc.<br />
# Avoid including a figure of the code for this example and explicitly describe the steps to the modeling and solution process instead. <br />
# Avoid pronouns such as “our” and “we”.<br />
* References<br />
# 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]]<br />
<br />
== [[Conjugate gradient methods]] ==<br />
* Theory, methodology, and/or algorithmic discussions<br />
# All equations need to be better formatted.<br />
# Please indent equation blocks.<br />
# Please properly format pseudocode.<br />
* A conclusion section<br />
# Consider adding future research directions<br />
== [[Geometric programming|Geometric Programming]] ==<br />
<br />
* Author list<br />
# Remove cornell ID<br />
* An introduction of the topic<br />
# Examples of applications in this section use the same reference. Please cite their individual sources.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# The symbol denoting the domain in the definition of a monomial is unclear. Please clarify it or fix this if it is incorrect.<br />
# Definition of posynomial refers to section 2.1 which is missing from the Wiki (sections are not numbered in the main text).<br />
# 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.<br />
# Additional theory on the feasibility analysis could be provided in this section.<br />
* At least one numerical example<br />
# In the transformation example, the last two constraints could also be simplified. Please update them as well.<br />
* A section to discuss and/or illustrate the applications<br />
# The figure in this section needs to be labeled. <br />
# The figure needs to be resized and perhaps aligned to the center. <br />
* A conclusion section:<br />
# Please avoid vague language such as: “This makes”.<br />
# Please avoid opinionated statements: “one of the best ways”.<br />
* References<br />
# 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]]<br />
# This Wiki has very few references. A quick Google Scholar search may provide relevant references.<br />
<br />
== [[Adam]] ==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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.<br />
* At least one numerical example<br />
<br />
* A section to discuss and/or illustrate the applications<br />
<br />
* A conclusion section <br />
* References<br />
== [[A-star algorithm|a* algorithm]] ==<br />
<br />
* Author list<br />
* An introduction of the topic:<br />
# Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.<br />
# There are no citations in the introduction. Please cite every source.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Please add the mathematical description of the algorithm. (Insufficient) <br />
# 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”.<br />
* At least one numerical example<br />
# The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.<br />
* A section to discuss and/or illustrate the applications<br />
* A conclusion section<br />
* References<br />
<br />
== [[Job shop scheduling|Job-Shop Scheduling Problem]] ==<br />
<br />
* An introduction of the topic<br />
# 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.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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.<br />
# 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.<br />
# 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.<br />
# 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.<br />
# Use LaTex code or equation editor to display all equations and variables in this section and all other sections as well.<br />
# Check grammar in this section. For example, phrases like “are as follows” need to be followed by a colon and not a period. <br />
# Consider rewriting the assumptions as a list in this section. <br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
# 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.<br />
# 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.<br />
# A numerical example should be simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments).<br />
* A section to discuss and/or illustrate the applications<br />
# 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. <br />
* A conclusion section<br />
# The meaning of “Operations applications” is unclear. Please explain or update if necessary.<br />
# The current conclusion section does not properly summarize the problem. Please refer to other Wiki examples for an idea to update the section accordingly.<br />
* References<br />
# 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]] <br />
# Please reference media sources like reference 5 appropriately.<br />
# A simple Google Scholar search would give you many "formal" references.<br />
<br />
== [[Optimization in game theory]] ==<br />
<br />
* Author list: remove cornell IDs. <br />
* An introduction of the topic<br />
# 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]] <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Why only a subsection on "Nash Equilibrium" is included in "Theory" section? Please re-format.<br />
# Please edit references.<br />
# Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm. <br />
# Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.<br />
* At least one numerical example<br />
# Please organize the last part in a more readable format. Questions may be in bold and numbered, answers are more direct, etc.<br />
# Remember to cite all images and tables. <br />
# 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.<br />
* A section to discuss and/or illustrate the applications<br />
# Very good, link the reference and cite all sources. <br />
* A conclusion section<br />
# Please add more summarizing especially from theory sentences and avoid long sentences. <br />
* References<br />
# 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]]<br />
# Reference primary sources rather than Wikipedia<br />
# Incorrect reference style. Please correct.<br />
<br />
== [[Trust-region methods]] ==<br />
* An introduction of the topic<br />
** Avoid pronouns such as “we”. This goes for all other sections as well.<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Organization of ideas in this section needs work.<br />
# 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.<br />
# Please format the algorithm in proper algorithmic pseudocode format.<br />
* References<br />
# Incorrect reference style.<br />
<br />
*There are numerous misspellings, grammatical errors, and incorrect claims. Please fix these.<br />
<br />
== [[Momentum]] ==<br />
* An introduction of the topic<br />
# 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.<br />
# Remove bold on “Momentum”.<br />
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# <br />
# 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.<br />
# 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.<br />
# Avoid pronouns such as “you”.<br />
* At least one numerical example<br />
# 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.<br />
# Please try to label the plots that explains what each line color means.<br />
# Starting point for SGD with momentum is different in explanation and the table. Please fix the same.<br />
* A section to discuss and/or illustrate the applications<br />
# Please use correct terminology like “optimizing non-convex functions” and not “training non-convex models”.<br />
* References<br />
# 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.<br />
<br />
== [[Stochastic dynamic programming|Stochastic Dynamic programming]] ==<br />
<br />
* Author list<br />
# Remove cornell ID<br />
* An introduction of the topic<br />
# Discussion on applications should be moved to a separate section.<br />
* Theory, methodology, and/or algorithmic discussions <br />
# Remove the grey box background of equations.<br />
* At least one numerical example <br />
* A section to discuss and/or illustrate the applications <br />
* A conclusion section <br />
* References<br />
# 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]]<br />
<br />
== [[Outer-approximation (OA)|Outer-approximation]] ==<br />
<br />
* An introduction of the topic <br />
# See formatting guideline below<br />
# Avoid opinionated statements such as “MINLP problems are usually the hardest to solve”.<br />
# Rearrange the text such that the MINLP formulation is in the theory section and keep the introduction in words only. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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<br />
# The sentence “The Outer-Approximation (OA) algorithm was first proposed by Duran and and Grossmann in 1986 to solve MINLP problems.” needs a reference. <br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
# “Minimize” and “subject to” should be “min” and “s.t.” in MathType<br />
* A section to discuss and/or illustrate the applications<br />
# 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)<br />
# 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. <br />
# 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.<br />
# Consider reformatting to make steps more readable. Inserting spaces and breaking down steps would help. <br />
* A conclusion section<br />
# Too short. Consider discussion on future research direction and discussion on uncertainty<br />
# 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)”. <br />
* References<br />
# 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]]<br />
# Remove "Template:Reflist"<br />
<br />
== [[Unit commitment problem]] ==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
# Please expand the introduction and avoid discussions of examples or specific applications in this section.<br />
# The sentence “Nonlinear, Non-convex programming optimization problem.” doesn’t make sense by itself and Non-convex shouldn’t be capitalized. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Figure/image format should be revised to better display the content.<br />
# Uppercase characters are used randomly (e.g., “non-convex transmission Constraints”) . Please follow correct language conventions for sentence structure.<br />
# 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. <br />
# Don’t say “written in matrix form as equation..” and just cite the reference, actually write out the equation. <br />
# Properly label the figure in this section with a figure number and improve visibility by making it larger. <br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
# Label the figures in this section properly with figure numbers.<br />
# Fix typo “while minimize” to “while minimizing”. <br />
# Avoid pronouns such as “we”. <br />
# Use the equation editor when typing equations. <br />
# 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.<br />
# 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).<br />
* A section to discuss and/or illustrate the applications:<br />
# I suggest changing the order of the subtitles here. For example, Single-Period Unit Commitment. <br />
* A conclusion section <br />
* References<br />
<br />
== [[Frank-Wolfe]] ==<br />
<br />
* Author list: <br />
* An introduction of the topic<br />
# I suggest highlighting disadvantages along with advantages. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# “[n x 1] matrix” please use the equation editor to express mathematical descriptions and symbols (p,b, etc)<br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
# Please show at least a few iterations. Even for smaller examples if needed. Report the final solution. <br />
# Please use the LaTex code or equation editor for min and include s.t., etc.<br />
# 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.<br />
* A section to discuss and/or illustrate the applications: <br />
* A conclusion section<br />
# Same as the introduction. Pros and cons should be evaluated together!<br />
* References<br />
# 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]]<br />
<br />
== [[Line search methods|Line Search Method]] ==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
# Expand the introduction and avoid discussion on some of the specific steps in the solution process. <br />
# Provide references here. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# The phrase “are as follows” in the steepest descent method discussion needs to be followed by a colon. <br />
# Rephrase “has a nice convergence theory” and cite a reference for this claim.<br />
# Avoid pronouns such as “we”.<br />
# Add citation after “.. proposed by Phillip Wolfe in 1969.”<br />
# Figure 1 is between two sections. Please fix this issue. <br />
* At least one numerical example:<br />
# Add some space between iterations or subsection break<br />
* A section to discuss and/or illustrate the applications:<br />
# Too few references in this section. <br />
# Last paragraph makes some claims without references. <br />
* A conclusion section <br />
* References<br />
# 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]]<br />
# More references should be added. A simple Google Scholar search would give you many references.<br />
<br />
== [[Piecewise linear approximation|Piecewise Linear Approximation]]==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
# 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. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Fix typo “to force the x’ values become associated with”. <br />
* At least one numerical example <br />
* A section to discuss and/or illustrate the applications<br />
# Please aim for a maximum average sentence length of ~25 words. Some of these longer sentences are hard to read. <br />
* A conclusion section<br />
# 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.<br />
* References<br />
# Include hyperlinks to sources when possible.<br />
<br />
== [[Mathematical programming with equilibrium constraints|Mathematical Programming with Equilibrium constraints]] ==<br />
<br />
* An introduction of the topic<br />
# 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.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# The meaning of parameter vector x is unclear. Please add more information or update if necessary.<br />
# 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.<br />
# Use equations instead of images to represent math programs and equations in the Implicit Descent and SQP subsection.<br />
# Apart from the steps for each solution technique, please also add a few sentences that describe each method.<br />
* At least one numerical example<br />
# Please define the terms like NCP, MP before abbreviating them. Also try not to unnecessarily abbreviate simple terms.<br />
# Equations should be typed by LaTex. Images for equations are unacceptable.<br />
# GAMS code is strongly discouraged. Please solve the problem "step-by-step".<br />
# 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.<br />
# Avoid using figures in the equations (subject to etc)<br />
* A section to discuss and/or illustrate the applications<br />
# Add references to “power management, highway pricing, chemical process engineering, and traffic planning.”<br />
* A conclusion section<br />
* References<br />
# 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]]<br />
# This Wiki contains very few references. Please check the list below and run a quick Google (Scholar) search to identify relevant literature.<br />
<br />
== [[Wing shape optimization|Wing shape Optimization]] ==<br />
<br />
* Author list: Remove cornell ID<br />
* 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.<br />
* An introduction of the topic<br />
# 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.)<br />
# Avoid discussion involving finer details of subject methods in this section. <br />
# In the titles, please change the font from bold to normal to have consistent formatting in the site. Same applies to box of content!<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Properly cite the CFD package, don’t just include a link. <br />
# Properly label the figure with a figure number.<br />
# Consider removing white space between isolated sentences to improve readability. <br />
* At least one numerical example<br />
# If you’ve already defined an abbreviation (CFD), there is no need to define it again. Just use the abbreviation.<br />
# Avoid pronouns such as “we” or “they”.<br />
# Phrases like “under the following” need to be followed by a colon.<br />
# 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.<br />
# “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. <br />
# Avoid inserting inline citations like “[4] introduces an..” as it is a bit informal when you don’t explicitly name the subject.<br />
# 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.<br />
# 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.<br />
# 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.<br />
# 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).<br />
* A section to discuss and/or illustrate the applications<br />
# Some characters are randomly capitalized in this section. <br />
* A conclusion section<br />
# 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. <br />
* References<br />
# 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]]<br />
<br />
== [[Interior-point method for NLP|Interior point method for NLP]] ==<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
** Need discussion about the concept of “central path” and the notion of self concordance<br />
** 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.<br />
** Fix typo “optimisation”.<br />
== [[AdaGrad|Adagrad]] ==<br />
* At least one numerical example<br />
# In the first sentence, “..take the following numerical example” should be followed by a colon. <br />
* A section to discuss and/or illustrate the applications<br />
# This section is too short; include specific applications in which input features are sparse and Adagrad excels.<br />
* <br />
* References <br />
<br />
# References not properly formatted<br />
<br />
== [[McCormick envelopes|McCormick Envelopes]] ==<br />
<br />
* Author list: OK but I suggest removing NetID<br />
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.<br />
* An introduction of the topic<br />
# First sentence is hard to read. Please consider keeping sentences below 25-30 words. <br />
# No references provided. Please cite all sources. <br />
# Figure 1 is provided in the middle between two sections. Please include in the introduction section. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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]]<br />
# When using mathematical expressions and symbols, please use the equation editor. (e.g., x*y, exy + y, sin (x+y) - x2)<br />
* At least one numerical example<br />
# Please add a few sentences to show the transition from problem to solution. <br />
# The solution technique should be clearly presented, and solved "step-by-step".<br />
# GAMS code is unnecessary. Please provide detailed step-by-step calculation results.<br />
* A section to discuss and/or illustrate the applications<br />
# Having a list is not enough. Please explain at least three applications in a few sentences each. <br />
# 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.<br />
* A conclusion section: <br />
* References<br />
# 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]]<br />
# Please follow the standard reference style - the current format is incorrect.<br />
<br />
== [[Branch and bound (BB) for MINLP|Branch and Bound for MINLP]] ==<br />
<br />
* Author list:<br />
** Remove NetIDS<br />
** Please remove abbreviations from the title (i.e. BB).<br />
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.<br />
* An introduction of the topic<br />
# 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]]<br />
# 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.<br />
# An illustration might be useful here. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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.<br />
# Use linked citations please as the Wiki template above. <br />
# 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.<br />
# Step 2 is missing yet it is referenced in the text multiple times. Please address this in addition to the above comment.<br />
# An illustration might be useful here as well. <br />
# Please explain what a Gomory Cut is. If the topic is available on optimization.cb.cornell.edu, you can link it. <br />
# The current equations seem to be simple text written in Italics. All mathematical symbols and equations should be formatted via LaTex.<br />
# Please format the math programs with equations and notations using formulations in lecture notes as templates.<br />
* At least one numerical example<br />
# Please add a few sentences to show the transition from problem to solution.<br />
# 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).<br />
# 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.<br />
# 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.<br />
# Make sure your example is not taken from a book as that is strictly disallowed. <br />
* A section to discuss and/or illustrate the applications<br />
# 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.<br />
# 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.<br />
* A conclusion section:<br />
# 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. <br />
# Please use summarizing sentences to describe earlier sections instead of introducing new concepts/discussion. <br />
* References<br />
# Too few references overall, you should aggregate information from multiple sources. A quick Google scholar search could provide relevant references.<br />
# 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]]<br />
# Please follow the standard reference style - the current format is incorrect.</div>Asa279https://optimization.cbe.cornell.edu/index.php?title=2021_Cornell_Optimization_Open_Textbook_Feedback&diff=61522021 Cornell Optimization Open Textbook Feedback2021-12-18T19:07:09Z<p>Asa279: /* Chance constraint method */</p>
<hr />
<div>== [[Lagrangean duality|Lagrangian duality]] ==<br />
* Author list, sections and TOC<br />
# Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.<br />
# Remove cornell ID from Author list<br />
* An introduction of the topic<br />
# 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.<br />
# Definitions of LR and its relation to duality should be double checked and re-written.<br />
# Only one reference is present in this section. Please add more relevant references by expanding this section.<br />
# Consider merging the “introduction” and “history” sections.<br />
# In the titles, please change the font from bold to normal to have consistent formatting in the site.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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.<br />
# 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 (,).<br />
# 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.<br />
# 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.<br />
# Last step of the “process” subsection also needs updating according to the previous comments.<br />
# The inline notations should also be typed using LaTex.<br />
# Please use the LaTex code or equation editor for min, s.t., etc.<br />
* At least one numerical example<br />
# 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.<br />
# All consecutive steps need to be updated since the dual variables would be updated.<br />
# After substitution the nonlinear function should be further simplified. The current expression reads like a highly nonlinear function but can be easily simplified.<br />
# 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.<br />
# Please use the LaTex code or equation editor for min, s.t., etc.<br />
* A section to discuss and/or illustrate the applications<br />
# Bullet points could be used to state the last four real-world examples that explain the physical meaning of the primal and dual problems.<br />
# Add references for the last set of applications. <br />
* A conclusion section<br />
# This section contains a few typos. Please fix the same.<br />
* References<br />
# Some citations' hyperlinks are displaying.<br />
<br />
== [[Disjunctive inequalities|Disjunctive Inequalities]] ==<br />
* Author list<br />
* An introduction of the topic<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
<br />
* At least one numerical example<br />
<br />
* A section to discuss and/or illustrate the applications<br />
<br />
* A conclusion section<br />
<br />
* References<br />
==[[Stochastic programming|Stochastic Programming]]==<br />
<br />
* An introduction of the topic<br />
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.<br />
* Theory, methodology, and/or algorithmic discussions<br />
** The symbol “xi” in the methodology subsection should be explained.<br />
** The inline notations (`x1`, `s1`) should also be typed using LaTex.<br />
<br />
* A section to discuss and/or illustrate the applications;<br />
# I suggest eliminating citing the last name of the first author (i.e. Zhou et al.)<br />
==[[Exponential transformation|Exponential Transformation]]==<br />
<br />
* Author list<br />
* An introduction of the topic<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
<br />
* At least one numerical example<br />
<br />
* A section to discuss and/or illustrate the applications<br />
<br />
* A conclusion section<br />
<br />
* References<br />
== [[Portfolio optimization|Portfolio Optimization]] ==<br />
<br />
* Author list<br />
<br />
* An introduction of the topic<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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.”<br />
* At least one numerical example<br />
# Fix misspelling “dolling decision variables”.<br />
* A section to discuss and/or illustrate the applications<br />
<br />
* A conclusion section<br />
# Need some commas here (second sentence hard to read).<br />
* References<br />
# Remove white space between end of sentences and reference numbers.<br />
<br />
== [[Chance-constraint method|Chance constraint method]] ==<br />
<br />
* Author list: <br />
* An introduction of the topic<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Some normal text was expressed as equation.<br />
* At least one numerical example<br />
<br />
* A section to discuss and/or illustrate the applications<br />
<br />
* A conclusion section<br />
<br />
* References<br />
== [[Bayesian Optimization]] ==<br />
* Introduction<br />
# Discussion on applications should be moved to a separate section.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Captions need reformatting.<br />
# Consider italicizing keywords rather than bolding.<br />
# Please add a citation to the first sentence. <br />
# Avoid pronouns such as “we”.<br />
# Acquisition function figure could be made larger and clearer to improve readability.<br />
* At least one numerical example<br />
# Any references to functions or methods in code ‘e.g. fmin’ should be properly formatted as code-stylized text.<br />
# Please use the equation editor for min, st., etc.<br />
# Avoid including a figure of the code for this example and explicitly describe the steps to the modeling and solution process instead. <br />
# Avoid pronouns such as “our” and “we”.<br />
* References<br />
# 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]]<br />
<br />
== [[Conjugate gradient methods]] ==<br />
* Theory, methodology, and/or algorithmic discussions<br />
# All equations need to be better formatted.<br />
# Please indent equation blocks.<br />
# Please properly format pseudocode.<br />
* A conclusion section<br />
# Consider adding future research directions<br />
== [[Geometric programming|Geometric Programming]] ==<br />
<br />
* Author list<br />
# Remove cornell ID<br />
* An introduction of the topic<br />
# Examples of applications in this section use the same reference. Please cite their individual sources.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# The symbol denoting the domain in the definition of a monomial is unclear. Please clarify it or fix this if it is incorrect.<br />
# Definition of posynomial refers to section 2.1 which is missing from the Wiki (sections are not numbered in the main text).<br />
# 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.<br />
# Additional theory on the feasibility analysis could be provided in this section.<br />
* At least one numerical example<br />
# In the transformation example, the last two constraints could also be simplified. Please update them as well.<br />
* A section to discuss and/or illustrate the applications<br />
# The figure in this section needs to be labeled. <br />
# The figure needs to be resized and perhaps aligned to the center. <br />
* A conclusion section:<br />
# Please avoid vague language such as: “This makes”.<br />
# Please avoid opinionated statements: “one of the best ways”.<br />
* References<br />
# 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]]<br />
# This Wiki has very few references. A quick Google Scholar search may provide relevant references.<br />
<br />
== [[Adam]] ==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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.<br />
* At least one numerical example<br />
<br />
* A section to discuss and/or illustrate the applications<br />
<br />
* A conclusion section <br />
* References<br />
== [[A-star algorithm|a* algorithm]] ==<br />
<br />
* Author list: Remove cornell ID<br />
* Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.<br />
* An introduction of the topic:<br />
# Weird spacing between paragraphs. Please fix this issue.<br />
# In the titles, please change the font from bold to normal to have consistent formatting in the site. <br />
# Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.<br />
# There are no citations in the introduction. Please cite every source.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Please add the mathematical description of the algorithm.<br />
# 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]]<br />
# 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”.<br />
# In algorithms, it is a standard to add high-level description (i.e. pseudocode or flowchart). Please incorporate it. <br />
# 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.<br />
* At least one numerical example<br />
# The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.<br />
# Instead of writing things like “The above image..”, label each figure and use the figure number to refer to it in text. <br />
# 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. <br />
* A section to discuss and/or illustrate the applications<br />
# No references in the applications. Please cite every source <br />
# Preferably, add at least an additional application. <br />
* A conclusion section<br />
# Conclusion should summarize descriptions. Please modify it to provide a summary. <br />
# Please pay attention to the length and structure of sentences here and in the full page. First sentence is hard to read.<br />
* References<br />
# 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]]<br />
# Incorrect reference style. Please follow the example and use the template.<br />
<br />
== [[Job shop scheduling|Job-Shop Scheduling Problem]] ==<br />
<br />
* An introduction of the topic<br />
# 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.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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.<br />
# 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.<br />
# 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.<br />
# 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.<br />
# Use LaTex code or equation editor to display all equations and variables in this section and all other sections as well.<br />
# Check grammar in this section. For example, phrases like “are as follows” need to be followed by a colon and not a period. <br />
# Consider rewriting the assumptions as a list in this section. <br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
# 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.<br />
# 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.<br />
# A numerical example should be simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments).<br />
* A section to discuss and/or illustrate the applications<br />
# 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. <br />
* A conclusion section<br />
# The meaning of “Operations applications” is unclear. Please explain or update if necessary.<br />
# The current conclusion section does not properly summarize the problem. Please refer to other Wiki examples for an idea to update the section accordingly.<br />
* References<br />
# 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]] <br />
# Please reference media sources like reference 5 appropriately.<br />
# A simple Google Scholar search would give you many "formal" references.<br />
<br />
== [[Optimization in game theory]] ==<br />
<br />
* Author list: remove cornell IDs. <br />
* An introduction of the topic<br />
# 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]] <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Why only a subsection on "Nash Equilibrium" is included in "Theory" section? Please re-format.<br />
# Please edit references.<br />
# Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm. <br />
# Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.<br />
* At least one numerical example<br />
# Please organize the last part in a more readable format. Questions may be in bold and numbered, answers are more direct, etc.<br />
# Remember to cite all images and tables. <br />
# 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.<br />
* A section to discuss and/or illustrate the applications<br />
# Very good, link the reference and cite all sources. <br />
* A conclusion section<br />
# Please add more summarizing especially from theory sentences and avoid long sentences. <br />
* References<br />
# 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]]<br />
# Reference primary sources rather than Wikipedia<br />
# Incorrect reference style. Please correct.<br />
<br />
== [[Trust-region methods]] ==<br />
* An introduction of the topic<br />
** Avoid pronouns such as “we”. This goes for all other sections as well.<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Organization of ideas in this section needs work.<br />
# 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.<br />
# Please format the algorithm in proper algorithmic pseudocode format.<br />
* References<br />
# Incorrect reference style.<br />
<br />
*There are numerous misspellings, grammatical errors, and incorrect claims. Please fix these.<br />
<br />
== [[Momentum]] ==<br />
* An introduction of the topic<br />
# 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.<br />
# Remove bold on “Momentum”.<br />
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# <br />
# 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.<br />
# 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.<br />
# Avoid pronouns such as “you”.<br />
* At least one numerical example<br />
# 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.<br />
# Please try to label the plots that explains what each line color means.<br />
# Starting point for SGD with momentum is different in explanation and the table. Please fix the same.<br />
* A section to discuss and/or illustrate the applications<br />
# Please use correct terminology like “optimizing non-convex functions” and not “training non-convex models”.<br />
* References<br />
# 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.<br />
<br />
== [[Stochastic dynamic programming|Stochastic Dynamic programming]] ==<br />
<br />
* Author list<br />
# Remove cornell ID<br />
* An introduction of the topic<br />
# Discussion on applications should be moved to a separate section.<br />
* Theory, methodology, and/or algorithmic discussions <br />
# Remove the grey box background of equations.<br />
* At least one numerical example <br />
* A section to discuss and/or illustrate the applications <br />
* A conclusion section <br />
* References<br />
# 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]]<br />
<br />
== [[Outer-approximation (OA)|Outer-approximation]] ==<br />
<br />
* An introduction of the topic <br />
# See formatting guideline below<br />
# Avoid opinionated statements such as “MINLP problems are usually the hardest to solve”.<br />
# Rearrange the text such that the MINLP formulation is in the theory section and keep the introduction in words only. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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<br />
# The sentence “The Outer-Approximation (OA) algorithm was first proposed by Duran and and Grossmann in 1986 to solve MINLP problems.” needs a reference. <br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
# “Minimize” and “subject to” should be “min” and “s.t.” in MathType<br />
* A section to discuss and/or illustrate the applications<br />
# 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)<br />
# 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. <br />
# 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.<br />
# Consider reformatting to make steps more readable. Inserting spaces and breaking down steps would help. <br />
* A conclusion section<br />
# Too short. Consider discussion on future research direction and discussion on uncertainty<br />
# 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)”. <br />
* References<br />
# 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]]<br />
# Remove "Template:Reflist"<br />
<br />
== [[Unit commitment problem]] ==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
# Please expand the introduction and avoid discussions of examples or specific applications in this section.<br />
# The sentence “Nonlinear, Non-convex programming optimization problem.” doesn’t make sense by itself and Non-convex shouldn’t be capitalized. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Figure/image format should be revised to better display the content.<br />
# Uppercase characters are used randomly (e.g., “non-convex transmission Constraints”) . Please follow correct language conventions for sentence structure.<br />
# 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. <br />
# Don’t say “written in matrix form as equation..” and just cite the reference, actually write out the equation. <br />
# Properly label the figure in this section with a figure number and improve visibility by making it larger. <br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
# Label the figures in this section properly with figure numbers.<br />
# Fix typo “while minimize” to “while minimizing”. <br />
# Avoid pronouns such as “we”. <br />
# Use the equation editor when typing equations. <br />
# 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.<br />
# 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).<br />
* A section to discuss and/or illustrate the applications:<br />
# I suggest changing the order of the subtitles here. For example, Single-Period Unit Commitment. <br />
* A conclusion section <br />
* References<br />
<br />
== [[Frank-Wolfe]] ==<br />
<br />
* Author list: <br />
* An introduction of the topic<br />
# I suggest highlighting disadvantages along with advantages. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# “[n x 1] matrix” please use the equation editor to express mathematical descriptions and symbols (p,b, etc)<br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
# Please show at least a few iterations. Even for smaller examples if needed. Report the final solution. <br />
# Please use the LaTex code or equation editor for min and include s.t., etc.<br />
# 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.<br />
* A section to discuss and/or illustrate the applications: <br />
* A conclusion section<br />
# Same as the introduction. Pros and cons should be evaluated together!<br />
* References<br />
# 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]]<br />
<br />
== [[Line search methods|Line Search Method]] ==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
# Expand the introduction and avoid discussion on some of the specific steps in the solution process. <br />
# Provide references here. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# The phrase “are as follows” in the steepest descent method discussion needs to be followed by a colon. <br />
# Rephrase “has a nice convergence theory” and cite a reference for this claim.<br />
# Avoid pronouns such as “we”.<br />
# Add citation after “.. proposed by Phillip Wolfe in 1969.”<br />
# Figure 1 is between two sections. Please fix this issue. <br />
* At least one numerical example:<br />
# Add some space between iterations or subsection break<br />
* A section to discuss and/or illustrate the applications:<br />
# Too few references in this section. <br />
# Last paragraph makes some claims without references. <br />
* A conclusion section <br />
* References<br />
# 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]]<br />
# More references should be added. A simple Google Scholar search would give you many references.<br />
<br />
== [[Piecewise linear approximation|Piecewise Linear Approximation]]==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
# 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. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Fix typo “to force the x’ values become associated with”. <br />
* At least one numerical example <br />
* A section to discuss and/or illustrate the applications<br />
# Please aim for a maximum average sentence length of ~25 words. Some of these longer sentences are hard to read. <br />
* A conclusion section<br />
# 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.<br />
* References<br />
# Include hyperlinks to sources when possible.<br />
<br />
== [[Mathematical programming with equilibrium constraints|Mathematical Programming with Equilibrium constraints]] ==<br />
<br />
* An introduction of the topic<br />
# 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.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# The meaning of parameter vector x is unclear. Please add more information or update if necessary.<br />
# 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.<br />
# Use equations instead of images to represent math programs and equations in the Implicit Descent and SQP subsection.<br />
# Apart from the steps for each solution technique, please also add a few sentences that describe each method.<br />
* At least one numerical example<br />
# Please define the terms like NCP, MP before abbreviating them. Also try not to unnecessarily abbreviate simple terms.<br />
# Equations should be typed by LaTex. Images for equations are unacceptable.<br />
# GAMS code is strongly discouraged. Please solve the problem "step-by-step".<br />
# 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.<br />
# Avoid using figures in the equations (subject to etc)<br />
* A section to discuss and/or illustrate the applications<br />
# Add references to “power management, highway pricing, chemical process engineering, and traffic planning.”<br />
* A conclusion section<br />
* References<br />
# 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]]<br />
# This Wiki contains very few references. Please check the list below and run a quick Google (Scholar) search to identify relevant literature.<br />
<br />
== [[Wing shape optimization|Wing shape Optimization]] ==<br />
<br />
* Author list: Remove cornell ID<br />
* 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.<br />
* An introduction of the topic<br />
# 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.)<br />
# Avoid discussion involving finer details of subject methods in this section. <br />
# In the titles, please change the font from bold to normal to have consistent formatting in the site. Same applies to box of content!<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Properly cite the CFD package, don’t just include a link. <br />
# Properly label the figure with a figure number.<br />
# Consider removing white space between isolated sentences to improve readability. <br />
* At least one numerical example<br />
# If you’ve already defined an abbreviation (CFD), there is no need to define it again. Just use the abbreviation.<br />
# Avoid pronouns such as “we” or “they”.<br />
# Phrases like “under the following” need to be followed by a colon.<br />
# 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.<br />
# “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. <br />
# Avoid inserting inline citations like “[4] introduces an..” as it is a bit informal when you don’t explicitly name the subject.<br />
# 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.<br />
# 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.<br />
# 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.<br />
# 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).<br />
* A section to discuss and/or illustrate the applications<br />
# Some characters are randomly capitalized in this section. <br />
* A conclusion section<br />
# 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. <br />
* References<br />
# 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]]<br />
<br />
== [[Interior-point method for NLP|Interior point method for NLP]] ==<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
** Need discussion about the concept of “central path” and the notion of self concordance<br />
** 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.<br />
** Fix typo “optimisation”.<br />
== [[AdaGrad|Adagrad]] ==<br />
* At least one numerical example<br />
# In the first sentence, “..take the following numerical example” should be followed by a colon. <br />
* A section to discuss and/or illustrate the applications<br />
# This section is too short; include specific applications in which input features are sparse and Adagrad excels.<br />
* <br />
* References <br />
<br />
# References not properly formatted<br />
<br />
== [[McCormick envelopes|McCormick Envelopes]] ==<br />
<br />
* Author list: OK but I suggest removing NetID<br />
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.<br />
* An introduction of the topic<br />
# First sentence is hard to read. Please consider keeping sentences below 25-30 words. <br />
# No references provided. Please cite all sources. <br />
# Figure 1 is provided in the middle between two sections. Please include in the introduction section. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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]]<br />
# When using mathematical expressions and symbols, please use the equation editor. (e.g., x*y, exy + y, sin (x+y) - x2)<br />
* At least one numerical example<br />
# Please add a few sentences to show the transition from problem to solution. <br />
# The solution technique should be clearly presented, and solved "step-by-step".<br />
# GAMS code is unnecessary. Please provide detailed step-by-step calculation results.<br />
* A section to discuss and/or illustrate the applications<br />
# Having a list is not enough. Please explain at least three applications in a few sentences each. <br />
# 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.<br />
* A conclusion section: <br />
* References<br />
# 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]]<br />
# Please follow the standard reference style - the current format is incorrect.<br />
<br />
== [[Branch and bound (BB) for MINLP|Branch and Bound for MINLP]] ==<br />
<br />
* Author list:<br />
** Remove NetIDS<br />
** Please remove abbreviations from the title (i.e. BB).<br />
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.<br />
* An introduction of the topic<br />
# 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]]<br />
# 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.<br />
# An illustration might be useful here. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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.<br />
# Use linked citations please as the Wiki template above. <br />
# 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.<br />
# Step 2 is missing yet it is referenced in the text multiple times. Please address this in addition to the above comment.<br />
# An illustration might be useful here as well. <br />
# Please explain what a Gomory Cut is. If the topic is available on optimization.cb.cornell.edu, you can link it. <br />
# The current equations seem to be simple text written in Italics. All mathematical symbols and equations should be formatted via LaTex.<br />
# Please format the math programs with equations and notations using formulations in lecture notes as templates.<br />
* At least one numerical example<br />
# Please add a few sentences to show the transition from problem to solution.<br />
# 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).<br />
# 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.<br />
# 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.<br />
# Make sure your example is not taken from a book as that is strictly disallowed. <br />
* A section to discuss and/or illustrate the applications<br />
# 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.<br />
# 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.<br />
* A conclusion section:<br />
# 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. <br />
# Please use summarizing sentences to describe earlier sections instead of introducing new concepts/discussion. <br />
* References<br />
# Too few references overall, you should aggregate information from multiple sources. A quick Google scholar search could provide relevant references.<br />
# 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]]<br />
# Please follow the standard reference style - the current format is incorrect.</div>Asa279https://optimization.cbe.cornell.edu/index.php?title=2021_Cornell_Optimization_Open_Textbook_Feedback&diff=60322021 Cornell Optimization Open Textbook Feedback2021-12-16T19:11:39Z<p>Asa279: /* Exponential Transformation */</p>
<hr />
<div>== [[Lagrangean duality|Lagrangian duality]] ==<br />
* Author list, sections and TOC<br />
# Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.<br />
# Remove cornell ID from Author list<br />
* An introduction of the topic<br />
# 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.<br />
# Definitions of LR and its relation to duality should be double checked and re-written.<br />
# Only one reference is present in this section. Please add more relevant references by expanding this section.<br />
# Consider merging the “introduction” and “history” sections.<br />
# In the titles, please change the font from bold to normal to have consistent formatting in the site.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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.<br />
# 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 (,).<br />
# 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.<br />
# 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.<br />
# Last step of the “process” subsection also needs updating according to the previous comments.<br />
# The inline notations should also be typed using LaTex.<br />
# Please use the LaTex code or equation editor for min, s.t., etc.<br />
* At least one numerical example<br />
# 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.<br />
# All consecutive steps need to be updated since the dual variables would be updated.<br />
# After substitution the nonlinear function should be further simplified. The current expression reads like a highly nonlinear function but can be easily simplified.<br />
# 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.<br />
# Please use the LaTex code or equation editor for min, s.t., etc.<br />
* A section to discuss and/or illustrate the applications<br />
# Bullet points could be used to state the last four real-world examples that explain the physical meaning of the primal and dual problems.<br />
# Add references for the last set of applications. <br />
* A conclusion section<br />
# This section contains a few typos. Please fix the same.<br />
* References<br />
# Some citations' hyperlinks are displaying.<br />
<br />
== [[Disjunctive inequalities|Disjunctive Inequalities]] ==<br />
<br />
* Author list<br />
# Missing course section and semester<br />
# Remove cornell ID<br />
* An introduction of the topic<br />
# No citations are present in this section.<br />
# “mixed-integer programming (MIP)” should be used instead of “multiple integer programming (MIP)”. Please fix this error.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# The abbreviation MILP is not previously defined. Please fix this issue.<br />
# You consistently use the negative sign instead of the NOT operator for y (-y instead of ¬y). <br />
# Some inconsistencies with the spacing of variables, constraints, etc., under the “General” section that need to be fixed.<br />
# 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.<br />
* At least one numerical example<br />
# 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.<br />
# Add space between vee (V) operator and brackets in first line of Latex<br />
# Please format variables correctly, for example, use <math>x_1</math> instead of x1.<br />
* A section to discuss and/or illustrate the applications<br />
# Please format the equations appropriately either by using latex code or the visual editor. These images are NOT acceptable!<br />
* A conclusion section<br />
# There is no conclusion presented in this section at all.<br />
* References<br />
# 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. <br />
# There are many papers on this topic. A simple Google (Scholar) search could provide you with sufficient references to cite. <br />
# Many important references of this topic are missing.<br />
# 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]]<br />
<br />
==[[Stochastic programming|Stochastic Programming]] ==<br />
<br />
* Author list: Remove cornell IDs<br />
* An introduction of the topic<br />
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki. <br />
# 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.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Please avoid direct inline linkbacks to Wikipedia.<br />
# The symbol “xi” in the methodology subsection should be explained.<br />
* At least one numerical example<br />
# Copying a numerical example "entirely" from a textbook is inappropriate. Your team should come up with a "numerical" case.<br />
# No specific application context is needed for a numerical example.<br />
# The inline notations (`x1`, `s1`) should also be typed using LaTex.<br />
# Label all tables with a table number for better readability. <br />
# 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. <br />
* A section to discuss and/or illustrate the applications;<br />
# I suggest eliminating citing the last name of the first author (i.e. Zhou et al.)<br />
* A conclusion section <br />
* References<br />
# URLs of some citations are not properly formatted (not showing the hyperlinks).<br />
<br />
== [[Exponential transformation|Exponential Transformation]] ==<br />
<br />
* Author list<br />
* An introduction of the topic<br />
<br />
* Theory, methodology, and/or algorithmic discussions<br />
<br />
* At least one numerical example<br />
<br />
* A section to discuss and/or illustrate the applications<br />
<br />
* A conclusion section<br />
<br />
* References<br />
== [[Portfolio optimization|Portfolio Optimization]] ==<br />
<br />
* Author list<br />
# Remove cornell id<br />
* An introduction of the topic<br />
# 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. <br />
# Amount of whitespace can be reduced by changing the orientation of Figure 1 and the sentences in this section.<br />
# 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. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# A brief mention of modern portfolio theory (i.e.. Markowitz) would be appropriate in this section. <br />
# 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.<br />
# Use LaTex to distinguish variables written within a sentence, such as m and n. <br />
# 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.”<br />
# An explanation of a few common constraints would be helpful, rather than just including a table. <br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
# Solving the numerical example by GAMS is inappropriate. Please provide detailed step-by-step calculation results.<br />
# All tables need to be labeled.<br />
# Include figure number in label for consistency. <br />
# Fix misspelling “dolling decision variables”. <br />
# Use LaTex for all variables, equations, and constraints here.<br />
# Example 2 table is hard to read, so making it bigger would help. <br />
# Remove the “Using excel as the solver” part from the sentence before the solution discussion. <br />
# Some grammatical errors here (phrases such as “.. is as follows” should be followed by a colon). <br />
* A section to discuss and/or illustrate the applications<br />
# Rephrase “Portfolio optimization can be used to screen investment projects that meet investors, rationally allocate investment amounts, etc.”<br />
# Not sure “relevant” is the correct word choice here. <br />
# 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. <br />
* A conclusion section<br />
# Need some commas here.<br />
# The sentence “Linear programming has been around since the 1940’s and has such a wide base of applications” is not necessary. <br />
* References<br />
# 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]]<br />
# Remove white space between end of sentences and reference numbers.<br />
<br />
== [[Chance-constraint method|Chance constraint method]] ==<br />
<br />
* Author list: <br />
* An introduction of the topic<br />
# 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”<br />
# In “Chance-constraint”, it is capitalized randomly throughout the introduction. Please correct. <br />
# 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.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Please add a citation to the first sentence. <br />
# Xi is an uncertainty/randomness variable. It is better to use clear language. <br />
# 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.<br />
# Theory is insufficient. Please expand and explain different approaches. <br />
# Please add pros and cons explicitly as a list. <br />
# Explain the physical meaning for examples of chance constraints along with all the notations used.<br />
# 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. <br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
# Please remove this example as it is directly from this book. The example should be purely numerical without any background.<br />
# Please use the equation editor for min, st., etc.<br />
# 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. <br />
# Please change the table format so as not to confuse the reader. <br />
# Multiple instances of [Chart to be added] are missing.<br />
# Example is incomplete. <br />
# Avoid pronouns such as “we”.<br />
* A section to discuss and/or illustrate the applications<br />
# Please connect several grammatical and spelling errors: “real life application”, Energy creation, particularly in renewable sources, have high variabilities”, and others<br />
# “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. <br />
* A conclusion section<br />
# 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.<br />
# 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. <br />
* References<br />
# 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]]<br />
# More references should be added. A simple Google Scholar search would give you many references.<br />
<br />
== [[Bayesian Optimization]] ==<br />
* Section titles should not be "bold". Please double check using source editor on the section titles.<br />
* 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.<br />
* Author list: Remove cornell ID, Please check names<br />
* Introduction<br />
# 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.<br />
# 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.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Captions need reformatting.<br />
# Consider italicizing keywords rather than bolding.<br />
# Please add a citation to the first sentence. <br />
# 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.<br />
# Avoid pronouns such as “we”.<br />
# Please write equations in the Wiki instead of attaching images for equations.<br />
# Acquisition function figure could be made larger and clearer to improve readability.<br />
* At least one numerical example<br />
# Any references to functions or methods in code ‘e.g. fmin’ should be properly formatted as code-stylized text.<br />
# Please use the equation editor for min, st., etc.<br />
# Avoid including a figure of the code for this example and explicitly describe the steps to the modeling and solution process instead. <br />
# Avoid pronouns such as “our” and “we”.<br />
* A section to discuss and/or illustrate the applications <br />
* A conclusion section<br />
# Please do not use brackets to enclose lists.<br />
# Some claims here should be supported by references. Please cite each source after its sentence. <br />
* References<br />
# 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]]<br />
# Try to avoid references to “pop” machine learning blogs where anyone can be an author. (e.g. towardsdatascience)<br />
# All references are URLs. Please cite publications and literature.<br />
# A simple Google Scholar search would give you many references.<br />
<br />
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.<br />
<br />
== [[Conjugate gradient methods]] ==<br />
<br />
* Author list: Remove cornell ID<br />
* Introduction<br />
# All inline notations (e.g., `x`, `A`) should be typed using LaTex.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# All equations need to be better formatted.<br />
# Is Gauss-Newton no longer referenced?<br />
# 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.<br />
# Please indent equation blocks.<br />
# Please properly format pseudocode.<br />
* At least one numerical example<br />
# Steps should be accompanied with explanation, or reference to the corresponding step in the pseudocode.<br />
# Please properly format in a more organized manner, aligning equations appropriately and demarcating steps appropriately.<br />
* A section to discuss and/or illustrate the applications <br />
# Consider including 2 additional examples of applications<br />
* A conclusion section<br />
# Consider adding future research directions<br />
* References<br />
# Reference primary sources rather than Wikipedia<br />
# Too few references.<br />
# More references should be added. A simple Google Scholar search would give you many references.<br />
<br />
== [[Geometric programming|Geometric Programming]] ==<br />
<br />
* Author list<br />
# Remove cornell ID<br />
* An introduction of the topic<br />
# Examples of applications in this section use the same reference. Please cite their individual sources.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# The symbol denoting the domain in the definition of a monomial is unclear. Please clarify it or fix this if it is incorrect.<br />
# Definition of posynomial refers to section 2.1 which is missing from the Wiki (sections are not numbered in the main text).<br />
# 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.<br />
# Additional theory on the feasibility analysis could be provided in this section.<br />
* At least one numerical example<br />
# In the transformation example, the last two constraints could also be simplified. Please update them as well.<br />
* A section to discuss and/or illustrate the applications<br />
# The figure in this section needs to be labeled. <br />
# The figure needs to be resized and perhaps aligned to the center. <br />
* A conclusion section:<br />
# Please avoid vague language such as: “This makes”.<br />
# Please avoid opinionated statements: “one of the best ways”.<br />
* References<br />
# 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]]<br />
# This Wiki has very few references. A quick Google Scholar search may provide relevant references.<br />
<br />
== [[Adam]] ==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
# Some grammatical errors here, mostly related to the need for commas in certain places (e.g., “Before Adam..”).<br />
# Some minor errors with parts of speech throughout the section, need to revisit phrases such as “which has broader scope in future for”, etc. <br />
# Try splitting up some of the longer sentences in this section, a couple are hard to read.<br />
# 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. <br />
# What does adam stand for? Introduction is insufficient. Please expand. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Revise grammar here, noticing some missing commas and uncapitalized word after period.<br />
# Rephrase “second one is to update the old position with the updated position”.<br />
# Use LaTex code or equation editor to display all equations and variables in this section, and actual subscripts instead of “m_t”, etc. <br />
# 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. <br />
# Remove white space before the period in RMSP discussion.<br />
# Please provide a pseudocode. <br />
# Please use list the two methods here “Adam is a combination of two gradient descent methods which are explained below”<br />
# Please expand the theory section significantly. Theoretical convergence properties should be discussed, even if briefly.<br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
* A section to discuss and/or illustrate the applications<br />
# Same comment as before, consider replacing inline citations after words like “According to..”. <br />
* A conclusion section <br />
* References<br />
# 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]]<br />
# Try to avoid references to blogs and use peer-reviewed academic references instead. <br />
# Too few references.<br />
# More references should be added. A simple Google Scholar search would give you many references.<br />
<br />
== [[A-star algorithm|a* algorithm]] ==<br />
<br />
* Author list: Remove cornell ID<br />
* Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.<br />
* An introduction of the topic:<br />
# Weird spacing between paragraphs. Please fix this issue.<br />
# In the titles, please change the font from bold to normal to have consistent formatting in the site. <br />
# Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.<br />
# There are no citations in the introduction. Please cite every source.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Please add the mathematical description of the algorithm.<br />
# 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]]<br />
# 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”.<br />
# In algorithms, it is a standard to add high-level description (i.e. pseudocode or flowchart). Please incorporate it. <br />
# 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.<br />
* At least one numerical example<br />
# The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.<br />
# Instead of writing things like “The above image..”, label each figure and use the figure number to refer to it in text. <br />
# 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. <br />
* A section to discuss and/or illustrate the applications<br />
# No references in the applications. Please cite every source <br />
# Preferably, add at least an additional application. <br />
* A conclusion section<br />
# Conclusion should summarize descriptions. Please modify it to provide a summary. <br />
# Please pay attention to the length and structure of sentences here and in the full page. First sentence is hard to read.<br />
* References<br />
# 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]]<br />
# Incorrect reference style. Please follow the example and use the template.<br />
<br />
== [[Job shop scheduling|Job-Shop Scheduling Problem]] ==<br />
<br />
* An introduction of the topic<br />
# 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.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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.<br />
# 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.<br />
# 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.<br />
# 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.<br />
# Use LaTex code or equation editor to display all equations and variables in this section and all other sections as well.<br />
# Check grammar in this section. For example, phrases like “are as follows” need to be followed by a colon and not a period. <br />
# Consider rewriting the assumptions as a list in this section. <br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
# 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.<br />
# 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.<br />
# A numerical example should be simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments).<br />
* A section to discuss and/or illustrate the applications<br />
# 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. <br />
* A conclusion section<br />
# The meaning of “Operations applications” is unclear. Please explain or update if necessary.<br />
# The current conclusion section does not properly summarize the problem. Please refer to other Wiki examples for an idea to update the section accordingly.<br />
* References<br />
# 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]] <br />
# Please reference media sources like reference 5 appropriately.<br />
# A simple Google Scholar search would give you many "formal" references.<br />
<br />
== [[Optimization in game theory]] ==<br />
<br />
* Author list: remove cornell IDs. <br />
* An introduction of the topic<br />
# 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]] <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Why only a subsection on "Nash Equilibrium" is included in "Theory" section? Please re-format.<br />
# Please edit references.<br />
# Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm. <br />
# Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.<br />
* At least one numerical example<br />
# Please organize the last part in a more readable format. Questions may be in bold and numbered, answers are more direct, etc.<br />
# Remember to cite all images and tables. <br />
# 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.<br />
* A section to discuss and/or illustrate the applications<br />
# Very good, link the reference and cite all sources. <br />
* A conclusion section<br />
# Please add more summarizing especially from theory sentences and avoid long sentences. <br />
* References<br />
# 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]]<br />
# Reference primary sources rather than Wikipedia<br />
# Incorrect reference style. Please correct.<br />
<br />
== [[Trust-region methods]] ==<br />
<br />
* Author list:<br />
# Remove cornell IDs. Author is also spelled incorrectly. <br />
# Add the course section.<br />
* An introduction of the topic<br />
# 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]] <br />
# 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.<br />
# Avoid pronouns such as “we”. This goes for all other sections as well.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Organization of ideas in this section needs work.<br />
# 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.<br />
# Each approach should have accompanying explanation and motivation for why it is being discussed. It is not enough to outline the algorithm.<br />
# Please make sure symbols are properly subscripted and superscripted (e.g. “pk” should be “p_k”<br />
# Please format the algorithm in proper algorithmic pseudocode format.<br />
# Little to no discussion on global convergence guarantees<br />
# Please include discussion about the advantages and disadvantages of the algorithm<br />
# Fix typo “couchy point”.<br />
* At least one numerical example<br />
# Any code functions (uminfunc) should have proper text formatting.<br />
# The graph needs a better caption explaining how the axes are labeled and what data points are being shown.<br />
# Please increase the quality of the figure. It is hard to see the red line. <br />
# 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.”<br />
* A section to discuss and/or illustrate the applications<br />
# 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).<br />
* A conclusion section<br />
# Please add more summary, future research directions for example is a good start.<br />
* References<br />
# Incorrect reference style.<br />
# Please consider having the references as this Wiki template, <nowiki>https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization</nowiki><br />
# More references should be added. A simple Google Scholar search would give you many references.<br />
<br />
*There are numerous misspellings, grammatical errors, and incorrect claims. Please fix these.<br />
<br />
== [[Momentum]] ==<br />
<br />
* Author list<br />
# Remove cornell ID<br />
* An introduction of the topic<br />
# 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.<br />
# Remove bold on “Momentum”.<br />
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Equation formatting is very poor and should be formalized.<br />
# 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.<br />
# 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.<br />
# 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.<br />
# Avoid pronouns such as “you”.<br />
* At least one numerical example<br />
# 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.<br />
# Please try to label the plots that explains what each line color means.<br />
# Starting point for SGD with momentum is different in explanation and the table. Please fix the same.<br />
* A section to discuss and/or illustrate the applications<br />
# Please use correct terminology like “optimizing non-convex functions” and not “training non-convex models”.<br />
# Adam, Adadelta, and RMSprop are variants of SGD that already use momentum. Please double check the writing and update if necessary.<br />
* A conclusion section<br />
# Please refrain from using words like “zig zag” effects.<br />
* References<br />
# 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.<br />
<br />
== [[Stochastic dynamic programming|Stochastic Dynamic programming]] ==<br />
<br />
* Author list<br />
# Remove cornell ID<br />
* An introduction of the topic<br />
# Discussion on applications should be moved to a separate section.<br />
* Theory, methodology, and/or algorithmic discussions <br />
# Remove the grey box background of equations.<br />
* At least one numerical example <br />
* A section to discuss and/or illustrate the applications <br />
* A conclusion section <br />
* References<br />
# 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]]<br />
<br />
== [[Outer-approximation (OA)|Outer-approximation]] ==<br />
<br />
* An introduction of the topic <br />
# See formatting guideline below<br />
# Avoid opinionated statements such as “MINLP problems are usually the hardest to solve”.<br />
# Rearrange the text such that the MINLP formulation is in the theory section and keep the introduction in words only. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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<br />
# The sentence “The Outer-Approximation (OA) algorithm was first proposed by Duran and and Grossmann in 1986 to solve MINLP problems.” needs a reference. <br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
# “Minimize” and “subject to” should be “min” and “s.t.” in MathType<br />
* A section to discuss and/or illustrate the applications<br />
# 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)<br />
# 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. <br />
# 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.<br />
# Consider reformatting to make steps more readable. Inserting spaces and breaking down steps would help. <br />
* A conclusion section<br />
# Too short. Consider discussion on future research direction and discussion on uncertainty<br />
# 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)”. <br />
* References<br />
# 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]]<br />
# Remove "Template:Reflist"<br />
<br />
== [[Unit commitment problem]] ==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
# Please expand the introduction and avoid discussions of examples or specific applications in this section.<br />
# The sentence “Nonlinear, Non-convex programming optimization problem.” doesn’t make sense by itself and Non-convex shouldn’t be capitalized. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Figure/image format should be revised to better display the content.<br />
# Uppercase characters are used randomly (e.g., “non-convex transmission Constraints”) . Please follow correct language conventions for sentence structure.<br />
# 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. <br />
# Don’t say “written in matrix form as equation..” and just cite the reference, actually write out the equation. <br />
# Properly label the figure in this section with a figure number and improve visibility by making it larger. <br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
# Label the figures in this section properly with figure numbers.<br />
# Fix typo “while minimize” to “while minimizing”. <br />
# Avoid pronouns such as “we”. <br />
# Use the equation editor when typing equations. <br />
# 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.<br />
# 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).<br />
* A section to discuss and/or illustrate the applications:<br />
# I suggest changing the order of the subtitles here. For example, Single-Period Unit Commitment. <br />
* A conclusion section <br />
* References<br />
<br />
== [[Frank-Wolfe]] ==<br />
<br />
* Author list: <br />
* An introduction of the topic<br />
# I suggest highlighting disadvantages along with advantages. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# “[n x 1] matrix” please use the equation editor to express mathematical descriptions and symbols (p,b, etc)<br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
# Please show at least a few iterations. Even for smaller examples if needed. Report the final solution. <br />
# Please use the LaTex code or equation editor for min and include s.t., etc.<br />
# 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.<br />
* A section to discuss and/or illustrate the applications: <br />
* A conclusion section<br />
# Same as the introduction. Pros and cons should be evaluated together!<br />
* References<br />
# 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]]<br />
<br />
== [[Line search methods|Line Search Method]] ==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
# Expand the introduction and avoid discussion on some of the specific steps in the solution process. <br />
# Provide references here. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# The phrase “are as follows” in the steepest descent method discussion needs to be followed by a colon. <br />
# Rephrase “has a nice convergence theory” and cite a reference for this claim.<br />
# Avoid pronouns such as “we”.<br />
# Add citation after “.. proposed by Phillip Wolfe in 1969.”<br />
# Figure 1 is between two sections. Please fix this issue. <br />
* At least one numerical example:<br />
# Add some space between iterations or subsection break<br />
* A section to discuss and/or illustrate the applications:<br />
# Too few references in this section. <br />
# Last paragraph makes some claims without references. <br />
* A conclusion section <br />
* References<br />
# 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]]<br />
# More references should be added. A simple Google Scholar search would give you many references.<br />
<br />
== [[Piecewise linear approximation|Piecewise Linear Approximation]]==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
# 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. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Fix typo “to force the x’ values become associated with”. <br />
* At least one numerical example <br />
* A section to discuss and/or illustrate the applications<br />
# Please aim for a maximum average sentence length of ~25 words. Some of these longer sentences are hard to read. <br />
* A conclusion section<br />
# 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.<br />
* References<br />
# Include hyperlinks to sources when possible.<br />
<br />
== [[Mathematical programming with equilibrium constraints|Mathematical Programming with Equilibrium constraints]] ==<br />
<br />
* An introduction of the topic<br />
# 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.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# The meaning of parameter vector x is unclear. Please add more information or update if necessary.<br />
# 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.<br />
# Use equations instead of images to represent math programs and equations in the Implicit Descent and SQP subsection.<br />
# Apart from the steps for each solution technique, please also add a few sentences that describe each method.<br />
* At least one numerical example<br />
# Please define the terms like NCP, MP before abbreviating them. Also try not to unnecessarily abbreviate simple terms.<br />
# Equations should be typed by LaTex. Images for equations are unacceptable.<br />
# GAMS code is strongly discouraged. Please solve the problem "step-by-step".<br />
# 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.<br />
# Avoid using figures in the equations (subject to etc)<br />
* A section to discuss and/or illustrate the applications<br />
# Add references to “power management, highway pricing, chemical process engineering, and traffic planning.”<br />
* A conclusion section<br />
* References<br />
# 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]]<br />
# This Wiki contains very few references. Please check the list below and run a quick Google (Scholar) search to identify relevant literature.<br />
<br />
== [[Wing shape optimization|Wing shape Optimization]] ==<br />
<br />
* Author list: Remove cornell ID<br />
* 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.<br />
* An introduction of the topic<br />
# 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.)<br />
# Avoid discussion involving finer details of subject methods in this section. <br />
# In the titles, please change the font from bold to normal to have consistent formatting in the site. Same applies to box of content!<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Properly cite the CFD package, don’t just include a link. <br />
# Properly label the figure with a figure number.<br />
# Consider removing white space between isolated sentences to improve readability. <br />
* At least one numerical example<br />
# If you’ve already defined an abbreviation (CFD), there is no need to define it again. Just use the abbreviation.<br />
# Avoid pronouns such as “we” or “they”.<br />
# Phrases like “under the following” need to be followed by a colon.<br />
# 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.<br />
# “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. <br />
# Avoid inserting inline citations like “[4] introduces an..” as it is a bit informal when you don’t explicitly name the subject.<br />
# 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.<br />
# 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.<br />
# 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.<br />
# 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).<br />
* A section to discuss and/or illustrate the applications<br />
# Some characters are randomly capitalized in this section. <br />
* A conclusion section<br />
# 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. <br />
* References<br />
# 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]]<br />
<br />
== [[Interior-point method for NLP|Interior point method for NLP]] ==<br />
<br />
* An introduction of the topic: <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Primal-Dual formulation and comparison to the Barrier Method is not discussed.<br />
# Include brief discussion about big O convergence rates.<br />
# Need discussion about the concept of “central path” and the notion of self concordance<br />
# 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.<br />
# Graphs and images are incorrectly formatted to the page. Consider proper alignment with respect to the text body.<br />
# Use explicitly typed Latex equations instead of images to represent math programs and equations.<br />
# Fix typo “optimisation”.<br />
# Use LaTex code or equation editor to display all equations and variables (e.g., “xi ”, “μ”, etc.).<br />
* At least one numerical example:<br />
# There are formatting issues with figures 2,3. Please make sure to embed them within their respective sections. <br />
* A section to discuss and/or illustrate the applications<br />
* A conclusion section <br />
# Minor character code typos in the conclusion.<br />
# Also, please add more discussion in this section. Future research directions is a good start.<br />
# There is a box ""<br />
* References<br />
<br />
== [[AdaGrad|Adagrad]] ==<br />
<br />
* An introduction of the topic: <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Include discussion on its variants (most important is AdaDelta).<br />
# Include disadvantages of Adagrad, since this provides motivation for the discussion on the variants and improvements of Adagrad<br />
# Include comparisons to other popular optimizers (particularly important is comparisons to regular SGD and Adam)<br />
# 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.<br />
# Algorithm image is blurry. Either increase the fidelity or write the pseudocode directly in the wiki editor.<br />
* At least one numerical example<br />
# In the first sentence, “..take the following numerical example” should be followed by a colon. <br />
# Fix typo “trayectory”.<br />
* A section to discuss and/or illustrate the applications<br />
# This section is too short; include specific applications in which input features are sparse and Adagrad excels.<br />
# Add reference to the claim “Mainly, it is a good choice for deep learning models with sparse input features”.<br />
* A conclusion section <br />
* References <br />
<br />
# Too few references overall, you should aggregate information from multiple sources (even if the base algorithm itself comes from a singular paper)<br />
<br />
== [[McCormick envelopes|McCormick Envelopes]] ==<br />
<br />
* Author list: OK but I suggest removing NetID<br />
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.<br />
* An introduction of the topic<br />
# First sentence is hard to read. Please consider keeping sentences below 25-30 words. <br />
# No references provided. Please cite all sources. <br />
# Figure 1 is provided in the middle between two sections. Please include in the introduction section. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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]]<br />
# When using mathematical expressions and symbols, please use the equation editor. (e.g., x*y, exy + y, sin (x+y) - x2)<br />
* At least one numerical example<br />
# Please add a few sentences to show the transition from problem to solution. <br />
# The solution technique should be clearly presented, and solved "step-by-step".<br />
# GAMS code is unnecessary. Please provide detailed step-by-step calculation results.<br />
* A section to discuss and/or illustrate the applications<br />
# Having a list is not enough. Please explain at least three applications in a few sentences each. <br />
# 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.<br />
* A conclusion section: <br />
* References<br />
# 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]]<br />
# Please follow the standard reference style - the current format is incorrect.<br />
<br />
== [[Branch and bound (BB) for MINLP|Branch and Bound for MINLP]] ==<br />
<br />
* Author list:<br />
** Remove NetIDS<br />
** Please remove abbreviations from the title (i.e. BB).<br />
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.<br />
* An introduction of the topic<br />
# 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]]<br />
# 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.<br />
# An illustration might be useful here. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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.<br />
# Use linked citations please as the Wiki template above. <br />
# 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.<br />
# Step 2 is missing yet it is referenced in the text multiple times. Please address this in addition to the above comment.<br />
# An illustration might be useful here as well. <br />
# Please explain what a Gomory Cut is. If the topic is available on optimization.cb.cornell.edu, you can link it. <br />
# The current equations seem to be simple text written in Italics. All mathematical symbols and equations should be formatted via LaTex.<br />
# Please format the math programs with equations and notations using formulations in lecture notes as templates.<br />
* At least one numerical example<br />
# Please add a few sentences to show the transition from problem to solution.<br />
# 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).<br />
# 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.<br />
# 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.<br />
# Make sure your example is not taken from a book as that is strictly disallowed. <br />
* A section to discuss and/or illustrate the applications<br />
# 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.<br />
# 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.<br />
* A conclusion section:<br />
# 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. <br />
# Please use summarizing sentences to describe earlier sections instead of introducing new concepts/discussion. <br />
* References<br />
# Too few references overall, you should aggregate information from multiple sources. A quick Google scholar search could provide relevant references.<br />
# 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]]<br />
# Please follow the standard reference style - the current format is incorrect.</div>Asa279https://optimization.cbe.cornell.edu/index.php?title=2021_Cornell_Optimization_Open_Textbook_Feedback&diff=47972021 Cornell Optimization Open Textbook Feedback2021-12-06T02:42:01Z<p>Asa279: /* McCormick Envelopes */</p>
<hr />
<div>== [[Lagrangean duality|Lagrangian duality]] ==<br />
* Author list, sections and TOC<br />
# Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.<br />
# Remove cornell ID from Author list<br />
* An introduction of the topic<br />
# 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.<br />
# Definitions of LR and its relation to duality should be double checked and re-written.<br />
# Only one reference is present in this section. Please add more relevant references by expanding this section.<br />
# Consider merging the “introduction” and “history” sections.<br />
# In the titles, please change the font from bold to normal to have consistent formatting in the site.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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.<br />
# 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 (,).<br />
# 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.<br />
# 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.<br />
# Last step of the “process” subsection also needs updating according to the previous comments.<br />
# The inline notations should also be typed using LaTex.<br />
# Please use the LaTex code or equation editor for min, s.t., etc.<br />
* At least one numerical example<br />
# 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.<br />
# All consecutive steps need to be updated since the dual variables would be updated.<br />
# After substitution the nonlinear function should be further simplified. The current expression reads like a highly nonlinear function but can be easily simplified.<br />
# 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.<br />
# Please use the LaTex code or equation editor for min, s.t., etc.<br />
* A section to discuss and/or illustrate the applications<br />
# Bullet points could be used to state the last four real-world examples that explain the physical meaning of the primal and dual problems.<br />
# Add references for the last set of applications. <br />
* A conclusion section<br />
# This section contains a few typos. Please fix the same.<br />
* References<br />
# Some citations' hyperlinks are displaying.<br />
<br />
== [[Disjunctive inequalities|Disjunctive Inequalities]] ==<br />
<br />
* Author list<br />
# Missing course section and semester<br />
# Remove cornell ID<br />
* An introduction of the topic<br />
# No citations are present in this section.<br />
# “mixed-integer programming (MIP)” should be used instead of “multiple integer programming (MIP)”. Please fix this error.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# The abbreviation MILP is not previously defined. Please fix this issue.<br />
# You consistently use the negative sign instead of the NOT operator for y (-y instead of ¬y). <br />
# Some inconsistencies with the spacing of variables, constraints, etc., under the “General” section that need to be fixed.<br />
# 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.<br />
* At least one numerical example<br />
# 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.<br />
# Add space between vee (V) operator and brackets in first line of Latex<br />
# Please format variables correctly, for example, use <math>x_1</math> instead of x1.<br />
* A section to discuss and/or illustrate the applications<br />
# Please format the equations appropriately either by using latex code or the visual editor. These images are NOT acceptable!<br />
* A conclusion section<br />
# There is no conclusion presented in this section at all.<br />
* References<br />
# 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. <br />
# There are many papers on this topic. A simple Google (Scholar) search could provide you with sufficient references to cite. <br />
# Many important references of this topic are missing.<br />
# 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]]<br />
<br />
==[[Stochastic programming|Stochastic Programming]] ==<br />
<br />
* Author list: Remove cornell IDs<br />
* An introduction of the topic<br />
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki. <br />
# 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.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Please avoid direct inline linkbacks to Wikipedia.<br />
# The symbol “xi” in the methodology subsection should be explained.<br />
* At least one numerical example<br />
# Copying a numerical example "entirely" from a textbook is inappropriate. Your team should come up with a "numerical" case.<br />
# No specific application context is needed for a numerical example.<br />
# The inline notations (`x1`, `s1`) should also be typed using LaTex.<br />
# Label all tables with a table number for better readability. <br />
# 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. <br />
* A section to discuss and/or illustrate the applications;<br />
# I suggest eliminating citing the last name of the first author (i.e. Zhou et al.)<br />
* A conclusion section <br />
* References<br />
# URLs of some citations are not properly formatted (not showing the hyperlinks).<br />
<br />
== [[Exponential transformation|Exponential Transformation]] ==<br />
<br />
* Author list<br />
# Missing course section<br />
# Remove cornell ID<br />
* An introduction of the topic<br />
# Please expand the introduction.<br />
# Please aim for a maximum average sentence length of ~25 words. Last sentence with 51 words is hard to read. <br />
# Second Sentence: please change the word “they” as it could make the meaning ambiguous<br />
# 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. <br />
# If you use abbreviations, please introduce them (e.g. NLP,MINLP)<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Please explain the transformation in words along with equations<br />
# Terms like posynomial should be described in detail.<br />
# Please move the numerical example to the section below<br />
# The “(eq 1)” is not needed here.<br />
# Please expand this section.<br />
* At least one numerical example<br />
# In the third equation of the numerical example, it is confusing to have coefficients after numbers. Some readers may read it as an exponent.<br />
# Last equation in this section after “further linearization” is incorrect. This equation cannot be further linearized, please fix this.<br />
# Please explain the steps in the numerical examples in detail. The step-by-step solution should be provided. <br />
# 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.<br />
* A section to discuss and/or illustrate the applications<br />
# Missing part of text: “Proof of convexity of with positive definite test of Hessian…”<br />
# Applications are not numerical examples. Please refer to this link for example of applications: [[Duality|https://optimization.cbe.cornell.edu/index.php?title=Duality]]<br />
# Citation 7 is missing in current applications<br />
# The section current applications is redundant<br />
# Please use the LaTex code or equation editor for min, s.t., etc.<br />
# 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. <br />
# The convexification application of MINLP can be further simplified for binary variables. Please refer to the lecture slides for more information.<br />
* A conclusion section<br />
# 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. <br />
* References<br />
# 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]]<br />
# Citation 7 is missing in current applications<br />
<br />
== [[Sparse Reconstruction with Compressed Sensing|Sparse reconstruction with Compressed Sensing]] ==<br />
This Wiki needs a significant rewrite. Please go through the comments for details.<br />
<br />
* An introduction of the topic<br />
# 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.<br />
# This section includes several typos like “sub modual”. Please fix them throughout the wiki and delete them if not required.<br />
# Many abbreviations are used before previously defining them. Please define these abbreviations before using them in the text.<br />
# This section is incomprehensible in its current form. Please rewrite with proper comprehension.<br />
# 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).<br />
# Try to place the figure at the top of the Wiki between the main text.<br />
# Avoid pronouns such as “we”.<br />
# I suggest the use of more formal abstract illustrations. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Equations and symbols need proper reformatting.<br />
# 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.<br />
# All equations need to be better formatted.<br />
<br />
* At least one numerical example<br />
# Numerical example is missing.<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
* A section to discuss and/or illustrate the applications<br />
# Having a list is not enough. Please explain at least three applications in a few sentences each.<br />
* A conclusion section<br />
# Conclusion section is missing.<br />
* References<br />
# 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]]<br />
# More references should be added. A simple Google Scholar search would give you many references.<br />
<br />
== [[Portfolio optimization|Portfolio Optimization]] ==<br />
<br />
* Author list<br />
# Remove cornell id<br />
* An introduction of the topic<br />
# 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. <br />
# Amount of whitespace can be reduced by changing the orientation of Figure 1 and the sentences in this section.<br />
# 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. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# A brief mention of modern portfolio theory (i.e.. Markowitz) would be appropriate in this section. <br />
# 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.<br />
# Use LaTex to distinguish variables written within a sentence, such as m and n. <br />
# 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.”<br />
# An explanation of a few common constraints would be helpful, rather than just including a table. <br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
# Solving the numerical example by GAMS is inappropriate. Please provide detailed step-by-step calculation results.<br />
# All tables need to be labeled.<br />
# Include figure number in label for consistency. <br />
# Fix misspelling “dolling decision variables”. <br />
# Use LaTex for all variables, equations, and constraints here.<br />
# Example 2 table is hard to read, so making it bigger would help. <br />
# Remove the “Using excel as the solver” part from the sentence before the solution discussion. <br />
# Some grammatical errors here (phrases such as “.. is as follows” should be followed by a colon). <br />
* A section to discuss and/or illustrate the applications<br />
# Rephrase “Portfolio optimization can be used to screen investment projects that meet investors, rationally allocate investment amounts, etc.”<br />
# Not sure “relevant” is the correct word choice here. <br />
# 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. <br />
* A conclusion section<br />
# Need some commas here.<br />
# The sentence “Linear programming has been around since the 1940’s and has such a wide base of applications” is not necessary. <br />
* References<br />
# 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]]<br />
# Remove white space between end of sentences and reference numbers.<br />
<br />
== [[Chance-constraint method|Chance constraint method]] ==<br />
<br />
* Author list: <br />
* An introduction of the topic<br />
# 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”<br />
# In “Chance-constraint”, it is capitalized randomly throughout the introduction. Please correct. <br />
# 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.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Please add a citation to the first sentence. <br />
# Xi is an uncertainty/randomness variable. It is better to use clear language. <br />
# 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.<br />
# Theory is insufficient. Please expand and explain different approaches. <br />
# Please add pros and cons explicitly as a list. <br />
# Explain the physical meaning for examples of chance constraints along with all the notations used.<br />
# 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. <br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
# Please remove this example as it is directly from this book. The example should be purely numerical without any background.<br />
# Please use the equation editor for min, st., etc.<br />
# 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. <br />
# Please change the table format so as not to confuse the reader. <br />
# Multiple instances of [Chart to be added] are missing.<br />
# Example is incomplete. <br />
# Avoid pronouns such as “we”.<br />
* A section to discuss and/or illustrate the applications<br />
# Please connect several grammatical and spelling errors: “real life application”, Energy creation, particularly in renewable sources, have high variabilities”, and others<br />
# “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. <br />
* A conclusion section<br />
# 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.<br />
# 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. <br />
* References<br />
# 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]]<br />
# More references should be added. A simple Google Scholar search would give you many references.<br />
<br />
== [[Bayesian Optimization]] ==<br />
* Section titles should not be "bold". Please double check using source editor on the section titles.<br />
* 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.<br />
* Author list: Remove cornell ID, Please check names<br />
* Introduction<br />
# 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.<br />
# 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.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Captions need reformatting.<br />
# Consider italicizing keywords rather than bolding.<br />
# Please add a citation to the first sentence. <br />
# 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.<br />
# Avoid pronouns such as “we”.<br />
# Please write equations in the Wiki instead of attaching images for equations.<br />
# Acquisition function figure could be made larger and clearer to improve readability.<br />
* At least one numerical example<br />
# Any references to functions or methods in code ‘e.g. fmin’ should be properly formatted as code-stylized text.<br />
# Please use the equation editor for min, st., etc.<br />
# Avoid including a figure of the code for this example and explicitly describe the steps to the modeling and solution process instead. <br />
# Avoid pronouns such as “our” and “we”.<br />
* A section to discuss and/or illustrate the applications <br />
* A conclusion section<br />
# Please do not use brackets to enclose lists.<br />
# Some claims here should be supported by references. Please cite each source after its sentence. <br />
* References<br />
# 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]]<br />
# Try to avoid references to “pop” machine learning blogs where anyone can be an author. (e.g. towardsdatascience)<br />
# All references are URLs. Please cite publications and literature.<br />
# A simple Google Scholar search would give you many references.<br />
<br />
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.<br />
<br />
== [[Conjugate gradient methods]] ==<br />
<br />
* Author list: Remove cornell ID<br />
* Introduction<br />
# All inline notations (e.g., `x`, `A`) should be typed using LaTex.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# All equations need to be better formatted.<br />
# Is Gauss-Newton no longer referenced?<br />
# 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.<br />
# Please indent equation blocks.<br />
# Please properly format pseudocode.<br />
* At least one numerical example<br />
# Steps should be accompanied with explanation, or reference to the corresponding step in the pseudocode.<br />
# Please properly format in a more organized manner, aligning equations appropriately and demarcating steps appropriately.<br />
* A section to discuss and/or illustrate the applications <br />
# Consider including 2 additional examples of applications<br />
* A conclusion section<br />
# Consider adding future research directions<br />
* References<br />
# Reference primary sources rather than Wikipedia<br />
# Too few references.<br />
# More references should be added. A simple Google Scholar search would give you many references.<br />
<br />
== [[Geometric programming|Geometric Programming]] ==<br />
<br />
* Author list<br />
# Remove cornell ID<br />
* An introduction of the topic<br />
# Examples of applications in this section use the same reference. Please cite their individual sources.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# The symbol denoting the domain in the definition of a monomial is unclear. Please clarify it or fix this if it is incorrect.<br />
# Definition of posynomial refers to section 2.1 which is missing from the Wiki (sections are not numbered in the main text).<br />
# 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.<br />
# Additional theory on the feasibility analysis could be provided in this section.<br />
* At least one numerical example<br />
# 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.<br />
* A section to discuss and/or illustrate the applications<br />
# The figure in this section needs to be labeled. <br />
# The figure needs to be resized and perhaps aligned to the center. <br />
* A conclusion section:<br />
# Please avoid vague language such as: “This makes”.<br />
# Please avoid opinionated statements: “one of the best ways”.<br />
* References<br />
# 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]]<br />
# This Wiki has very few references. A quick Google Scholar search may provide relevant references.<br />
<br />
== [[Adam]] ==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
# Some grammatical errors here, mostly related to the need for commas in certain places (e.g., “Before Adam..”).<br />
# Some minor errors with parts of speech throughout the section, need to revisit phrases such as “which has broader scope in future for”, etc. <br />
# Try splitting up some of the longer sentences in this section, a couple are hard to read.<br />
# 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. <br />
# What does adam stand for? Introduction is insufficient. Please expand. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Revise grammar here, noticing some missing commas and uncapitalized word after period.<br />
# Rephrase “second one is to update the old position with the updated position”.<br />
# Use LaTex code or equation editor to display all equations and variables in this section, and actual subscripts instead of “m_t”, etc. <br />
# 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. <br />
# Remove white space before the period in RMSP discussion.<br />
# Please provide a pseudocode. <br />
# Please use list the two methods here “Adam is a combination of two gradient descent methods which are explained below”<br />
# Please expand the theory section significantly. Theoretical convergence properties should be discussed, even if briefly.<br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
* A section to discuss and/or illustrate the applications<br />
# Same comment as before, consider replacing inline citations after words like “According to..”. <br />
* A conclusion section <br />
* References<br />
# 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]]<br />
# Try to avoid references to blogs and use peer-reviewed academic references instead. <br />
# Too few references.<br />
# More references should be added. A simple Google Scholar search would give you many references.<br />
<br />
== [[A-star algorithm|a* algorithm]] ==<br />
<br />
* Author list: Remove cornell ID<br />
* Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.<br />
* An introduction of the topic:<br />
# Weird spacing between paragraphs. Please fix this issue.<br />
# In the titles, please change the font from bold to normal to have consistent formatting in the site. <br />
# Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.<br />
# There are no citations in the introduction. Please cite every source.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Please add the mathematical description of the algorithm.<br />
# 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]]<br />
# 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”.<br />
# In algorithms, it is a standard to add high-level description (i.e. pseudocode or flowchart). Please incorporate it. <br />
# 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.<br />
* At least one numerical example<br />
# The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.<br />
# Instead of writing things like “The above image..”, label each figure and use the figure number to refer to it in text. <br />
# 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. <br />
* A section to discuss and/or illustrate the applications<br />
# No references in the applications. Please cite every source <br />
# Preferably, add at least an additional application. <br />
* A conclusion section<br />
# Conclusion should summarize descriptions. Please modify it to provide a summary. <br />
# Please pay attention to the length and structure of sentences here and in the full page. First sentence is hard to read.<br />
* References<br />
# 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]]<br />
# Incorrect reference style. Please follow the example and use the template.<br />
<br />
== [[Job shop scheduling|Job-Shop Scheduling Problem]] ==<br />
<br />
* An introduction of the topic<br />
# 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.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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.<br />
# 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.<br />
# 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.<br />
# 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.<br />
# Use LaTex code or equation editor to display all equations and variables in this section and all other sections as well.<br />
# Check grammar in this section. For example, phrases like “are as follows” need to be followed by a colon and not a period. <br />
# Consider rewriting the assumptions as a list in this section. <br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
# 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.<br />
# 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.<br />
# A numerical example should be simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments).<br />
* A section to discuss and/or illustrate the applications<br />
# 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. <br />
* A conclusion section<br />
# The meaning of “Operations applications” is unclear. Please explain or update if necessary.<br />
# The current conclusion section does not properly summarize the problem. Please refer to other Wiki examples for an idea to update the section accordingly.<br />
* References<br />
# 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]] <br />
# Please reference media sources like reference 5 appropriately.<br />
# A simple Google Scholar search would give you many "formal" references.<br />
<br />
== [[Optimization in game theory]] ==<br />
<br />
* Author list: remove cornell IDs. <br />
* An introduction of the topic<br />
# 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]] <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Why only a subsection on "Nash Equilibrium" is included in "Theory" section? Please re-format.<br />
# Please edit references.<br />
# Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm. <br />
# Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.<br />
* At least one numerical example<br />
# Please organize the last part in a more readable format. Questions may be in bold and numbered, answers are more direct, etc.<br />
# Remember to cite all images and tables. <br />
# 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.<br />
* A section to discuss and/or illustrate the applications<br />
# Very good, link the reference and cite all sources. <br />
* A conclusion section<br />
# Please add more summarizing especially from theory sentences and avoid long sentences. <br />
* References<br />
# 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]]<br />
# Reference primary sources rather than Wikipedia<br />
# Incorrect reference style. Please correct.<br />
<br />
== [[Trust-region methods]] ==<br />
<br />
* Author list:<br />
# Remove cornell IDs. Author is also spelled incorrectly. <br />
# Add the course section.<br />
* An introduction of the topic<br />
# 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]] <br />
# 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.<br />
# Avoid pronouns such as “we”. This goes for all other sections as well.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Organization of ideas in this section needs work.<br />
# 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.<br />
# Each approach should have accompanying explanation and motivation for why it is being discussed. It is not enough to outline the algorithm.<br />
# Please make sure symbols are properly subscripted and superscripted (e.g. “pk” should be “p_k”<br />
# Please format the algorithm in proper algorithmic pseudocode format.<br />
# Little to no discussion on global convergence guarantees<br />
# Please include discussion about the advantages and disadvantages of the algorithm<br />
# Fix typo “couchy point”.<br />
* At least one numerical example<br />
# Any code functions (uminfunc) should have proper text formatting.<br />
# The graph needs a better caption explaining how the axes are labeled and what data points are being shown.<br />
# Please increase the quality of the figure. It is hard to see the red line. <br />
# 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.”<br />
* A section to discuss and/or illustrate the applications<br />
# 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).<br />
* A conclusion section<br />
# Please add more summary, future research directions for example is a good start.<br />
* References<br />
# Incorrect reference style.<br />
# Please consider having the references as this Wiki template, <nowiki>https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization</nowiki><br />
# More references should be added. A simple Google Scholar search would give you many references.<br />
<br />
*There are numerous misspellings, grammatical errors, and incorrect claims. Please fix these.<br />
<br />
== [[Momentum]] ==<br />
<br />
* Author list<br />
# Remove cornell ID<br />
* An introduction of the topic<br />
# 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.<br />
# Remove bold on “Momentum”.<br />
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Equation formatting is very poor and should be formalized.<br />
# 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.<br />
# 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.<br />
# 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.<br />
# Avoid pronouns such as “you”.<br />
* At least one numerical example<br />
# 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.<br />
# Please try to label the plots that explains what each line color means.<br />
# Starting point for SGD with momentum is different in explanation and the table. Please fix the same.<br />
* A section to discuss and/or illustrate the applications<br />
# Please use correct terminology like “optimizing non-convex functions” and not “training non-convex models”.<br />
# Adam, Adadelta, and RMSprop are variants of SGD that already use momentum. Please double check the writing and update if necessary.<br />
* A conclusion section<br />
# Please refrain from using words like “zig zag” effects.<br />
* References<br />
# 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.<br />
<br />
== [[Stochastic dynamic programming|Stochastic Dynamic programming]] ==<br />
<br />
* Author list<br />
# Remove cornell ID<br />
* An introduction of the topic<br />
# Discussion on applications should be moved to a separate section.<br />
* Theory, methodology, and/or algorithmic discussions <br />
# Remove the grey box background of equations.<br />
* At least one numerical example <br />
* A section to discuss and/or illustrate the applications <br />
* A conclusion section <br />
* References<br />
# 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]]<br />
<br />
== [[Outer-approximation (OA)|Outer-approximation]] ==<br />
<br />
* An introduction of the topic <br />
# See formatting guideline below<br />
# Avoid opinionated statements such as “MINLP problems are usually the hardest to solve”.<br />
# Rearrange the text such that the MINLP formulation is in the theory section and keep the introduction in words only. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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<br />
# The sentence “The Outer-Approximation (OA) algorithm was first proposed by Duran and and Grossmann in 1986 to solve MINLP problems.” needs a reference. <br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
# “Minimize” and “subject to” should be “min” and “s.t.” in MathType<br />
* A section to discuss and/or illustrate the applications<br />
# 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)<br />
# 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. <br />
# 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.<br />
# Consider reformatting to make steps more readable. Inserting spaces and breaking down steps would help. <br />
* A conclusion section<br />
# Too short. Consider discussion on future research direction and discussion on uncertainty<br />
# 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)”. <br />
* References<br />
# 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]]<br />
# Remove "Template:Reflist"<br />
<br />
== [[Unit commitment problem]] ==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
# Please expand the introduction and avoid discussions of examples or specific applications in this section.<br />
# The sentence “Nonlinear, Non-convex programming optimization problem.” doesn’t make sense by itself and Non-convex shouldn’t be capitalized. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Figure/image format should be revised to better display the content.<br />
# Uppercase characters are used randomly (e.g., “non-convex transmission Constraints”) . Please follow correct language conventions for sentence structure.<br />
# 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. <br />
# Don’t say “written in matrix form as equation..” and just cite the reference, actually write out the equation. <br />
# Properly label the figure in this section with a figure number and improve visibility by making it larger. <br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
# Label the figures in this section properly with figure numbers.<br />
# Fix typo “while minimize” to “while minimizing”. <br />
# Avoid pronouns such as “we”. <br />
# Use the equation editor when typing equations. <br />
# 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.<br />
# 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).<br />
* A section to discuss and/or illustrate the applications:<br />
# I suggest changing the order of the subtitles here. For example, Single-Period Unit Commitment. <br />
* A conclusion section <br />
* References<br />
<br />
== [[Frank-Wolfe]] ==<br />
<br />
* Author list: <br />
* An introduction of the topic<br />
# I suggest highlighting disadvantages along with advantages. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# “[n x 1] matrix” please use the equation editor to express mathematical descriptions and symbols (p,b, etc)<br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
# Please show at least a few iterations. Even for smaller examples if needed. Report the final solution. <br />
# Please use the LaTex code or equation editor for min and include s.t., etc.<br />
# 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.<br />
* A section to discuss and/or illustrate the applications: <br />
* A conclusion section<br />
# Same as the introduction. Pros and cons should be evaluated together!<br />
* References<br />
# 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]]<br />
<br />
== [[Line search methods|Line Search Method]] ==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
# Expand the introduction and avoid discussion on some of the specific steps in the solution process. <br />
# Provide references here. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# The phrase “are as follows” in the steepest descent method discussion needs to be followed by a colon. <br />
# Rephrase “has a nice convergence theory” and cite a reference for this claim.<br />
# Avoid pronouns such as “we”.<br />
# Add citation after “.. proposed by Phillip Wolfe in 1969.”<br />
# Figure 1 is between two sections. Please fix this issue. <br />
* At least one numerical example:<br />
# Add some space between iterations or subsection break<br />
* A section to discuss and/or illustrate the applications:<br />
# Too few references in this section. <br />
# Last paragraph makes some claims without references. <br />
* A conclusion section <br />
* References<br />
# 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]]<br />
# More references should be added. A simple Google Scholar search would give you many references.<br />
<br />
== [[Piecewise linear approximation|Piecewise Linear Approximation]]==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
# 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. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Fix typo “to force the x’ values become associated with”. <br />
* At least one numerical example <br />
* A section to discuss and/or illustrate the applications<br />
# Please aim for a maximum average sentence length of ~25 words. Some of these longer sentences are hard to read. <br />
* A conclusion section<br />
# 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.<br />
* References<br />
# Include hyperlinks to sources when possible.<br />
<br />
== [[Mathematical programming with equilibrium constraints|Mathematical Programming with Equilibrium constraints]] ==<br />
<br />
* An introduction of the topic<br />
# 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.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# The meaning of parameter vector x is unclear. Please add more information or update if necessary.<br />
# 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.<br />
# Use equations instead of images to represent math programs and equations in the Implicit Descent and SQP subsection.<br />
# Apart from the steps for each solution technique, please also add a few sentences that describe each method.<br />
* At least one numerical example<br />
# Please define the terms like NCP, MP before abbreviating them. Also try not to unnecessarily abbreviate simple terms.<br />
# Equations should be typed by LaTex. Images for equations are unacceptable.<br />
# GAMS code is strongly discouraged. Please solve the problem "step-by-step".<br />
# 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.<br />
# Avoid using figures in the equations (subject to etc)<br />
* A section to discuss and/or illustrate the applications<br />
# Add references to “power management, highway pricing, chemical process engineering, and traffic planning.”<br />
* A conclusion section<br />
* References<br />
# 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]]<br />
# This Wiki contains very few references. Please check the list below and run a quick Google (Scholar) search to identify relevant literature.<br />
<br />
== [[Wing shape optimization|Wing shape Optimization]] ==<br />
<br />
* Author list: Remove cornell ID<br />
* 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.<br />
* An introduction of the topic<br />
# 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.)<br />
# Avoid discussion involving finer details of subject methods in this section. <br />
# In the titles, please change the font from bold to normal to have consistent formatting in the site. Same applies to box of content!<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Properly cite the CFD package, don’t just include a link. <br />
# Properly label the figure with a figure number.<br />
# Consider removing white space between isolated sentences to improve readability. <br />
* At least one numerical example<br />
# If you’ve already defined an abbreviation (CFD), there is no need to define it again. Just use the abbreviation.<br />
# Avoid pronouns such as “we” or “they”.<br />
# Phrases like “under the following” need to be followed by a colon.<br />
# 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.<br />
# “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. <br />
# Avoid inserting inline citations like “[4] introduces an..” as it is a bit informal when you don’t explicitly name the subject.<br />
# 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.<br />
# 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.<br />
# 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.<br />
# 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).<br />
* A section to discuss and/or illustrate the applications<br />
# Some characters are randomly capitalized in this section. <br />
* A conclusion section<br />
# 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. <br />
* References<br />
# 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]]<br />
<br />
== [[Interior-point method for NLP|Interior point method for NLP]] ==<br />
<br />
* An introduction of the topic: <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Primal-Dual formulation and comparison to the Barrier Method is not discussed.<br />
# Include brief discussion about big O convergence rates.<br />
# Need discussion about the concept of “central path” and the notion of self concordance<br />
# 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.<br />
# Graphs and images are incorrectly formatted to the page. Consider proper alignment with respect to the text body.<br />
# Use explicitly typed Latex equations instead of images to represent math programs and equations.<br />
# Fix typo “optimisation”.<br />
# Use LaTex code or equation editor to display all equations and variables (e.g., “xi ”, “μ”, etc.).<br />
* At least one numerical example:<br />
# There are formatting issues with figures 2,3. Please make sure to embed them within their respective sections. <br />
* A section to discuss and/or illustrate the applications<br />
* A conclusion section <br />
# Minor character code typos in the conclusion.<br />
# Also, please add more discussion in this section. Future research directions is a good start.<br />
# There is a box ""<br />
* References<br />
<br />
== [[AdaGrad|Adagrad]] ==<br />
<br />
* An introduction of the topic: <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Include discussion on its variants (most important is AdaDelta).<br />
# Include disadvantages of Adagrad, since this provides motivation for the discussion on the variants and improvements of Adagrad<br />
# Include comparisons to other popular optimizers (particularly important is comparisons to regular SGD and Adam)<br />
# 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.<br />
# Algorithm image is blurry. Either increase the fidelity or write the pseudocode directly in the wiki editor.<br />
* At least one numerical example<br />
# In the first sentence, “..take the following numerical example” should be followed by a colon. <br />
# Fix typo “trayectory”.<br />
* A section to discuss and/or illustrate the applications<br />
# This section is too short; include specific applications in which input features are sparse and Adagrad excels.<br />
# Add reference to the claim “Mainly, it is a good choice for deep learning models with sparse input features”.<br />
* A conclusion section <br />
* References <br />
<br />
# Too few references overall, you should aggregate information from multiple sources (even if the base algorithm itself comes from a singular paper)<br />
<br />
== [[McCormick envelopes|McCormick Envelopes]] ==<br />
<br />
* Author list: OK but I suggest removing NetID<br />
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.<br />
* An introduction of the topic<br />
# First sentence is hard to read. Please consider keeping sentences below 25-30 words. <br />
# No references provided. Please cite all sources. <br />
# Figure 1 is provided in the middle between two sections. Please include in the introduction section. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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]]<br />
# When using mathematical expressions and symbols, please use the equation editor. (e.g., x*y, exy + y, sin (x+y) - x2)<br />
* At least one numerical example<br />
# Please add a few sentences to show the transition from problem to solution. <br />
# For the sample GAMS code, please place it in a code box<br />
* A section to discuss and/or illustrate the applications<br />
# Having a list is not enough. Please explain at least three applications in a few sentences each. <br />
# 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.<br />
* A conclusion section: <br />
* References<br />
# 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]]<br />
# Please follow the standard reference style - the current format is incorrect.<br />
== [[Branch and bound (BB) for MINLP|Branch and Bound for MINLP]] ==<br />
<br />
* Author list:<br />
** Remove NetIDS<br />
** Please remove abbreviations from the title (i.e. BB).<br />
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.<br />
* An introduction of the topic<br />
# 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]]<br />
# Introduction is very short for a well recognized topic. Please expand significantly. <br />
# An illustration might be useful here. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Use linked citations please as the Wiki template above. <br />
# 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.<br />
# An illustration might be useful here as well. <br />
# Please explain what a Gomory Cut is. If the topic is available on optimization.cb.cornell.edu, you can link it. <br />
* At least one numerical example<br />
# Please add a few sentences to show the transition from problem to solution.<br />
# 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).<br />
# 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.<br />
# Make sure your example is not taken from a book as that is strictly disallowed. <br />
* A section to discuss and/or illustrate the applications<br />
# 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).<br />
# 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.<br />
* A conclusion section:<br />
# 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. <br />
# Please use summarizing sentences to describe earlier sections instead of introducing new concepts/discussion. <br />
* References<br />
# Too few references overall, you should aggregate information from multiple sources. <br />
# 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]]<br />
# Please follow the standard reference style - the current format is incorrect.</div>Asa279https://optimization.cbe.cornell.edu/index.php?title=2021_Cornell_Optimization_Open_Textbook_Feedback&diff=47582021 Cornell Optimization Open Textbook Feedback2021-12-05T02:46:31Z<p>Asa279: </p>
<hr />
<div>== [[Lagrangean duality|Lagrangian duality]] ==<br />
* Author list, sections and TOC<br />
# Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.<br />
# Remove cornell ID from Author list<br />
* An introduction of the topic<br />
# 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.<br />
# Definitions of LR and its relation to duality should be double checked and re-written.<br />
# Only one reference is present in this section. Please add more relevant references by expanding this section.<br />
# Consider merging the “introduction” and “history” sections.<br />
# In the titles, please change the font from bold to normal to have consistent formatting in the site.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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.<br />
# 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 (,).<br />
# 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.<br />
# 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.<br />
# Last step of the “process” subsection also needs updating according to the previous comments.<br />
# The inline notations should also be typed using LaTex.<br />
# Please use the LaTex code or equation editor for min, s.t., etc.<br />
* At least one numerical example<br />
# 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.<br />
# All consecutive steps need to be updated since the dual variables would be updated.<br />
# After substitution the nonlinear function should be further simplified. The current expression reads like a highly nonlinear function but can be easily simplified.<br />
# Similar to the comments in the methodology section, inverting minimize to maximize is incorrect. Please update the dual objective function accordingly.<br />
# Please use the LaTex code or equation editor for min, s.t., etc.<br />
* A section to discuss and/or illustrate the applications<br />
# Bullet points could be used to state the last four real-world examples that explain the physical meaning of the primal and dual problems.<br />
# Add references for the last set of applications. <br />
* A conclusion section<br />
# This section contains a few typos. Please fix the same.<br />
* References<br />
# Some citations' hyperlinks are displaying.<br />
<br />
== [[Disjunctive inequalities|Disjunctive Inequalities]] ==<br />
<br />
* Author list<br />
# Missing course section and semester<br />
# Remove cornell ID<br />
* An introduction of the topic<br />
# No citations are present in this section.<br />
# “mixed-integer programming (MIP)” should be used instead of “multiple integer programming (MIP)”. Please fix this error.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# The abbreviation MILP is not previously defined. Please fix this issue.<br />
# You consistently use the negative sign instead of the NOT operator for y (-y instead of ¬y). <br />
# Some inconsistencies with the spacing of variables, constraints, etc., under the “General” section that need to be fixed.<br />
# 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.<br />
* At least one numerical example<br />
# 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.<br />
# Add space between vee (V) operator and brackets in first line of Latex<br />
# Please format variables correctly, for example, use x1 instead of x1.<br />
* A section to discuss and/or illustrate the applications<br />
# Please format the equations appropriately either by using latex code or the visual editor. These images are NOT acceptable!<br />
* A conclusion section<br />
# There is no conclusion presented in this section at all.<br />
* References<br />
# 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. <br />
# There are many papers on this topic. A simple Google (Scholar) search could provide you with sufficient references to cite. <br />
# Many important references of this topic are missing.<br />
# 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]]<br />
<br />
==[[Stochastic programming|Stochastic Programming]] ==<br />
<br />
* Author list: Remove cornell IDs<br />
* An introduction of the topic<br />
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki. <br />
# 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.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Please avoid direct inline linkbacks to Wikipedia.<br />
# The symbol “xi” in the methodology subsection should be explained.<br />
* At least one numerical example<br />
# Copying a numerical example "entirely" from a textbook is inappropriate. Your team should come up with a "numerical" case.<br />
# No specific application context is needed for a numerical example.<br />
# The inline notations (`x1`, `s1`) should also be typed using LaTex.<br />
# Label all tables with a table number for better readability. <br />
# 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. <br />
* A section to discuss and/or illustrate the applications;<br />
# I suggest eliminating citing the last name of the first author (i.e. Zhou et al.)<br />
* A conclusion section <br />
* References<br />
# URLs of some citations are not properly formatted (not showing the hyperlinks).<br />
<br />
== [[Exponential transformation|Exponential Transformation]] ==<br />
<br />
* Author list<br />
# Missing course section<br />
# Remove cornell ID<br />
* An introduction of the topic<br />
# Please expand the introduction.<br />
# Please aim for a maximum average sentence length of ~25 words. Last sentence with 51 words is hard to read. <br />
# Second Sentence: please change the word “they” as it could make the meaning ambiguous<br />
# 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. <br />
# If you use abbreviations, please introduce them (e.g. NLP,MINLP)<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Please explain the transformation in words along with equations<br />
# Terms like posynomial should be described in detail.<br />
# Please move the numerical example to the section below<br />
# The “(eq 1)” is not needed here.<br />
# Please expand this section.<br />
* At least one numerical example<br />
# In the third equation of the numerical example, it is confusing to have coefficients after numbers. Some readers may read it as an exponent.<br />
# Last equation in this section after “further linearization” is incorrect. This equation cannot be further linearized, please fix this.<br />
# Please explain the steps in the numerical examples in detail. The step-by-step solution should be provided. <br />
# 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.<br />
* A section to discuss and/or illustrate the applications<br />
# Missing part of text: “Proof of convexity of with positive definite test of Hessian…”<br />
# Applications are not numerical examples. Please refer to this link for example of applications: [[Duality|https://optimization.cbe.cornell.edu/index.php?title=Duality]]<br />
# Citation 7 is missing in current applications<br />
# The section current applications is redundant<br />
# Please use the LaTex code or equation editor for min, s.t., etc.<br />
# 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. <br />
# The convexification application of MINLP can be further simplified for binary variables. Please refer to the lecture slides for more information.<br />
* A conclusion section<br />
# 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. <br />
* References<br />
# 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]]<br />
# Citation 7 is missing in current applications<br />
<br />
== [[Sparse Reconstruction with Compressed Sensing|Sparse reconstruction with Compressed Sensing]] ==<br />
This Wiki needs a significant rewrite. Please go through the comments for details.<br />
<br />
* An introduction of the topic<br />
# 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.<br />
# This section includes several typos like “sub modual”. Please fix them throughout the wiki and delete them if not required.<br />
# Many abbreviations are used before previously defining them. Please define these abbreviations before using them in the text.<br />
# This section is incomprehensible in its current form. Please rewrite with proper comprehension.<br />
# Equations and math symbols need proper reformatting. The current version reads like text (along with equations) copy-pasted from a specific source.<br />
# Try to place the figure at the top of the Wiki between the main text.<br />
# Avoid pronouns such as “we”.<br />
# I suggest the use of more formal abstract illustrations. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Equations and symbols need proper reformatting.<br />
# 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.<br />
* At least one numerical example<br />
# Numerical example is missing.<br />
* A section to discuss and/or illustrate the applications<br />
# Having a list is not enough. Please explain at least three applications in a few sentences each.<br />
* A conclusion section<br />
# Conclusion section is missing.<br />
* References<br />
# 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]]<br />
<br />
== [[Portfolio optimization|Portfolio Optimization]] ==<br />
<br />
* Author list<br />
# Remove cornell id<br />
* An introduction of the topic<br />
# 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. <br />
# Amount of whitespace can be reduced by changing the orientation of Figure 1 and the sentences in this section.<br />
# 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. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# A brief mention of modern portfolio theory (i.e.. Markowitz) would be appropriate in this section. <br />
# 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.<br />
# Use LaTex to distinguish variables written within a sentence, such as m and n. <br />
# 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.”<br />
# An explanation of a few common constraints would be helpful, rather than just including a table. <br />
* At least one numerical example<br />
# All tables need to be labeled.<br />
# Include figure number in label for consistency. <br />
# Fix misspelling “dolling decision variables”. <br />
# Use LaTex for all variables, equations, and constraints here.<br />
# Example 2 table is hard to read, so making it bigger would help. <br />
# Remove the “Using excel as the solver” part from the sentence before the solution discussion. <br />
# Some grammatical errors here (phrases such as “.. is as follows” should be followed by a colon). <br />
* A section to discuss and/or illustrate the applications<br />
# Rephrase “Portfolio optimization can be used to screen investment projects that meet investors, rationally allocate investment amounts, etc.”<br />
# Not sure “relevant” is the correct word choice here. <br />
# 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. <br />
* A conclusion section<br />
# Need some commas here.<br />
# The sentence “Linear programming has been around since the 1940’s and has such a wide base of applications” is not necessary. <br />
* References<br />
# 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]]<br />
# Remove white space between end of sentences and reference numbers.<br />
<br />
== [[Chance-constraint method|Chance constraint method]] ==<br />
<br />
* Author list: <br />
* An introduction of the topic<br />
# 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”<br />
# In “Chance-constraint”, it is capitalized randomly throughout the introduction. Please correct. <br />
# 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.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Please add a citation to the first sentence. <br />
# Xi is an uncertainty/randomness variable. It is better to use clear language. <br />
# 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.<br />
# Theory is insufficient. Please expand and explain different approaches. <br />
# Please add pros and cons explicitly as a list. <br />
# Explain the physical meaning for examples of chance constraints along with all the notations used.<br />
# 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. <br />
* At least one numerical example<br />
# Please remove this example as it is directly from this book. The example should be purely numerical without any background.<br />
# Please use the equation editor for min, st., etc.<br />
# 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. <br />
# Please change the table format so as not to confuse the reader. <br />
# Multiple instances of [Chart to be added] are missing.<br />
# Example is incomplete. <br />
# Avoid pronouns such as “we”.<br />
* A section to discuss and/or illustrate the applications<br />
# Please connect several grammatical and spelling errors: “real life application”, Energy creation, particularly in renewable sources, have high variabilities”, and others<br />
# “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. <br />
* A conclusion section<br />
# 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.<br />
# 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. <br />
* References<br />
# 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]]<br />
<br />
== [[Bayesian Optimization | Bayesian Optimization]] ==<br />
<br />
* Contents: Subheadings for EI and the algorithm should not be bolded, Random words should not be capitalized.<br />
* Author list: Remove cornell ID, Please check names<br />
* Introduction<br />
# 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.<br />
# 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.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Captions need reformatting.<br />
# Consider italicizing keywords rather than bolding.<br />
# Please add a citation to the first sentence. <br />
# 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.<br />
# Avoid pronouns such as “we”.<br />
# Please write equations in the Wiki instead of attaching images for equations.<br />
# Acquisition function figure could be made larger and clearer to improve readability.<br />
* At least one numerical example<br />
# Any references to functions or methods in code ‘e.g. fmin’ should be properly formatted as code-stylized text.<br />
# Please use the equation editor for min, st., etc.<br />
# Avoid including a figure of the code for this example and explicitly describe the steps to the modeling and solution process instead. <br />
# Avoid pronouns such as “our” and “we”.<br />
* A section to discuss and/or illustrate the applications <br />
* A conclusion section<br />
# Please do not use brackets to enclose lists.<br />
# Some claims here should be supported by references. Please cite each source after its sentence. <br />
* References<br />
# 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]]<br />
# Try to avoid references to “pop” machine learning blogs where anyone can be an author. (e.g. towardsdatascience)<br />
<br />
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.<br />
<br />
== [[Conjugate gradient methods|Conjugate gradient methods ]] ==<br />
<br />
* Author list: Remove cornell ID<br />
* Introduction<br />
# All inline notations (e.g., `x`, `A`) should be typed using LaTex.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Is Gauss-Newton no longer referenced?<br />
# 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.<br />
# Please indent equation blocks.<br />
# Please properly format pseudocode.<br />
* At least one numerical example<br />
# Steps should be accompanied with explanation, or reference to the corresponding step in the pseudocode.<br />
* A section to discuss and/or illustrate the applications <br />
# Consider including 2 additional examples of applications<br />
* A conclusion section<br />
# Consider adding future research directions<br />
* References<br />
# Reference primary sources rather than Wikipedia<br />
# Too few references.<br />
<br />
== [[Geometric programming|Geometric Programming]] ==<br />
<br />
* Author list<br />
# Remove cornell ID<br />
* An introduction of the topic<br />
# Examples of applications in this section use the same reference. Please cite their individual sources.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# The symbol denoting the domain in the definition of a monomial is unclear. Please clarify it or fix this if it is incorrect.<br />
# Definition of posynomial refers to section 2.1 which is missing from the Wiki (sections are not numbered in the main text).<br />
# 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.<br />
# Additional theory on the feasibility analysis could be provided in this section.<br />
* At least one numerical example<br />
# 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.<br />
* A section to discuss and/or illustrate the applications<br />
# The figure in this section needs to be labeled. <br />
# The figure needs to be resized and perhaps aligned to the center. <br />
* A conclusion section:<br />
# Please avoid vague language such as: “This makes”.<br />
# Please avoid opinionated statements: “one of the best ways”.<br />
* References<br />
# 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]]<br />
<br />
== [[Adam|Adam]] ==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
# Some grammatical errors here, mostly related to the need for commas in certain places (e.g., “Before Adam..”).<br />
# Some minor errors with parts of speech throughout the section, need to revisit phrases such as “which has broader scope in future for”, etc. <br />
# Try splitting up some of the longer sentences in this section, a couple are hard to read.<br />
# 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. <br />
# What does adam stand for? Introduction is insufficient. Please expand. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Revise grammar here, noticing some missing commas and uncapitalized word after period.<br />
# Rephrase “second one is to update the old position with the updated position”.<br />
# Use LaTex code or equation editor to display all equations and variables in this section, and actual subscripts instead of “m_t”, etc. <br />
# 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. <br />
# Remove white space before the period in RMSP discussion.<br />
# Please provide a pseudocode. <br />
# Please use list the two methods here “Adam is a combination of two gradient descent methods which are explained below”<br />
# Please expand the theory section significantly. Theoretical convergence properties should be discussed, even if briefly.<br />
* At least one numerical example<br />
* A section to discuss and/or illustrate the applications<br />
# Same comment as before, consider replacing inline citations after words like “According to..”. <br />
* A conclusion section <br />
* References<br />
# 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]]<br />
# Try to avoid references to blogs and use peer-reviewed academic references instead. <br />
# Too few references.<br />
<br />
== [[A-star algorithm|a* algorithm]] ==<br />
<br />
* Author list:<br />
# Remove cornell ID<br />
* An introduction of the topic:<br />
# In the titles, please change the font from bold to normal to have consistent formatting in the site. <br />
# Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.<br />
# There are no citations in the introduction. Please cite every source.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Please add the mathematical description of the algorithm.<br />
# 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]]<br />
# 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”.<br />
# In algorithms, it is a standard to add high-level description (i.e. pseudocode or flowchart). Please incorporate it. <br />
# 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.<br />
* At least one numerical example<br />
# The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.<br />
# Instead of writing things like “The above image..”, label each figure and use the figure number to refer to it in text. <br />
# 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. <br />
* A section to discuss and/or illustrate the applications<br />
# No references in the applications. Please cite every source <br />
# Preferably, add at least an additional application. <br />
* A conclusion section<br />
# Conclusion should summarize descriptions. Please modify it to provide a summary. <br />
# Please pay attention to the length and structure of sentences here and in the full page. First sentence is hard to read.<br />
* References<br />
# 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]]<br />
<br />
== [[Job shop scheduling|Job-Shop Scheduling Problem]] ==<br />
<br />
* An introduction of the topic<br />
# 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.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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.<br />
# 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.<br />
# 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.<br />
# 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.<br />
# Use LaTex code or equation editor to display all equations and variables in this section and all other sections as well.<br />
# Check grammar in this section. For example, phrases like “are as follows” need to be followed by a colon and not a period. <br />
# Consider rewriting the assumptions as a list in this section. <br />
* At least one numerical example<br />
# 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.<br />
# 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.<br />
* A section to discuss and/or illustrate the applications<br />
# 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. <br />
* A conclusion section<br />
# The meaning of “Operations applications” is unclear. Please explain or update if necessary.<br />
# The current conclusion section does not properly summarize the problem. Please refer to other Wiki examples for an idea to update the section accordingly.<br />
* References<br />
# 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]] <br />
# Please reference media sources like reference 5 appropriately.<br />
<br />
== [[Optimization in game theory|Optimization in game theory]] ==<br />
<br />
* Author list: remove cornell IDs. <br />
* An introduction of the topic<br />
# 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]] <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Please edit references.<br />
# Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm. <br />
# Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.<br />
* At least one numerical example<br />
# Please organize the last part in a more readable format. Questions may be in bold and numbered, answers are more direct, etc.<br />
# Remember to cite all images and tables. <br />
# 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.<br />
* A section to discuss and/or illustrate the applications<br />
# Very good, link the reference and cite all sources. <br />
* A conclusion section<br />
# Please add more summarizing especially from theory sentences and avoid long sentences. <br />
* References<br />
# 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]]<br />
# Reference primary sources rather than Wikipedia<br />
<br />
== [[Trust-region methods|Trust-region methods]] ==<br />
<br />
* Author list:<br />
# Remove cornell IDs. Author is also spelled incorrectly. <br />
# Add the course section.<br />
* An introduction of the topic<br />
# 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]] <br />
# 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.<br />
# Avoid pronouns such as “we”. This goes for all other sections as well.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Organization of ideas in this section needs work.<br />
# 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.<br />
# Each approach should have accompanying explanation and motivation for why it is being discussed. It is not enough to outline the algorithm.<br />
# Please make sure symbols are properly subscripted and superscripted (e.g. “pk” should be “p_k”<br />
# Please format the algorithm in proper algorithmic pseudocode format.<br />
# Little to no discussion on global convergence guarantees<br />
# Please include discussion about the advantages and disadvantages of the algorithm<br />
# Fix typo “couchy point”.<br />
* At least one numerical example<br />
# Any code functions (uminfunc) should have proper text formatting.<br />
# The graph needs a better caption explaining how the axes are labeled and what data points are being shown.<br />
# Please increase the quality of the figure. It is hard to see the red line. <br />
# 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.”<br />
* A section to discuss and/or illustrate the applications<br />
# 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).<br />
* A conclusion section<br />
# Please add more summary, future research directions for example is a good start.<br />
* References<br />
# Please consider having the references as this Wiki template, <nowiki>https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization</nowiki><br />
<br />
There are numerous misspellings, grammatical errors, and incorrect claims. Please fix these.<br />
<br />
== [[Momentum|Momentum]] ==<br />
<br />
* Author list<br />
# Remove cornell ID<br />
* An introduction of the topic<br />
# 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.<br />
# Remove bold on “Momentum”.<br />
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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.<br />
# 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.<br />
# 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.<br />
# Avoid pronouns such as “you”.<br />
* At least one numerical example<br />
# Please try to label the plots that explains what each line color means.<br />
* A section to discuss and/or illustrate the applications<br />
# Please use correct terminology like “optimizing non-convex functions” and not “training non-convex models”.<br />
# Adam, Adadelta, and RMSprop are variants of SGD that already use momentum. Please double check the writing and update if necessary.<br />
* A conclusion section<br />
# Please refrain from using words like “zig zag” effects.<br />
* References<br />
# Almost all references used are URLs. Please try to add journal/conference articles or books for references, instead of directly citing the URLs.<br />
<br />
== [[Stochastic dynamic programming|Stochastic Dynamic programming]] ==<br />
<br />
* Author list<br />
# Remove cornell ID<br />
* An introduction of the topic<br />
# Discussion on applications should be moved to a separate section.<br />
* Theory, methodology, and/or algorithmic discussions <br />
# Remove the grey box background of equations.<br />
* At least one numerical example <br />
* A section to discuss and/or illustrate the applications <br />
* A conclusion section <br />
* References<br />
# 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]]<br />
<br />
== [[Outer-approximation (OA)|Outer-approximation]] ==<br />
<br />
* An introduction of the topic <br />
# See formatting guideline below<br />
# Avoid opinionated statements such as “MINLP problems are usually the hardest to solve”.<br />
# Rearrange the text such that the MINLP formulation is in the theory section and keep the introduction in words only. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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<br />
# The sentence “The Outer-Approximation (OA) algorithm was first proposed by Duran and and Grossmann in 1986 to solve MINLP problems.” needs a reference. <br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
# “Minimize” and “subject to” should be “min” and “s.t.” in MathType<br />
* A section to discuss and/or illustrate the applications<br />
# 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)<br />
# 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. <br />
# Place GAMS code in a single code box or remove it.<br />
# Consider reformatting to make steps more readable. Inserting spaces and breaking down steps would help. <br />
* A conclusion section<br />
# Too short. Consider discussion on future research direction and discussion on uncertainty<br />
# 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)”. <br />
* References<br />
# 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]]<br />
# Remove "Template:Reflist"<br />
<br />
== [[Unit commitment problem|Unit commitment problem]] ==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
# Please expand the introduction and avoid discussions of examples or specific applications in this section.<br />
# The sentence “Nonlinear, Non-convex programming optimization problem.” doesn’t make sense by itself and Non-convex shouldn’t be capitalized. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Figure/image format should be revised to better display the content.<br />
# Uppercase characters are used randomly (e.g., “non-convex transmission Constraints”) . Please follow correct language conventions for sentence structure.<br />
# 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. <br />
# Don’t say “written in matrix form as equation..” and just cite the reference, actually write out the equation. <br />
# Properly label the figure in this section with a figure number and improve visibility by making it larger. <br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
# Label the figures in this section properly with figure numbers.<br />
# Fix typo “while minimize” to “while minimizing”. <br />
# Avoid pronouns such as “we”. <br />
# Use the equation editor when typing equations. <br />
* A section to discuss and/or illustrate the applications:<br />
# I suggest changing the order of the subtitles here. For example, Single-Period Unit Commitment. <br />
* A conclusion section <br />
* References<br />
<br />
== [[Frank-Wolfe|Frank-Wolfe]] ==<br />
<br />
* Author list: <br />
* An introduction of the topic<br />
# I suggest highlighting disadvantages along with advantages. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# “[n x 1] matrix” please use the equation editor to express mathematical descriptions and symbols (p,b, etc)<br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
# Please show at least a few iterations. Even for smaller examples if needed. Report the final solution. <br />
# Please use the LaTex code or equation editor for min and include s.t., etc.<br />
# 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.<br />
* A section to discuss and/or illustrate the applications: <br />
* A conclusion section<br />
# Same as the introduction. Pros and cons should be evaluated together!<br />
* References<br />
# 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]]<br />
<br />
== [[Line search methods|Line Search Method]] ==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
# Expand the introduction and avoid discussion on some of the specific steps in the solution process. <br />
# Provide references here. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# The phrase “are as follows” in the steepest descent method discussion needs to be followed by a colon. <br />
# Rephrase “has a nice convergence theory” and cite a reference for this claim.<br />
# Avoid pronouns such as “we”.<br />
# Add citation after “.. proposed by Phillip Wolfe in 1969.”<br />
# Figure 1 is between two sections. Please fix this issue. <br />
* At least one numerical example:<br />
# Add some space between iterations or subsection break<br />
* A section to discuss and/or illustrate the applications:<br />
# Too few references in this section. <br />
# Last paragraph makes some claims without references. <br />
* A conclusion section <br />
* References<br />
# 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]]<br />
# More references should be added. A simple Google Scholar search would give you many references.<br />
<br />
== [[Piecewise linear approximation|Piecewise Linear Approximation]]==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
# 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. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Fix typo “to force the x’ values become associated with”. <br />
* At least one numerical example <br />
* A section to discuss and/or illustrate the applications<br />
# Please aim for a maximum average sentence length of ~25 words. Some of these longer sentences are hard to read. <br />
* A conclusion section<br />
# 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.<br />
* References<br />
# Include hyperlinks to sources when possible.<br />
<br />
== [[Mathematical programming with equilibrium constraints|Mathematical Programming with Equilibrium constraints]] ==<br />
<br />
* An introduction of the topic<br />
# 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.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# The meaning of parameter vector x is unclear. Please add more information or update if necessary.<br />
# 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.<br />
# Use equations instead of images to represent math programs and equations in the Implicit Descent and SQP subsection.<br />
# Apart from the steps for each solution technique, please also add a few sentences that describe each method.<br />
* At least one numerical example<br />
# Please define the terms like NCP, MP before abbreviating them. Also try not to unnecessarily abbreviate simple terms.<br />
# Equations should be typed by LaTex. Images for equations are unacceptable.<br />
# GAMS code is strongly discouraged. Please solve the problem "step-by-step".<br />
# 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.<br />
# Avoid using figures in the equations (subject to etc)<br />
* A section to discuss and/or illustrate the applications<br />
# Add references to “power management, highway pricing, chemical process engineering, and traffic planning.”<br />
* A conclusion section<br />
* References<br />
# 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]]<br />
<br />
== [[Wing shape optimization|Wing shape Optimization]] ==<br />
<br />
* Author list: Remove cornell ID<br />
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.<br />
* An introduction of the topic<br />
# 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.)<br />
# Avoid discussion involving finer details of subject methods in this section. <br />
# In the titles, please change the font from bold to normal to have consistent formatting in the site. Same applies to box of content!<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Properly cite the CFD package, don’t just include a link. <br />
# Properly label the figure with a figure number.<br />
# Consider removing white space between isolated sentences to improve readability. <br />
* At least one numerical example<br />
# If you’ve already defined an abbreviation (CFD), there is no need to define it again. Just use the abbreviation.<br />
# Avoid pronouns such as “we” or “they”.<br />
# Phrases like “under the following” need to be followed by a colon.<br />
# 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.<br />
# “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. <br />
# Avoid inserting inline citations like “[4] introduces an..” as it is a bit informal when you don’t explicitly name the subject.<br />
# 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.<br />
* A section to discuss and/or illustrate the applications<br />
# Some characters are randomly capitalized in this section. <br />
* A conclusion section<br />
# 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. <br />
* References<br />
# 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]]<br />
<br />
== [[Interior-point method for NLP|Interior point method for NLP]] ==<br />
<br />
* An introduction of the topic: <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Primal-Dual formulation and comparison to the Barrier Method is not discussed.<br />
# Include brief discussion about big O convergence rates.<br />
# Need discussion about the concept of “central path” and the notion of self concordance<br />
# 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.<br />
# Graphs and images are incorrectly formatted to the page. Consider proper alignment with respect to the text body.<br />
# Use explicitly typed Latex equations instead of images to represent math programs and equations.<br />
# Fix typo “optimisation”.<br />
# Use LaTex code or equation editor to display all equations and variables (e.g., “xi ”, “μ”, etc.).<br />
* At least one numerical example:<br />
# There are formatting issues with figures 2,3. Please make sure to embed them within their respective sections. <br />
* A section to discuss and/or illustrate the applications<br />
* A conclusion section <br />
# Minor character code typos in the conclusion.<br />
# Also, please add more discussion in this section. Future research directions is a good start.<br />
# There is a box ""<br />
* References<br />
<br />
== [[AdaGrad|Adagrad]] ==<br />
<br />
* An introduction of the topic: <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Include discussion on its variants (most important is AdaDelta).<br />
# Include disadvantages of Adagrad, since this provides motivation for the discussion on the variants and improvements of Adagrad<br />
# Include comparisons to other popular optimizers (particularly important is comparisons to regular SGD and Adam)<br />
# 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.<br />
* At least one numerical example<br />
# In the first sentence, “..take the following numerical example” should be followed by a colon. <br />
# Fix typo “trayectory”.<br />
* A section to discuss and/or illustrate the applications<br />
# This section is too short; include specific applications in which input features are sparse and Adagrad excels.<br />
# Add reference to the claim “Mainly, it is a good choice for deep learning models with sparse input features”.<br />
* A conclusion section <br />
* References <br />
<br />
# Too few references overall, you should aggregate information from multiple sources (even if the base algorithm itself comes from a singular paper)<br />
<br />
== [[McCormick envelopes|McCormick Envelopes]] ==<br />
<br />
* Author list: OK but I suggest removing NetID<br />
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.<br />
* An introduction of the topic<br />
# First sentence is hard to read. Please consider keeping sentences below 25-30 words. <br />
# No references provided. Please cite all sources. <br />
# Figure 1 is provided in the middle between two sections. Please include in the introduction section. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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]]<br />
# When using mathematical expressions and symbols, please use the equation editor. (e.g., x*y, exy + y, sin (x+y) - x2)<br />
* At least one numerical example<br />
# Please add a few sentences to show the transition from problem to solution. <br />
# For the sample GAMS code, please place it in a code box<br />
* A section to discuss and/or illustrate the applications<br />
# Having a list is not enough. Please explain at least three applications in a few sentences each. <br />
# 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.<br />
* A conclusion section: <br />
* References<br />
# 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]]<br />
# Please follow the standard reference style - the current format is incorrect.</div>Asa279https://optimization.cbe.cornell.edu/index.php?title=2021_Cornell_Optimization_Open_Textbook_Feedback&diff=47572021 Cornell Optimization Open Textbook Feedback2021-12-05T02:35:04Z<p>Asa279: /* Chance constraint method */</p>
<hr />
<div>== [[Lagrangean duality|Lagrangian duality]] ==<br />
* Author list, sections and TOC<br />
# Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.<br />
# Remove cornell ID from Author list<br />
* An introduction of the topic<br />
# 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.<br />
# Definitions of LR and its relation to duality should be double checked and re-written.<br />
# Only one reference is present in this section. Please add more relevant references by expanding this section.<br />
# Consider merging the “introduction” and “history” sections.<br />
# In the titles, please change the font from bold to normal to have consistent formatting in the site.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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.<br />
# 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 (,).<br />
# 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.<br />
# 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.<br />
# Last step of the “process” subsection also needs updating according to the previous comments.<br />
# The inline notations should also be typed using LaTex.<br />
# Please use the LaTex code or equation editor for min, s.t., etc.<br />
* At least one numerical example<br />
# 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.<br />
# All consecutive steps need to be updated since the dual variables would be updated.<br />
# After substitution the nonlinear function should be further simplified. The current expression reads like a highly nonlinear function but can be easily simplified.<br />
# Similar to the comments in the methodology section, inverting minimize to maximize is incorrect. Please update the dual objective function accordingly.<br />
# Please use the LaTex code or equation editor for min, s.t., etc.<br />
* A section to discuss and/or illustrate the applications<br />
# Bullet points could be used to state the last four real-world examples that explain the physical meaning of the primal and dual problems.<br />
# Add references for the last set of applications. <br />
* A conclusion section<br />
# This section contains a few typos. Please fix the same.<br />
* References<br />
# Some citations' hyperlinks are displaying.<br />
<br />
== [[Disjunctive inequalities|Disjunctive Inequalities]] ==<br />
<br />
* Author list<br />
# Missing course section and semester<br />
# Remove cornell ID<br />
* An introduction of the topic<br />
# No citations are present in this section.<br />
# “mixed-integer programming (MIP)” should be used instead of “multiple integer programming (MIP)”. Please fix this error.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# The abbreviation MILP is not previously defined. Please fix this issue.<br />
# You consistently use the negative sign instead of the NOT operator for y (-y instead of ¬y). <br />
# Some inconsistencies with the spacing of variables, constraints, etc., under the “General” section that need to be fixed.<br />
# 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.<br />
* At least one numerical example<br />
# 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.<br />
# Add space between vee (V) operator and brackets in first line of Latex<br />
# Please format variables correctly, for example, use x1 instead of x1.<br />
* A section to discuss and/or illustrate the applications<br />
# Please format the equations appropriately either by using latex code or the visual editor. These images are NOT acceptable!<br />
* A conclusion section<br />
# There is no conclusion presented in this section at all.<br />
* References<br />
# 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. <br />
# There are many papers on this topic. A simple Google (Scholar) search could provide you with sufficient references to cite. <br />
# Many important references of this topic are missing.<br />
# 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]]<br />
<br />
==[[Stochastic programming|Stochastic Programming]] ==<br />
<br />
* Author list: Remove cornell IDs<br />
* An introduction of the topic<br />
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki. <br />
# 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.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Please avoid direct inline linkbacks to Wikipedia.<br />
# The symbol “xi” in the methodology subsection should be explained.<br />
* At least one numerical example<br />
# Copying a numerical example "entirely" from a textbook is inappropriate. Your team should come up with a "numerical" case.<br />
# No specific application context is needed for a numerical example.<br />
# The inline notations (`x1`, `s1`) should also be typed using LaTex.<br />
# Label all tables with a table number for better readability. <br />
# 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. <br />
* A section to discuss and/or illustrate the applications;<br />
# I suggest eliminating citing the last name of the first author (i.e. Zhou et al.)<br />
* A conclusion section <br />
* References<br />
# URLs of some citations are not properly formatted (not showing the hyperlinks).<br />
<br />
== [[Exponential transformation|Exponential Transformation]] ==<br />
<br />
* Author list<br />
# Missing course section<br />
# Remove cornell ID<br />
* An introduction of the topic<br />
# Please expand the introduction.<br />
# Please aim for a maximum average sentence length of ~25 words. Last sentence with 51 words is hard to read. <br />
# Second Sentence: please change the word “they” as it could make the meaning ambiguous<br />
# 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. <br />
# If you use abbreviations, please introduce them (e.g. NLP,MINLP)<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Please explain the transformation in words along with equations<br />
# Terms like posynomial should be described in detail.<br />
# Please move the numerical example to the section below<br />
# The “(eq 1)” is not needed here.<br />
# Please expand this section.<br />
* At least one numerical example<br />
# In the third equation of the numerical example, it is confusing to have coefficients after numbers. Some readers may read it as an exponent.<br />
# Last equation in this section after “further linearization” is incorrect. This equation cannot be further linearized, please fix this.<br />
# Please explain the steps in the numerical examples in detail. The step-by-step solution should be provided. <br />
* A section to discuss and/or illustrate the applications<br />
# Missing part of text: “Proof of convexity of with positive definite test of Hessian…”<br />
# Applications are not numerical examples. Please refer to this link for example of applications: [[Duality|https://optimization.cbe.cornell.edu/index.php?title=Duality]]<br />
# Citation 7 is missing in current applications<br />
# The section current applications is redundant<br />
# Please use the LaTex code or equation editor for min, s.t., etc.<br />
# 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. <br />
# The convexification application of MINLP can be further simplified for binary variables. Please refer to the lecture slides for more information.<br />
* A conclusion section<br />
# 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. <br />
* References<br />
# 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]]<br />
# Citation 7 is missing in current applications<br />
<br />
== [[Sparse Reconstruction with Compressed Sensing|Sparse reconstruction with Compressed Sensing]] ==<br />
This Wiki needs a significant rewrite. Please go through the comments for details.<br />
<br />
* An introduction of the topic<br />
# 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.<br />
# This section includes several typos like “sub modual”. Please fix them throughout the wiki and delete them if not required.<br />
# Many abbreviations are used before previously defining them. Please define these abbreviations before using them in the text.<br />
# This section is incomprehensible in its current form. Please rewrite with proper comprehension.<br />
# Equations and math symbols need proper reformatting. The current version reads like text (along with equations) copy-pasted from a specific source.<br />
# Try to place the figure at the top of the Wiki between the main text.<br />
# Avoid pronouns such as “we”.<br />
# I suggest the use of more formal abstract illustrations. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Equations and symbols need proper reformatting.<br />
# 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.<br />
* At least one numerical example<br />
# Numerical example is missing.<br />
* A section to discuss and/or illustrate the applications<br />
# Having a list is not enough. Please explain at least three applications in a few sentences each.<br />
* A conclusion section<br />
# Conclusion section is missing.<br />
* References<br />
# 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]]<br />
<br />
== [[Portfolio optimization|Portfolio Optimization]] ==<br />
<br />
* Author list<br />
# Remove cornell id<br />
* An introduction of the topic<br />
# 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. <br />
# Amount of whitespace can be reduced by changing the orientation of Figure 1 and the sentences in this section.<br />
# 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. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# A brief mention of modern portfolio theory (i.e.. Markowitz) would be appropriate in this section. <br />
# 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.<br />
# Use LaTex to distinguish variables written within a sentence, such as m and n. <br />
# 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.”<br />
# An explanation of a few common constraints would be helpful, rather than just including a table. <br />
* At least one numerical example<br />
# All tables need to be labeled.<br />
# Include figure number in label for consistency. <br />
# Fix misspelling “dolling decision variables”. <br />
# Use LaTex for all variables, equations, and constraints here.<br />
# Example 2 table is hard to read, so making it bigger would help. <br />
# Remove the “Using excel as the solver” part from the sentence before the solution discussion. <br />
# Some grammatical errors here (phrases such as “.. is as follows” should be followed by a colon). <br />
* A section to discuss and/or illustrate the applications<br />
# Rephrase “Portfolio optimization can be used to screen investment projects that meet investors, rationally allocate investment amounts, etc.”<br />
# Not sure “relevant” is the correct word choice here. <br />
# 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. <br />
* A conclusion section<br />
# Need some commas here.<br />
# The sentence “Linear programming has been around since the 1940’s and has such a wide base of applications” is not necessary. <br />
* References<br />
# 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]]<br />
# Remove white space between end of sentences and reference numbers.<br />
<br />
== [[Chance-constraint method|Chance constraint method]] ==<br />
<br />
* Author list: <br />
* An introduction of the topic<br />
# 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”<br />
# In “Chance-constraint”, it is capitalized randomly throughout the introduction. Please correct. <br />
# 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.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Please add a citation to the first sentence. <br />
# Xi is an uncertainty/randomness variable. It is better to use clear language. <br />
# 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.<br />
# Theory is insufficient. Please expand and explain different approaches. <br />
# Please add pros and cons explicitly as a list. <br />
# Explain the physical meaning for examples of chance constraints along with all the notations used.<br />
# 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. <br />
* At least one numerical example<br />
# Please remove this example as it is directly from this book. The example should be purely numerical without any background.<br />
# Please use the equation editor for min, st., etc.<br />
# 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. <br />
# Please change the table format so as not to confuse the reader. <br />
# Multiple instances of [Chart to be added] are missing.<br />
# Example is incomplete. <br />
# Avoid pronouns such as “we”.<br />
* A section to discuss and/or illustrate the applications<br />
# Please connect several grammatical and spelling errors: “real life application”, Energy creation, particularly in renewable sources, have high variabilities”, and others<br />
# “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. <br />
* A conclusion section<br />
# 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.<br />
# 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. <br />
* References<br />
# 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]]<br />
<br />
== [[Bayesian Optimization | Bayesian Optimization]] ==<br />
<br />
* Contents: Subheadings for EI and the algorithm should not be bolded, Random words should not be capitalized.<br />
* Author list: Remove cornell ID, Please check names<br />
* Introduction<br />
# 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.<br />
# 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.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Captions need reformatting.<br />
# Consider italicizing keywords rather than bolding.<br />
# Please add a citation to the first sentence. <br />
# 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.<br />
# Avoid pronouns such as “we”.<br />
# Please write equations in the Wiki instead of attaching images for equations.<br />
# Acquisition function figure could be made larger and clearer to improve readability.<br />
* At least one numerical example<br />
# Any references to functions or methods in code ‘e.g. fmin’ should be properly formatted as code-stylized text.<br />
# Please use the equation editor for min, st., etc.<br />
# Avoid including a figure of the code for this example and explicitly describe the steps to the modeling and solution process instead. <br />
# Avoid pronouns such as “our” and “we”.<br />
* A section to discuss and/or illustrate the applications <br />
* A conclusion section<br />
# Please do not use brackets to enclose lists.<br />
# Some claims here should be supported by references. Please cite each source after its sentence. <br />
* References<br />
# 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]]<br />
# Try to avoid references to “pop” machine learning blogs where anyone can be an author. (e.g. towardsdatascience)<br />
<br />
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.<br />
<br />
== [[Conjugate gradient methods|Conjugate gradient methods ]] ==<br />
<br />
* Author list: Remove cornell ID<br />
* Introduction<br />
# All inline notations (e.g., `x`, `A`) should be typed using LaTex.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Is Gauss-Newton no longer referenced?<br />
# 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.<br />
# Please indent equation blocks.<br />
# Please properly format pseudocode.<br />
* At least one numerical example<br />
# Steps should be accompanied with explanation, or reference to the corresponding step in the pseudocode.<br />
* A section to discuss and/or illustrate the applications <br />
# Consider including 2 additional examples of applications<br />
* A conclusion section<br />
# Consider adding future research directions<br />
* References<br />
# Reference primary sources rather than Wikipedia<br />
# Too few references.<br />
<br />
== [[Geometric programming|Geometric Programming]] ==<br />
<br />
* Author list<br />
# Remove cornell ID<br />
* An introduction of the topic<br />
# Examples of applications in this section use the same reference. Please cite their individual sources.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# The symbol denoting the domain in the definition of a monomial is unclear. Please clarify it or fix this if it is incorrect.<br />
# Definition of posynomial refers to section 2.1 which is missing from the Wiki (sections are not numbered in the main text).<br />
# 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.<br />
# Additional theory on the feasibility analysis could be provided in this section.<br />
* At least one numerical example<br />
# 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.<br />
* A section to discuss and/or illustrate the applications<br />
# The figure in this section needs to be labeled. <br />
# The figure needs to be resized and perhaps aligned to the center. <br />
* A conclusion section:<br />
# Please avoid vague language such as: “This makes”.<br />
# Please avoid opinionated statements: “one of the best ways”.<br />
* References<br />
# 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]]<br />
<br />
== [[Adam|Adam]] ==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
# Some grammatical errors here, mostly related to the need for commas in certain places (e.g., “Before Adam..”).<br />
# Some minor errors with parts of speech throughout the section, need to revisit phrases such as “which has broader scope in future for”, etc. <br />
# Try splitting up some of the longer sentences in this section, a couple are hard to read.<br />
# 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. <br />
# What does adam stand for? Introduction is insufficient. Please expand. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Revise grammar here, noticing some missing commas and uncapitalized word after period.<br />
# Rephrase “second one is to update the old position with the updated position”.<br />
# Use LaTex code or equation editor to display all equations and variables in this section, and actual subscripts instead of “m_t”, etc. <br />
# 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. <br />
# Remove white space before the period in RMSP discussion.<br />
# Please provide a pseudocode. <br />
# Please use list the two methods here “Adam is a combination of two gradient descent methods which are explained below”<br />
# Please expand the theory section significantly. Theoretical convergence properties should be discussed, even if briefly.<br />
* At least one numerical example<br />
* A section to discuss and/or illustrate the applications<br />
# Same comment as before, consider replacing inline citations after words like “According to..”. <br />
* A conclusion section <br />
* References<br />
# 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]]<br />
# Try to avoid references to blogs and use peer-reviewed academic references instead. <br />
# Too few references.<br />
<br />
== [[A-star algorithm|a* algorithm]] ==<br />
<br />
* Author list:<br />
# Remove cornell ID<br />
* An introduction of the topic:<br />
# In the titles, please change the font from bold to normal to have consistent formatting in the site. <br />
# Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.<br />
# There are no citations in the introduction. Please cite every source.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Please add the mathematical description of the algorithm.<br />
# 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]]<br />
# 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”.<br />
# In algorithms, it is a standard to add high-level description (i.e. pseudocode or flowchart). Please incorporate it. <br />
# 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.<br />
* At least one numerical example<br />
# The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.<br />
# Instead of writing things like “The above image..”, label each figure and use the figure number to refer to it in text. <br />
# 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. <br />
* A section to discuss and/or illustrate the applications<br />
# No references in the applications. Please cite every source <br />
# Preferably, add at least an additional application. <br />
* A conclusion section<br />
# Conclusion should summarize descriptions. Please modify it to provide a summary. <br />
# Please pay attention to the length and structure of sentences here and in the full page. First sentence is hard to read.<br />
* References<br />
# 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]]<br />
<br />
== [[Job shop scheduling|Job-Shop Scheduling Problem]] ==<br />
<br />
* An introduction of the topic<br />
# 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.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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.<br />
# 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.<br />
# 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.<br />
# 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.<br />
# Use LaTex code or equation editor to display all equations and variables in this section and all other sections as well.<br />
# Check grammar in this section. For example, phrases like “are as follows” need to be followed by a colon and not a period. <br />
# Consider rewriting the assumptions as a list in this section. <br />
* At least one numerical example<br />
# 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.<br />
# 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.<br />
* A section to discuss and/or illustrate the applications<br />
# 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. <br />
* A conclusion section<br />
# The meaning of “Operations applications” is unclear. Please explain or update if necessary.<br />
# The current conclusion section does not properly summarize the problem. Please refer to other Wiki examples for an idea to update the section accordingly.<br />
* References<br />
# 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]] <br />
# Please reference media sources like reference 5 appropriately.<br />
<br />
== [[Optimization in game theory|Optimization in game theory]] ==<br />
<br />
* Author list: remove cornell IDs. <br />
* An introduction of the topic<br />
# 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]] <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Please edit references.<br />
# Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm. <br />
# Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.<br />
* At least one numerical example<br />
# Please organize the last part in a more readable format. Questions may be in bold and numbered, answers are more direct, etc.<br />
# Remember to cite all images and tables. <br />
* A section to discuss and/or illustrate the applications<br />
# Very good, link the reference and cite all sources. <br />
* A conclusion section<br />
# Please add more summarizing especially from theory sentences and avoid long sentences. <br />
* References<br />
# 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]]<br />
# Reference primary sources rather than Wikipedia<br />
<br />
== [[Trust-region methods|Trust-region methods]] ==<br />
<br />
* Author list:<br />
# Remove cornell IDs. Author is also spelled incorrectly. <br />
# Add the course section.<br />
* An introduction of the topic<br />
# 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]] <br />
# 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.<br />
# Avoid pronouns such as “we”. This goes for all other sections as well.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Organization of ideas in this section needs work.<br />
# 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.<br />
# Each approach should have accompanying explanation and motivation for why it is being discussed. It is not enough to outline the algorithm.<br />
# Please make sure symbols are properly subscripted and superscripted (e.g. “pk” should be “p_k”<br />
# Please format the algorithm in proper algorithmic pseudocode format.<br />
# Little to no discussion on global convergence guarantees<br />
# Please include discussion about the advantages and disadvantages of the algorithm<br />
# Fix typo “couchy point”.<br />
* At least one numerical example<br />
# Any code functions (uminfunc) should have proper text formatting.<br />
# The graph needs a better caption explaining how the axes are labeled and what data points are being shown.<br />
# Please increase the quality of the figure. It is hard to see the red line. <br />
# 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.”<br />
* A section to discuss and/or illustrate the applications<br />
# 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).<br />
* A conclusion section<br />
# Please add more summary, future research directions for example is a good start.<br />
* References<br />
# Please consider having the references as this Wiki template, <nowiki>https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization</nowiki><br />
<br />
There are numerous misspellings, grammatical errors, and incorrect claims. Please fix these.<br />
<br />
== [[Momentum|Momentum]] ==<br />
<br />
* Author list<br />
# Remove cornell ID<br />
* An introduction of the topic<br />
# 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.<br />
# Remove bold on “Momentum”.<br />
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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.<br />
# 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.<br />
# 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.<br />
# Avoid pronouns such as “you”.<br />
* At least one numerical example<br />
# Please try to label the plots that explains what each line color means.<br />
* A section to discuss and/or illustrate the applications<br />
# Please use correct terminology like “optimizing non-convex functions” and not “training non-convex models”.<br />
# Adam, Adadelta, and RMSprop are variants of SGD that already use momentum. Please double check the writing and update if necessary.<br />
* A conclusion section<br />
# Please refrain from using words like “zig zag” effects.<br />
* References<br />
# Almost all references used are URLs. Please try to add journal/conference articles or books for references, instead of directly citing the URLs.<br />
<br />
== [[Stochastic dynamic programming|Stochastic Dynamic programming]] ==<br />
<br />
* Author list<br />
# Remove cornell ID<br />
* An introduction of the topic<br />
# Discussion on applications should be moved to a separate section.<br />
* Theory, methodology, and/or algorithmic discussions <br />
# Remove the grey box background of equations.<br />
* At least one numerical example <br />
* A section to discuss and/or illustrate the applications <br />
* A conclusion section <br />
* References<br />
# 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]]<br />
<br />
== [[Outer-approximation (OA)|Outer-approximation]] ==<br />
<br />
* An introduction of the topic <br />
# See formatting guideline below<br />
# Avoid opinionated statements such as “MINLP problems are usually the hardest to solve”.<br />
# Rearrange the text such that the MINLP formulation is in the theory section and keep the introduction in words only. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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<br />
# The sentence “The Outer-Approximation (OA) algorithm was first proposed by Duran and and Grossmann in 1986 to solve MINLP problems.” needs a reference. <br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
# “Minimize” and “subject to” should be “min” and “s.t.” in MathType<br />
* A section to discuss and/or illustrate the applications<br />
# 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)<br />
# 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. <br />
# Place GAMS code in a single code box or remove it.<br />
# Consider reformatting to make steps more readable. Inserting spaces and breaking down steps would help. <br />
* A conclusion section<br />
# Too short. Consider discussion on future research direction and discussion on uncertainty<br />
# 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)”. <br />
* References<br />
# 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]]<br />
# Remove "Template:Reflist"<br />
<br />
== [[Unit commitment problem|Unit commitment problem]] ==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
# Please expand the introduction and avoid discussions of examples or specific applications in this section.<br />
# The sentence “Nonlinear, Non-convex programming optimization problem.” doesn’t make sense by itself and Non-convex shouldn’t be capitalized. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Figure/image format should be revised to better display the content.<br />
# Uppercase characters are used randomly (e.g., “non-convex transmission Constraints”) . Please follow correct language conventions for sentence structure.<br />
# 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. <br />
# Don’t say “written in matrix form as equation..” and just cite the reference, actually write out the equation. <br />
# Properly label the figure in this section with a figure number and improve visibility by making it larger. <br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
# Label the figures in this section properly with figure numbers.<br />
# Fix typo “while minimize” to “while minimizing”. <br />
# Avoid pronouns such as “we”. <br />
# Use the equation editor when typing equations. <br />
* A section to discuss and/or illustrate the applications:<br />
# I suggest changing the order of the subtitles here. For example, Single-Period Unit Commitment. <br />
* A conclusion section <br />
* References<br />
<br />
== [[Frank-Wolfe|Frank-Wolfe]] ==<br />
<br />
* Author list: <br />
* An introduction of the topic<br />
# I suggest highlighting disadvantages along with advantages. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# “[n x 1] matrix” please use the equation editor to express mathematical descriptions and symbols (p,b, etc)<br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
# Please show at least a few iterations. Even for smaller examples if needed. Report the final solution. <br />
# Please use the LaTex code or equation editor for min and include s.t., etc.<br />
* A section to discuss and/or illustrate the applications: <br />
* A conclusion section<br />
# Same as the introduction. Pros and cons should be evaluated together!<br />
* References<br />
# 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]]<br />
<br />
== [[Line search methods|Line Search Method]] ==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
# Expand the introduction and avoid discussion on some of the specific steps in the solution process. <br />
# Provide references here. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# The phrase “are as follows” in the steepest descent method discussion needs to be followed by a colon. <br />
# Rephrase “has a nice convergence theory” and cite a reference for this claim.<br />
# Avoid pronouns such as “we”.<br />
# Add citation after “.. proposed by Phillip Wolfe in 1969.”<br />
# Figure 1 is between two sections. Please fix this issue. <br />
* At least one numerical example:<br />
# Add some space between iterations or subsection break<br />
* A section to discuss and/or illustrate the applications:<br />
# Too few references in this section. <br />
# Last paragraph makes some claims without references. <br />
* A conclusion section <br />
* References<br />
# 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]]<br />
# More references should be added. A simple Google Scholar search would give you many references.<br />
<br />
== [[Piecewise linear approximation|Piecewise Linear Approximation]]==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
# 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. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Fix typo “to force the x’ values become associated with”. <br />
* At least one numerical example <br />
* A section to discuss and/or illustrate the applications<br />
# Please aim for a maximum average sentence length of ~25 words. Some of these longer sentences are hard to read. <br />
* A conclusion section<br />
# 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.<br />
* References<br />
# Include hyperlinks to sources when possible.<br />
<br />
== [[Mathematical programming with equilibrium constraints|Mathematical Programming with Equilibrium constraints]] ==<br />
<br />
* An introduction of the topic<br />
# 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.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# The meaning of parameter vector x is unclear. Please add more information or update if necessary.<br />
# 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.<br />
# Use equations instead of images to represent math programs and equations in the Implicit Descent and SQP subsection.<br />
# Apart from the steps for each solution technique, please also add a few sentences that describe each method.<br />
* At least one numerical example<br />
# Please define the terms like NCP, MP before abbreviating them. Also try not to unnecessarily abbreviate simple terms.<br />
# Equations should be typed by LaTex. Images for equations are unacceptable.<br />
# GAMS code is strongly discouraged. Please solve the problem "step-by-step".<br />
# 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.<br />
# Avoid using figures in the equations (subject to etc)<br />
* A section to discuss and/or illustrate the applications<br />
# Add references to “power management, highway pricing, chemical process engineering, and traffic planning.”<br />
* A conclusion section<br />
* References<br />
# 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]]<br />
<br />
== [[Wing shape optimization|Wing shape Optimization]] ==<br />
<br />
* Author list: Remove cornell ID<br />
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.<br />
* An introduction of the topic<br />
# 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.)<br />
# Avoid discussion involving finer details of subject methods in this section. <br />
# In the titles, please change the font from bold to normal to have consistent formatting in the site. Same applies to box of content!<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Properly cite the CFD package, don’t just include a link. <br />
# Properly label the figure with a figure number.<br />
# Consider removing white space between isolated sentences to improve readability. <br />
* At least one numerical example<br />
# If you’ve already defined an abbreviation (CFD), there is no need to define it again. Just use the abbreviation.<br />
# Avoid pronouns such as “we” or “they”.<br />
# Phrases like “under the following” need to be followed by a colon.<br />
# 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.<br />
# “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. <br />
# Avoid inserting inline citations like “[4] introduces an..” as it is a bit informal when you don’t explicitly name the subject.<br />
# 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.<br />
* A section to discuss and/or illustrate the applications<br />
# Some characters are randomly capitalized in this section. <br />
* A conclusion section<br />
# 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. <br />
* References<br />
# 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]]<br />
<br />
== [[Interior-point method for NLP|Interior point method for NLP]] ==<br />
<br />
* An introduction of the topic: <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Primal-Dual formulation and comparison to the Barrier Method is not discussed.<br />
# Include brief discussion about big O convergence rates.<br />
# Need discussion about the concept of “central path” and the notion of self concordance<br />
# 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.<br />
# Graphs and images are incorrectly formatted to the page. Consider proper alignment with respect to the text body.<br />
# Use explicitly typed Latex equations instead of images to represent math programs and equations.<br />
# Fix typo “optimisation”.<br />
# Use LaTex code or equation editor to display all equations and variables (e.g., “xi ”, “μ”, etc.).<br />
* At least one numerical example:<br />
# There are formatting issues with figures 2,3. Please make sure to embed them within their respective sections. <br />
* A section to discuss and/or illustrate the applications<br />
* A conclusion section <br />
# Minor character code typos in the conclusion.<br />
# Also, please add more discussion in this section. Future research directions is a good start.<br />
# There is a box ""<br />
* References<br />
<br />
== [[AdaGrad|Adagrad]] ==<br />
<br />
* An introduction of the topic: <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Include discussion on its variants (most important is AdaDelta).<br />
# Include disadvantages of Adagrad, since this provides motivation for the discussion on the variants and improvements of Adagrad<br />
# Include comparisons to other popular optimizers (particularly important is comparisons to regular SGD and Adam)<br />
# 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.<br />
* At least one numerical example<br />
# In the first sentence, “..take the following numerical example” should be followed by a colon. <br />
# Fix typo “trayectory”.<br />
* A section to discuss and/or illustrate the applications<br />
# This section is too short; include specific applications in which input features are sparse and Adagrad excels.<br />
# Add reference to the claim “Mainly, it is a good choice for deep learning models with sparse input features”.<br />
* A conclusion section <br />
* References <br />
<br />
# Too few references overall, you should aggregate information from multiple sources (even if the base algorithm itself comes from a singular paper)<br />
<br />
== [[McCormick envelopes|McCormick Envelopes]] ==<br />
<br />
* Author list: OK but I suggest removing NetID<br />
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.<br />
* An introduction of the topic<br />
# First sentence is hard to read. Please consider keeping sentences below 25-30 words. <br />
# No references provided. Please cite all sources. <br />
# Figure 1 is provided in the middle between two sections. Please include in the introduction section. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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]]<br />
# When using mathematical expressions and symbols, please use the equation editor. (e.g., x*y, exy + y, sin (x+y) - x2)<br />
* At least one numerical example<br />
# Please add a few sentences to show the transition from problem to solution. <br />
# For the sample GAMS code, please place it in a code box<br />
* A section to discuss and/or illustrate the applications<br />
# Having a list is not enough. Please explain at least three applications in a few sentences each. <br />
# 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.<br />
* A conclusion section: <br />
* References<br />
# 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]]<br />
# Please follow the standard reference style - the current format is incorrect.</div>Asa279https://optimization.cbe.cornell.edu/index.php?title=2021_Cornell_Optimization_Open_Textbook_Feedback&diff=47562021 Cornell Optimization Open Textbook Feedback2021-12-05T02:28:54Z<p>Asa279: /* Exponential Transformation */</p>
<hr />
<div>== [[Lagrangean duality|Lagrangian duality]] ==<br />
* Author list, sections and TOC<br />
# Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.<br />
# Remove cornell ID from Author list<br />
* An introduction of the topic<br />
# 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.<br />
# Definitions of LR and its relation to duality should be double checked and re-written.<br />
# Only one reference is present in this section. Please add more relevant references by expanding this section.<br />
# Consider merging the “introduction” and “history” sections.<br />
# In the titles, please change the font from bold to normal to have consistent formatting in the site.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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.<br />
# 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 (,).<br />
# 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.<br />
# 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.<br />
# Last step of the “process” subsection also needs updating according to the previous comments.<br />
# The inline notations should also be typed using LaTex.<br />
# Please use the LaTex code or equation editor for min, s.t., etc.<br />
* At least one numerical example<br />
# 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.<br />
# All consecutive steps need to be updated since the dual variables would be updated.<br />
# After substitution the nonlinear function should be further simplified. The current expression reads like a highly nonlinear function but can be easily simplified.<br />
# Similar to the comments in the methodology section, inverting minimize to maximize is incorrect. Please update the dual objective function accordingly.<br />
# Please use the LaTex code or equation editor for min, s.t., etc.<br />
* A section to discuss and/or illustrate the applications<br />
# Bullet points could be used to state the last four real-world examples that explain the physical meaning of the primal and dual problems.<br />
# Add references for the last set of applications. <br />
* A conclusion section<br />
# This section contains a few typos. Please fix the same.<br />
* References<br />
# Some citations' hyperlinks are displaying.<br />
<br />
== [[Disjunctive inequalities|Disjunctive Inequalities]] ==<br />
<br />
* Author list<br />
# Missing course section and semester<br />
# Remove cornell ID<br />
* An introduction of the topic<br />
# No citations are present in this section.<br />
# “mixed-integer programming (MIP)” should be used instead of “multiple integer programming (MIP)”. Please fix this error.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# The abbreviation MILP is not previously defined. Please fix this issue.<br />
# You consistently use the negative sign instead of the NOT operator for y (-y instead of ¬y). <br />
# Some inconsistencies with the spacing of variables, constraints, etc., under the “General” section that need to be fixed.<br />
# 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.<br />
* At least one numerical example<br />
# 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.<br />
# Add space between vee (V) operator and brackets in first line of Latex<br />
# Please format variables correctly, for example, use x1 instead of x1.<br />
* A section to discuss and/or illustrate the applications<br />
# Please format the equations appropriately either by using latex code or the visual editor. These images are NOT acceptable!<br />
* A conclusion section<br />
# There is no conclusion presented in this section at all.<br />
* References<br />
# 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. <br />
# There are many papers on this topic. A simple Google (Scholar) search could provide you with sufficient references to cite. <br />
# Many important references of this topic are missing.<br />
# 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]]<br />
<br />
==[[Stochastic programming|Stochastic Programming]] ==<br />
<br />
* Author list: Remove cornell IDs<br />
* An introduction of the topic<br />
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki. <br />
# 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.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Please avoid direct inline linkbacks to Wikipedia.<br />
# The symbol “xi” in the methodology subsection should be explained.<br />
* At least one numerical example<br />
# Copying a numerical example "entirely" from a textbook is inappropriate. Your team should come up with a "numerical" case.<br />
# No specific application context is needed for a numerical example.<br />
# The inline notations (`x1`, `s1`) should also be typed using LaTex.<br />
# Label all tables with a table number for better readability. <br />
# 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. <br />
* A section to discuss and/or illustrate the applications;<br />
# I suggest eliminating citing the last name of the first author (i.e. Zhou et al.)<br />
* A conclusion section <br />
* References<br />
# URLs of some citations are not properly formatted (not showing the hyperlinks).<br />
<br />
== [[Exponential transformation|Exponential Transformation]] ==<br />
<br />
* Author list<br />
# Missing course section<br />
# Remove cornell ID<br />
* An introduction of the topic<br />
# Please expand the introduction.<br />
# Please aim for a maximum average sentence length of ~25 words. Last sentence with 51 words is hard to read. <br />
# Second Sentence: please change the word “they” as it could make the meaning ambiguous<br />
# 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. <br />
# If you use abbreviations, please introduce them (e.g. NLP,MINLP)<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Please explain the transformation in words along with equations<br />
# Terms like posynomial should be described in detail.<br />
# Please move the numerical example to the section below<br />
# The “(eq 1)” is not needed here.<br />
# Please expand this section.<br />
* At least one numerical example<br />
# In the third equation of the numerical example, it is confusing to have coefficients after numbers. Some readers may read it as an exponent.<br />
# Last equation in this section after “further linearization” is incorrect. This equation cannot be further linearized, please fix this.<br />
# Please explain the steps in the numerical examples in detail. The step-by-step solution should be provided. <br />
* A section to discuss and/or illustrate the applications<br />
# Missing part of text: “Proof of convexity of with positive definite test of Hessian…”<br />
# Applications are not numerical examples. Please refer to this link for example of applications: [[Duality|https://optimization.cbe.cornell.edu/index.php?title=Duality]]<br />
# Citation 7 is missing in current applications<br />
# The section current applications is redundant<br />
# Please use the LaTex code or equation editor for min, s.t., etc.<br />
# 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. <br />
# The convexification application of MINLP can be further simplified for binary variables. Please refer to the lecture slides for more information.<br />
* A conclusion section<br />
# 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. <br />
* References<br />
# 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]]<br />
# Citation 7 is missing in current applications<br />
<br />
== [[Sparse Reconstruction with Compressed Sensing|Sparse reconstruction with Compressed Sensing]] ==<br />
This Wiki needs a significant rewrite. Please go through the comments for details.<br />
<br />
* An introduction of the topic<br />
# 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.<br />
# This section includes several typos like “sub modual”. Please fix them throughout the wiki and delete them if not required.<br />
# Many abbreviations are used before previously defining them. Please define these abbreviations before using them in the text.<br />
# This section is incomprehensible in its current form. Please rewrite with proper comprehension.<br />
# Equations and math symbols need proper reformatting. The current version reads like text (along with equations) copy-pasted from a specific source.<br />
# Try to place the figure at the top of the Wiki between the main text.<br />
# Avoid pronouns such as “we”.<br />
# I suggest the use of more formal abstract illustrations. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Equations and symbols need proper reformatting.<br />
# 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.<br />
* At least one numerical example<br />
# Numerical example is missing.<br />
* A section to discuss and/or illustrate the applications<br />
# Having a list is not enough. Please explain at least three applications in a few sentences each.<br />
* A conclusion section<br />
# Conclusion section is missing.<br />
* References<br />
# 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]]<br />
<br />
== [[Portfolio optimization|Portfolio Optimization]] ==<br />
<br />
* Author list<br />
# Remove cornell id<br />
* An introduction of the topic<br />
# 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. <br />
# Amount of whitespace can be reduced by changing the orientation of Figure 1 and the sentences in this section.<br />
# 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. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# A brief mention of modern portfolio theory (i.e.. Markowitz) would be appropriate in this section. <br />
# 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.<br />
# Use LaTex to distinguish variables written within a sentence, such as m and n. <br />
# 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.”<br />
# An explanation of a few common constraints would be helpful, rather than just including a table. <br />
* At least one numerical example<br />
# All tables need to be labeled.<br />
# Include figure number in label for consistency. <br />
# Fix misspelling “dolling decision variables”. <br />
# Use LaTex for all variables, equations, and constraints here.<br />
# Example 2 table is hard to read, so making it bigger would help. <br />
# Remove the “Using excel as the solver” part from the sentence before the solution discussion. <br />
# Some grammatical errors here (phrases such as “.. is as follows” should be followed by a colon). <br />
* A section to discuss and/or illustrate the applications<br />
# Rephrase “Portfolio optimization can be used to screen investment projects that meet investors, rationally allocate investment amounts, etc.”<br />
# Not sure “relevant” is the correct word choice here. <br />
# 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. <br />
* A conclusion section<br />
# Need some commas here.<br />
# The sentence “Linear programming has been around since the 1940’s and has such a wide base of applications” is not necessary. <br />
* References<br />
# 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]]<br />
# Remove white space between end of sentences and reference numbers.<br />
<br />
== [[Chance-constraint method|Chance constraint method]] ==<br />
<br />
* Author list: <br />
* An introduction of the topic<br />
# 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”<br />
# In “Chance-constraint”, it is capitalized randomly throughout the introduction. Please correct. <br />
# 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.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Please add a citation to the first sentence. <br />
# Xi is an uncertainty/randomness variable. It is better to use clear language. <br />
# 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.<br />
# Theory is insufficient. Please expand and explain different approaches. <br />
# Please add pros and cons explicitly as a list. <br />
# Explain the physical meaning for examples of chance constraints along with all the notations used.<br />
* At least one numerical example<br />
# Please use the equation editor for min, st., etc.<br />
# 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. <br />
# Please change the table format so as not to confuse the reader. <br />
# Multiple instances of [Chart to be added] are missing.<br />
# Example is incomplete. <br />
# Avoid pronouns such as “we”.<br />
* A section to discuss and/or illustrate the applications<br />
# Please connect several grammatical and spelling errors: “real life application”, Energy creation, particularly in renewable sources, have high variabilities”, and others<br />
# “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. <br />
* A conclusion section<br />
# 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.<br />
# 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. <br />
* References<br />
# 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]]<br />
<br />
== [[Bayesian Optimization | Bayesian Optimization]] ==<br />
<br />
* Contents: Subheadings for EI and the algorithm should not be bolded, Random words should not be capitalized.<br />
* Author list: Remove cornell ID, Please check names<br />
* Introduction<br />
# 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.<br />
# 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.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Captions need reformatting.<br />
# Consider italicizing keywords rather than bolding.<br />
# Please add a citation to the first sentence. <br />
# 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.<br />
# Avoid pronouns such as “we”.<br />
# Please write equations in the Wiki instead of attaching images for equations.<br />
# Acquisition function figure could be made larger and clearer to improve readability.<br />
* At least one numerical example<br />
# Any references to functions or methods in code ‘e.g. fmin’ should be properly formatted as code-stylized text.<br />
# Please use the equation editor for min, st., etc.<br />
# Avoid including a figure of the code for this example and explicitly describe the steps to the modeling and solution process instead. <br />
# Avoid pronouns such as “our” and “we”.<br />
* A section to discuss and/or illustrate the applications <br />
* A conclusion section<br />
# Please do not use brackets to enclose lists.<br />
# Some claims here should be supported by references. Please cite each source after its sentence. <br />
* References<br />
# 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]]<br />
# Try to avoid references to “pop” machine learning blogs where anyone can be an author. (e.g. towardsdatascience)<br />
<br />
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.<br />
<br />
== [[Conjugate gradient methods|Conjugate gradient methods ]] ==<br />
<br />
* Author list: Remove cornell ID<br />
* Introduction<br />
# All inline notations (e.g., `x`, `A`) should be typed using LaTex.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Is Gauss-Newton no longer referenced?<br />
# 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.<br />
# Please indent equation blocks.<br />
# Please properly format pseudocode.<br />
* At least one numerical example<br />
# Steps should be accompanied with explanation, or reference to the corresponding step in the pseudocode.<br />
* A section to discuss and/or illustrate the applications <br />
# Consider including 2 additional examples of applications<br />
* A conclusion section<br />
# Consider adding future research directions<br />
* References<br />
# Reference primary sources rather than Wikipedia<br />
# Too few references.<br />
<br />
== [[Geometric programming|Geometric Programming]] ==<br />
<br />
* Author list<br />
# Remove cornell ID<br />
* An introduction of the topic<br />
# Examples of applications in this section use the same reference. Please cite their individual sources.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# The symbol denoting the domain in the definition of a monomial is unclear. Please clarify it or fix this if it is incorrect.<br />
# Definition of posynomial refers to section 2.1 which is missing from the Wiki (sections are not numbered in the main text).<br />
# 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.<br />
# Additional theory on the feasibility analysis could be provided in this section.<br />
* At least one numerical example<br />
# 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.<br />
* A section to discuss and/or illustrate the applications<br />
# The figure in this section needs to be labeled. <br />
# The figure needs to be resized and perhaps aligned to the center. <br />
* A conclusion section:<br />
# Please avoid vague language such as: “This makes”.<br />
# Please avoid opinionated statements: “one of the best ways”.<br />
* References<br />
# 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]]<br />
<br />
== [[Adam|Adam]] ==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
# Some grammatical errors here, mostly related to the need for commas in certain places (e.g., “Before Adam..”).<br />
# Some minor errors with parts of speech throughout the section, need to revisit phrases such as “which has broader scope in future for”, etc. <br />
# Try splitting up some of the longer sentences in this section, a couple are hard to read.<br />
# 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. <br />
# What does adam stand for? Introduction is insufficient. Please expand. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Revise grammar here, noticing some missing commas and uncapitalized word after period.<br />
# Rephrase “second one is to update the old position with the updated position”.<br />
# Use LaTex code or equation editor to display all equations and variables in this section, and actual subscripts instead of “m_t”, etc. <br />
# 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. <br />
# Remove white space before the period in RMSP discussion.<br />
# Please provide a pseudocode. <br />
# Please use list the two methods here “Adam is a combination of two gradient descent methods which are explained below”<br />
# Please expand the theory section significantly. Theoretical convergence properties should be discussed, even if briefly.<br />
* At least one numerical example<br />
* A section to discuss and/or illustrate the applications<br />
# Same comment as before, consider replacing inline citations after words like “According to..”. <br />
* A conclusion section <br />
* References<br />
# 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]]<br />
# Try to avoid references to blogs and use peer-reviewed academic references instead. <br />
# Too few references.<br />
<br />
== [[A-star algorithm|a* algorithm]] ==<br />
<br />
* Author list:<br />
# Remove cornell ID<br />
* An introduction of the topic:<br />
# In the titles, please change the font from bold to normal to have consistent formatting in the site. <br />
# Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.<br />
# There are no citations in the introduction. Please cite every source.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Please add the mathematical description of the algorithm.<br />
# 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]]<br />
# 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”.<br />
# In algorithms, it is a standard to add high-level description (i.e. pseudocode or flowchart). Please incorporate it. <br />
# 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.<br />
* At least one numerical example<br />
# The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.<br />
# Instead of writing things like “The above image..”, label each figure and use the figure number to refer to it in text. <br />
* A section to discuss and/or illustrate the applications<br />
# No references in the applications. Please cite every source <br />
# Preferably, add at least an additional application. <br />
* A conclusion section<br />
# Conclusion should summarize descriptions. Please modify it to provide a summary. <br />
# Please pay attention to the length and structure of sentences here and in the full page. First sentence is hard to read.<br />
* References<br />
# 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]]<br />
<br />
== [[Job shop scheduling|Job-Shop Scheduling Problem]] ==<br />
<br />
* An introduction of the topic<br />
# 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.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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.<br />
# 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.<br />
# 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.<br />
# 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.<br />
# Use LaTex code or equation editor to display all equations and variables in this section and all other sections as well.<br />
# Check grammar in this section. For example, phrases like “are as follows” need to be followed by a colon and not a period. <br />
# Consider rewriting the assumptions as a list in this section. <br />
* At least one numerical example<br />
# 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.<br />
# 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.<br />
* A section to discuss and/or illustrate the applications<br />
# 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. <br />
* A conclusion section<br />
# The meaning of “Operations applications” is unclear. Please explain or update if necessary.<br />
# The current conclusion section does not properly summarize the problem. Please refer to other Wiki examples for an idea to update the section accordingly.<br />
* References<br />
# 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]] <br />
# Please reference media sources like reference 5 appropriately.<br />
<br />
== [[Optimization in game theory|Optimization in game theory]] ==<br />
<br />
* Author list: remove cornell IDs. <br />
* An introduction of the topic<br />
# 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]] <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Please edit references.<br />
# Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm. <br />
# Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.<br />
* At least one numerical example<br />
# Please organize the last part in a more readable format. Questions may be in bold and numbered, answers are more direct, etc.<br />
# Remember to cite all images and tables. <br />
* A section to discuss and/or illustrate the applications<br />
# Very good, link the reference and cite all sources. <br />
* A conclusion section<br />
# Please add more summarizing especially from theory sentences and avoid long sentences. <br />
* References<br />
# 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]]<br />
# Reference primary sources rather than Wikipedia<br />
<br />
== [[Trust-region methods|Trust-region methods]] ==<br />
<br />
* Author list:<br />
# Remove cornell IDs. Author is also spelled incorrectly. <br />
# Add the course section.<br />
* An introduction of the topic<br />
# 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]] <br />
# 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.<br />
# Avoid pronouns such as “we”. This goes for all other sections as well.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Organization of ideas in this section needs work.<br />
# 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.<br />
# Each approach should have accompanying explanation and motivation for why it is being discussed. It is not enough to outline the algorithm.<br />
# Please make sure symbols are properly subscripted and superscripted (e.g. “pk” should be “p_k”<br />
# Please format the algorithm in proper algorithmic pseudocode format.<br />
# Little to no discussion on global convergence guarantees<br />
# Please include discussion about the advantages and disadvantages of the algorithm<br />
# Fix typo “couchy point”.<br />
* At least one numerical example<br />
# Any code functions (uminfunc) should have proper text formatting.<br />
# The graph needs a better caption explaining how the axes are labeled and what data points are being shown.<br />
# Please increase the quality of the figure. It is hard to see the red line. <br />
# 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.”<br />
* A section to discuss and/or illustrate the applications<br />
# 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).<br />
* A conclusion section<br />
# Please add more summary, future research directions for example is a good start.<br />
* References<br />
# Please consider having the references as this Wiki template, <nowiki>https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization</nowiki><br />
<br />
There are numerous misspellings, grammatical errors, and incorrect claims. Please fix these.<br />
<br />
== [[Momentum|Momentum]] ==<br />
<br />
* Author list<br />
# Remove cornell ID<br />
* An introduction of the topic<br />
# 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.<br />
# Remove bold on “Momentum”.<br />
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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.<br />
# 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.<br />
# 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.<br />
# Avoid pronouns such as “you”.<br />
* At least one numerical example<br />
# Please try to label the plots that explains what each line color means.<br />
* A section to discuss and/or illustrate the applications<br />
# Please use correct terminology like “optimizing non-convex functions” and not “training non-convex models”.<br />
# Adam, Adadelta, and RMSprop are variants of SGD that already use momentum. Please double check the writing and update if necessary.<br />
* A conclusion section<br />
# Please refrain from using words like “zig zag” effects.<br />
* References<br />
# Almost all references used are URLs. Please try to add journal/conference articles or books for references, instead of directly citing the URLs.<br />
<br />
== [[Stochastic dynamic programming|Stochastic Dynamic programming]] ==<br />
<br />
* Author list<br />
# Remove cornell ID<br />
* An introduction of the topic<br />
# Discussion on applications should be moved to a separate section.<br />
* Theory, methodology, and/or algorithmic discussions <br />
# Remove the grey box background of equations.<br />
* At least one numerical example <br />
* A section to discuss and/or illustrate the applications <br />
* A conclusion section <br />
* References<br />
# 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]]<br />
<br />
== [[Outer-approximation (OA)|Outer-approximation]] ==<br />
<br />
* An introduction of the topic <br />
# See formatting guideline below<br />
# Avoid opinionated statements such as “MINLP problems are usually the hardest to solve”.<br />
# Rearrange the text such that the MINLP formulation is in the theory section and keep the introduction in words only. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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<br />
# The sentence “The Outer-Approximation (OA) algorithm was first proposed by Duran and and Grossmann in 1986 to solve MINLP problems.” needs a reference. <br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
# “Minimize” and “subject to” should be “min” and “s.t.” in MathType<br />
* A section to discuss and/or illustrate the applications<br />
# 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)<br />
# 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. <br />
# Place GAMS code in a single code box or remove it.<br />
# Consider reformatting to make steps more readable. Inserting spaces and breaking down steps would help. <br />
* A conclusion section<br />
# Too short. Consider discussion on future research direction and discussion on uncertainty<br />
# 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)”. <br />
* References<br />
# 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]]<br />
# Remove "Template:Reflist"<br />
<br />
== [[Unit commitment problem|Unit commitment problem]] ==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
# Please expand the introduction and avoid discussions of examples or specific applications in this section.<br />
# The sentence “Nonlinear, Non-convex programming optimization problem.” doesn’t make sense by itself and Non-convex shouldn’t be capitalized. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Figure/image format should be revised to better display the content.<br />
# Uppercase characters are used randomly (e.g., “non-convex transmission Constraints”) . Please follow correct language conventions for sentence structure.<br />
# 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. <br />
# Don’t say “written in matrix form as equation..” and just cite the reference, actually write out the equation. <br />
# Properly label the figure in this section with a figure number and improve visibility by making it larger. <br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
# Label the figures in this section properly with figure numbers.<br />
# Fix typo “while minimize” to “while minimizing”. <br />
# Avoid pronouns such as “we”. <br />
# Use the equation editor when typing equations. <br />
* A section to discuss and/or illustrate the applications:<br />
# I suggest changing the order of the subtitles here. For example, Single-Period Unit Commitment. <br />
* A conclusion section <br />
* References<br />
<br />
== [[Frank-Wolfe|Frank-Wolfe]] ==<br />
<br />
* Author list: <br />
* An introduction of the topic<br />
# I suggest highlighting disadvantages along with advantages. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# “[n x 1] matrix” please use the equation editor to express mathematical descriptions and symbols (p,b, etc)<br />
* At least one numerical example<br />
# Every iteration should be clearly presented, and solved "step-by-step".<br />
# Please show at least a few iterations. Even for smaller examples if needed. Report the final solution. <br />
# Please use the LaTex code or equation editor for min and include s.t., etc.<br />
* A section to discuss and/or illustrate the applications: <br />
* A conclusion section<br />
# Same as the introduction. Pros and cons should be evaluated together!<br />
* References<br />
# 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]]<br />
<br />
== [[Line search methods|Line Search Method]] ==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
# Expand the introduction and avoid discussion on some of the specific steps in the solution process. <br />
# Provide references here. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# The phrase “are as follows” in the steepest descent method discussion needs to be followed by a colon. <br />
# Rephrase “has a nice convergence theory” and cite a reference for this claim.<br />
# Avoid pronouns such as “we”.<br />
# Add citation after “.. proposed by Phillip Wolfe in 1969.”<br />
# Figure 1 is between two sections. Please fix this issue. <br />
* At least one numerical example:<br />
# Add some space between iterations or subsection break<br />
* A section to discuss and/or illustrate the applications:<br />
# Too few references in this section. <br />
# Last paragraph makes some claims without references. <br />
* A conclusion section <br />
* References<br />
# 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]]<br />
# More references should be added. A simple Google Scholar search would give you many references.<br />
<br />
== [[Piecewise linear approximation|Piecewise Linear Approximation]]==<br />
<br />
* Author list <br />
* An introduction of the topic<br />
# 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. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Fix typo “to force the x’ values become associated with”. <br />
* At least one numerical example <br />
* A section to discuss and/or illustrate the applications<br />
# Please aim for a maximum average sentence length of ~25 words. Some of these longer sentences are hard to read. <br />
* A conclusion section<br />
# 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.<br />
* References<br />
# Include hyperlinks to sources when possible.<br />
<br />
== [[Mathematical programming with equilibrium constraints|Mathematical Programming with Equilibrium constraints]] ==<br />
<br />
* An introduction of the topic<br />
# 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.<br />
* Theory, methodology, and/or algorithmic discussions<br />
# The meaning of parameter vector x is unclear. Please add more information or update if necessary.<br />
# 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.<br />
# Use equations instead of images to represent math programs and equations in the Implicit Descent and SQP subsection.<br />
# Apart from the steps for each solution technique, please also add a few sentences that describe each method.<br />
* At least one numerical example<br />
# Please define the terms like NCP, MP before abbreviating them. Also try not to unnecessarily abbreviate simple terms.<br />
# Equations should be typed by LaTex. Images for equations are unacceptable.<br />
# GAMS code is strongly discouraged. Please solve the problem "step-by-step".<br />
# 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.<br />
# Avoid using figures in the equations (subject to etc)<br />
* A section to discuss and/or illustrate the applications<br />
# Add references to “power management, highway pricing, chemical process engineering, and traffic planning.”<br />
* A conclusion section<br />
* References<br />
# 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]]<br />
<br />
== [[Wing shape optimization|Wing shape Optimization]] ==<br />
<br />
* Author list: Remove cornell ID<br />
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.<br />
* An introduction of the topic<br />
# 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.)<br />
# Avoid discussion involving finer details of subject methods in this section. <br />
# In the titles, please change the font from bold to normal to have consistent formatting in the site. Same applies to box of content!<br />
* Theory, methodology, and/or algorithmic discussions<br />
# Properly cite the CFD package, don’t just include a link. <br />
# Properly label the figure with a figure number.<br />
# Consider removing white space between isolated sentences to improve readability. <br />
* At least one numerical example<br />
# If you’ve already defined an abbreviation (CFD), there is no need to define it again. Just use the abbreviation.<br />
# Avoid pronouns such as “we” or “they”.<br />
# Phrases like “under the following” need to be followed by a colon.<br />
# 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.<br />
# “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. <br />
# Avoid inserting inline citations like “[4] introduces an..” as it is a bit informal when you don’t explicitly name the subject.<br />
# 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.<br />
* A section to discuss and/or illustrate the applications<br />
# Some characters are randomly capitalized in this section. <br />
* A conclusion section<br />
# 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. <br />
* References<br />
# 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]]<br />
<br />
== [[Interior-point method for NLP|Interior point method for NLP]] ==<br />
<br />
* An introduction of the topic: <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Primal-Dual formulation and comparison to the Barrier Method is not discussed.<br />
# Include brief discussion about big O convergence rates.<br />
# Need discussion about the concept of “central path” and the notion of self concordance<br />
# 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.<br />
# Graphs and images are incorrectly formatted to the page. Consider proper alignment with respect to the text body.<br />
# Use explicitly typed Latex equations instead of images to represent math programs and equations.<br />
# Fix typo “optimisation”.<br />
# Use LaTex code or equation editor to display all equations and variables (e.g., “xi ”, “μ”, etc.).<br />
* At least one numerical example:<br />
# There are formatting issues with figures 2,3. Please make sure to embed them within their respective sections. <br />
* A section to discuss and/or illustrate the applications<br />
* A conclusion section <br />
# Minor character code typos in the conclusion.<br />
# Also, please add more discussion in this section. Future research directions is a good start.<br />
# There is a box ""<br />
* References<br />
<br />
== [[AdaGrad|Adagrad]] ==<br />
<br />
* An introduction of the topic: <br />
* Theory, methodology, and/or algorithmic discussions<br />
# Include discussion on its variants (most important is AdaDelta).<br />
# Include disadvantages of Adagrad, since this provides motivation for the discussion on the variants and improvements of Adagrad<br />
# Include comparisons to other popular optimizers (particularly important is comparisons to regular SGD and Adam)<br />
# 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.<br />
* At least one numerical example<br />
# In the first sentence, “..take the following numerical example” should be followed by a colon. <br />
# Fix typo “trayectory”.<br />
* A section to discuss and/or illustrate the applications<br />
# This section is too short; include specific applications in which input features are sparse and Adagrad excels.<br />
# Add reference to the claim “Mainly, it is a good choice for deep learning models with sparse input features”.<br />
* A conclusion section <br />
* References <br />
<br />
# Too few references overall, you should aggregate information from multiple sources (even if the base algorithm itself comes from a singular paper)<br />
<br />
== [[McCormick envelopes|McCormick Envelopes]] ==<br />
<br />
* Author list: OK but I suggest removing NetID<br />
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.<br />
* An introduction of the topic<br />
# First sentence is hard to read. Please consider keeping sentences below 25-30 words. <br />
# No references provided. Please cite all sources. <br />
# Figure 1 is provided in the middle between two sections. Please include in the introduction section. <br />
* Theory, methodology, and/or algorithmic discussions<br />
# 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]]<br />
# When using mathematical expressions and symbols, please use the equation editor. (e.g., x*y, exy + y, sin (x+y) - x2)<br />
* At least one numerical example<br />
# Please add a few sentences to show the transition from problem to solution. <br />
# For the sample GAMS code, please place it in a code box<br />
* A section to discuss and/or illustrate the applications<br />
# Having a list is not enough. Please explain at least three applications in a few sentences each. <br />
# 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.<br />
* A conclusion section: <br />
* References<br />
# 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]]<br />
# Please follow the standard reference style - the current format is incorrect.</div>Asa279https://optimization.cbe.cornell.edu/index.php?title=McCormick_envelopes&diff=3067McCormick envelopes2021-11-17T23:52:26Z<p>Asa279: </p>
<hr />
<div>'''Introduction'''<br />
<br />
Optimization of a non-convex function f(x) is challenging since it may have multiple locally optimal points and it can take a significant amount of time or effort to determine if the problem has no solution or if the solution is global. Gradient based solvers are unable to certify optimality1. Different techniques are used to address this challenge depending on the characteristics of the problem. One technique used is convex envelopes2:<br />
<br />
Given a non-convex function f(x), g(x) is a convex envelope of f(x) for X <math>\in</math> S if:<br />
<br />
· g(x) is convex under-estimator of f(x)<br />
<br />
· g(x)>=h(x) for all convex under-estimators h(x)<br />
<br />
'''McCormick Envelopes'''<br />
<br />
In particular, for bilinear (e.g., x*y, x<sup>2</sup>) Non-Linear Programming (NLP) problems3, the McCormick Envelope is a type of convex relaxation used for optimization. <br />
<br />
In case of an NLP, an LP relaxation is derived by replacing each bilinear term with a new variable and adding four sets of constraints. In the case of an MINLP, an MILP relaxation is derived. This strategy is known as McCormick relaxation.<br />
<br />
The LP solution gives a lower bound and any feasible solution gives an upper bound.<br />
<br />
As noted by Scott et al4, McCormick envelopes are attractive due to their recursive nature of their definition, which affords wide applicability and easy implementation computationally. Furthermore, these relaxations are typically stronger than those resulting from convexification or linearization procedures. <br />
<br />
'''Derivation of McCormick Envelopes'''<br />
<br />
<br />
<math>w=xy</math><br />
<br />
<math>x^{L}\leq x\leq x^{U}<br />
</math><br />
<br />
<math>y^{L}\leq y\leq y^{U}</math><br />
<br />
where <math>x^{L}, x^{U}, y^{L}, y^{U} </math>are upper and lower bound values for <math>x</math> and <math>y</math>, respectively.<br />
<br />
<br />
<math>a=\left (x-x^{L} \right )</math><br />
<br />
<math>b=\left (y-y^{L} \right )</math><br />
<br />
<math>a * b\geq 0</math><br />
<br />
<math>a * b=\left ( x-x^{L} \right )\left ( y-y^{L} \right )=xy-x^{L}y-xy^{L}+x^{L}y^{L}\geq 0 </math><br />
<br />
<math>w\geq x^{L}y+xy^{L}-x^{L}y^{L}</math><br />
<br />
<br />
<math>a=\left ( x^{U}-x \right )</math><br />
<br />
<math>b = \left ( y^{U} -y\right )</math><br />
<br />
<math>w\geq x^{U}y+xy^{U}-x^{U}y^{U}</math><br />
<br />
<br />
<math>a=\left ( x^{U}-x\right )</math><br />
<br />
<math>b=\left ( y-y^{L} \right )</math><br />
<br />
<math>w\leq x^{U}y+xy^{L}-x^{U}y^{L}</math><br />
<br />
<br />
<math>a=\left ( x-x^{L} \right )</math><br />
<br />
<math>b=\left ( y^{U} \right )-y</math><br />
<br />
<math>w\leq xy^{U}+x^{L}y-x^{L}y^{U}</math><br />
<br />
The underestimators of the function are represented by:<br />
<br />
<math>w\geq x^{L}y+xy^{L}-x^{L}y^{L}</math><br />
<br />
<math>w\geq x^{U}y+xy^{U}-x^{U}y^{U}</math><br />
<br />
The overestimators of the function are represented by:<br />
<br />
<math>w\geq x^{U}y+xy^{L}-x^{U}y^{L}</math><br />
<br />
<math>w\geq x^{U}y+xy^{L}-x^{L}y^{U}</math><br />
<br />
<br />
'''Not sure if this is redundant''' <br />
<br />
<math>\textstyle \sum_{j=1}^n \displaystyle c_j x_j^* = \textstyle \sum_{i=1}^m \displaystyle b_i y_i^*</math><br />
<br />
<br />
<br />
<br />
'''Example: Convex Relaxation''' <br />
<br />
Good bounds are essential to focusing the feasible solution which may be obtained either by inspection or solving the optimization problem to minimize (maximize) x subject to the same constraints as the original problem.<br />
<br />
<br />
<br />
As noted by Hazaji, state-of-the-art global optimization solvers implement bound contraction techniques in order to improve this bounding procedure. Once bound propagation is completed,<br />
<br />
domain partitioning becomes necessary. Spatial branch and bound schemes [6, 7] are among the most effective partitioning methods in global optimization.<br />
<br />
By splitting the domain of a given variable, the solver is able to divide the original domain into two smaller regions, further tightening the convex relaxations of each partition.<br />
<br />
'''Example: Numerical'''<br />
<br />
'''Application'''<br />
<br />
Bilinear expressions are the most common nonconvex components in mathematical formulations modeling problems in: <sup>5</sup><br />
<br />
Chemical engineering 8, 9, 10, 11<br />
<br />
Process network problems12 (Quesada & Grossmann, 1995)<br />
<br />
Water networks13 (Bagajewicz, 2000) <br />
<br />
Pooling and blending14 (Haverly, 1978)<br />
<br />
Supply Chain and Transportation 15, 9, 10, 11<br />
<br />
Energy Systems 16 17 18 19<br />
<br />
'''Conclusion'''<br />
<br />
McCormick Envelopes provide a relaxation technique for bilinear non-convex nonlinear programming problems3. Since non-convex NLP are challenging to solve and may be time or resource intensive, McCormick envelopes are attractive due to their recursive nature of their definition, which affords wide applicability and easy implementation computationally. Furthermore, these relaxations are typically stronger than those resulting from convexification or linearization procedures4.<br />
<br />
'''References'''<br />
<br />
# Castro, Pedro. "A Tighter Piecewise McCormick Relaxation for Bilinear Problems." (n.d.): n. pag. 3 June 2014. Web. 6 June 2015. <<nowiki>http://minlp.cheme.cmu.edu/2014/papers/castro.pdf</nowiki><br />
# You, F (2021). Notes for a lecture on Mixed Integer Non-Linear Programming (MINLP). Archives for SYSEN 5800 Computational Optimization (2021FA), Cornell University, Ithaca, NY.<br />
# Dombrowski, J. (2015, June 7). Northwestern University Open Text Book on Process Optimization, McCormick Envelopes Retrieved from <nowiki>https://optimization.mccormick.northwestern.edu/index.php/McCormick_envelopes</nowiki><br />
# Scott, J. K. Stuber, M. D. & Barton, P. I. (2011). Generalized McCormick Relaxations. Journal of Global Optimization, Vol. 51, Issue 4, 569-606 doi: 10.1007/s10898-011-9664-7 <br />
# Hijazi, H., Perspective Envelopes for Bilinear Functions, unpublished manuscript, The Australian National University, Canberra, Australia 4841.pdf<br />
# Androulakis, I., Maranas, C., Floudas, C.: alphabb: A global optimization method for general constrained nonconvex problems. Journal of Global Optimization 7(4), 337{363 (1995)<br />
# Smith, E., Pantelides, C.: A symbolic reformulation/spatial branch-and-bound algorithm for the global optimisation of nonconvex fMINLPsg. Computers & Chemical Engineering 23(4), 457 { 478 (1999) <br />
# Geunes, J., Pardalos, P.: Supply chain optimization, vol. 98. Springer Science & BusinessMedia (2006)<br />
# Nahapetyan, A.: Bilinear programming: applications in the supply chain management bilinear programming: Applications in the supply chain management. In: C.A. Floudas, P.M. Pardalos (eds.) Encyclopedia of Optimization, pp. 282{288. Springer US (2009)<br />
# Nahapetyan, A.G., Pardalos, P.M.: A bilinear reduction based algorithm for solving capacitated multi-item dynamic pricing problems. Computers & Operations Research 35(5), 1601 { 1612 (2008). Part Special Issue: Algorithms and Computational Methods in Feasibility and Infeasibility<br />
# Rebennack, S., Nahapetyan, A., Pardalos, P.: Bilinear modeling solution approach for_xed charge network ow problems. Optimization Letters 3(3), 347{355 (2009) <br />
# Quesada, Ignacio & Grossmann, Ignacio. (1995). A Global Optimization Algorithm for Linear Fractional and Bilinear Programs. Journal of Global Optimization. 6. 39-76. 10.1007/BF01106605.<br />
# Bagajewicz, 2000<br />
# Haverly, 1978<br />
# Geunes, J., Pardalos, P.: Supply chain optimization, vol. 98. Springer Science & Business Media (2006) <br />
# Co_rin, C., Hijazi, H., Van Hentenryck, P., Lehmann, K.: Primal and dual bounds for optimal transmission switching. Proceedings of the 18th Power Syst. Computation Conf., Wroclaw Poland, PSCC (2014)<br />
# Gemine, Q., Ernst, D., Louveaux, Q., Corn_elusse, B.: Relaxations for multi-period optimal power ow problems with discrete decision variables. Proceedings of the 18th Power Syst. Computation Conf., Wroclaw, Poland, PSCC 2014 (2014)<br />
# Hijazi, H., Corin, C., Van Hentenryck, P.: Convex Quadratic Relaxations for Mixed-Integer Nonlinear Programs in Power Systems. NICTA Technical Report (2014)<br />
# Hijazi, H., Thiebaux, S.: Optimal AC distribution systems reconfiguration. Proceedings of the 18th Power Syst. Computation Conf., Wroclaw, Poland, PSCC 2014 (2014) <br /></div>Asa279https://optimization.cbe.cornell.edu/index.php?title=McCormick_envelopes&diff=3066McCormick envelopes2021-11-17T23:33:44Z<p>Asa279: </p>
<hr />
<div>'''Introduction'''<br />
<br />
Optimization of a non-convex function f(x) is challenging since it may have multiple locally optimal points and it can take a significant amount of time or effort to determine if the problem has no solution or if the solution is global. Gradient based solvers are unable to certify optimality1. Different techniques are used to address this challenge depending on the characteristics of the problem. One technique used is convex envelopes2:<br />
<br />
Given a non-convex function f(x), g(x) is a convex envelope of f(x) for X <math>\in</math> S if:<br />
<br />
· g(x) is convex under-estimator of f(x)<br />
<br />
· g(x)>=h(x) for all convex under-estimators h(x)<br />
<br />
'''McCormick Envelopes'''<br />
<br />
In particular, for bilinear (e.g., x*y, x<sup>2</sup>) Non-Linear Programming (NLP) problems3, the McCormick Envelope is a type of convex relaxation used for optimization. <br />
<br />
In case of an NLP, an LP relaxation is derived by replacing each bilinear term with a new variable and adding four sets of constraints. In the case of an MINLP, an MILP relaxation is derived. This strategy is known as McCormick relaxation.<br />
<br />
The LP solution gives a lower bound and any feasible solution gives an upper bound.<br />
<br />
As noted by Scott et al4, McCormick envelopes are attractive due to their recursive nature of their definition, which affords wide applicability and easy implementation computationally. Furthermore, these relaxations are typically stronger than those resulting from convexification or linearization procedures. <br />
<br />
'''Derivation of McCormick Envelopes'''<br />
<br />
<nowiki><math>w=xy </math></nowiki><br />
<br />
x^{L}\leq x\leq x^{U} \\<br />
<br />
y^{L}\leq y\leq y^{U} \\<br />
<br />
where \space\ x^{L}, x^{U}, y^{L}, y^{U} are \space\ upper \space\ and \space\ lower \space\ bound \space\ values \space\ for \space\ x \space\ and \space\ y \space\ respectively \\<br />
<br />
a=\left (x-x^{L} \right )\\<br />
<br />
b=\left (y-y^{L} \right )\\<br />
<br />
a * b\geq 0 \\<br />
<br />
a * b=\left ( x-x^{L} \right )\left ( y-y^{L} \right )=xy-x^{L}y-xy^{L}+x^{L}y^{L}\geq 0 \\<br />
<br />
w\geq x^{L}y+xy^{L}-x^{L}y^{L} \\<br />
<br />
\\<br />
<br />
a=\left ( x^{U}-x \right ) \\<br />
<br />
b = \left ( y^{U} -y\right ) \\<br />
<br />
w\geq x^{U}y+xy^{U}-x^{U}y^{U} \\<br />
<br />
\\<br />
<br />
a=\left ( x^{U}-x\right )\\<br />
<br />
b=\left ( y-y^{L} \right )\\<br />
<br />
w\leq x^{U}y+xy^{L}-x^{U}y^{L}\\<br />
<br />
\\<br />
<br />
a=\left ( x-x^{L} \right )\\<br />
<br />
b=\left ( y^{U} \right )-y\\<br />
<br />
w\leq xy^{U}+x^{L}y-x^{L}y^{U}\\<br />
<br />
The<space>underestimators<space>of<space>the<space>function<space>are<space>represented<space>by:\\<br />
<br />
w\geq x^{L}y+xy^{L}-x^{L}y^{L}\\<br />
<br />
w\geq x^{U}y+xy^{U}-x^{U}y^{U}\\<br />
<br />
The<space>overestimators<space>of<space>the<space>function<space>are<space>represented<space>by:\\<br />
<br />
w\geq x^{U}y+xy^{L}-x^{U}y^{L}\\<br />
<br />
w\geq x^{U}y+xy^{L}-x^{L}y^{U}\\<br />
<br />
\end{align*}<br />
<br />
<br />
<br />
<nowiki><math>\textstyle \sum_{j=1}^n \displaystyle c_j x_j^* = \textstyle \sum_{i=1}^m \displaystyle b_i y_i^*</math></nowiki><br />
<br />
<br />
<br />
'''Example: Convex Relaxation''' <br />
<br />
Good bounds are essential to focusing the feasible solution which may be obtained either by inspection or solving the optimization problem to minimize (maximize) x subject to the same constraints as the original problem.<br />
<br />
<br />
<br />
As noted by Hazaji, state-of-the-art global optimization solvers implement bound contraction techniques in order to improve this bounding procedure. Once bound propagation is completed,<br />
<br />
domain partitioning becomes necessary. Spatial branch and bound schemes [6, 7] are among the most effective partitioning methods in global optimization.<br />
<br />
By splitting the domain of a given variable, the solver is able to divide the original domain into two smaller regions, further tightening the convex relaxations of each partition.<br />
<br />
'''Example: Numerical'''<br />
<br />
'''Application'''<br />
<br />
Bilinear expressions are the most common nonconvex components in mathematical formulations modeling problems in: <sup>5</sup><br />
<br />
Chemical engineering 8, 9, 10, 11<br />
<br />
Process network problems12 (Quesada & Grossmann, 1995)<br />
<br />
Water networks13 (Bagajewicz, 2000) <br />
<br />
Pooling and blending14 (Haverly, 1978)<br />
<br />
Supply Chain and Transportation 15, 9, 10, 11<br />
<br />
Energy Systems 16 17 18 19<br />
<br />
'''Conclusion'''<br />
<br />
McCormick Envelopes provide a relaxation technique for bilinear non-convex nonlinear programming problems3. Since non-convex NLP are challenging to solve and may be time or resource intensive, McCormick envelopes are attractive due to their recursive nature of their definition, which affords wide applicability and easy implementation computationally. Furthermore, these relaxations are typically stronger than those resulting from convexification or linearization procedures4.<br />
<br />
'''References'''<br />
<br />
# Castro, Pedro. "A Tighter Piecewise McCormick Relaxation for Bilinear Problems." (n.d.): n. pag. 3 June 2014. Web. 6 June 2015. <<nowiki>http://minlp.cheme.cmu.edu/2014/papers/castro.pdf</nowiki><br />
# You, F (2021). Notes for a lecture on Mixed Integer Non-Linear Programming (MINLP). Archives for SYSEN 5800 Computational Optimization (2021FA), Cornell University, Ithaca, NY.<br />
# Dombrowski, J. (2015, June 7). Northwestern University Open Text Book on Process Optimization, McCormick Envelopes Retrieved from <nowiki>https://optimization.mccormick.northwestern.edu/index.php/McCormick_envelopes</nowiki><br />
# Scott, J. K. Stuber, M. D. & Barton, P. I. (2011). Generalized McCormick Relaxations. Journal of Global Optimization, Vol. 51, Issue 4, 569-606 doi: 10.1007/s10898-011-9664-7 <br />
# Hijazi, H., Perspective Envelopes for Bilinear Functions, unpublished manuscript, The Australian National University, Canberra, Australia 4841.pdf<br />
# Androulakis, I., Maranas, C., Floudas, C.: alphabb: A global optimization method for general constrained nonconvex problems. Journal of Global Optimization 7(4), 337{363 (1995)<br />
# Smith, E., Pantelides, C.: A symbolic reformulation/spatial branch-and-bound algorithm for the global optimisation of nonconvex fMINLPsg. Computers & Chemical Engineering 23(4), 457 { 478 (1999) <br />
# Geunes, J., Pardalos, P.: Supply chain optimization, vol. 98. Springer Science & BusinessMedia (2006)<br />
# Nahapetyan, A.: Bilinear programming: applications in the supply chain management bilinear programming: Applications in the supply chain management. In: C.A. Floudas, P.M. Pardalos (eds.) Encyclopedia of Optimization, pp. 282{288. Springer US (2009)<br />
# Nahapetyan, A.G., Pardalos, P.M.: A bilinear reduction based algorithm for solving capacitated multi-item dynamic pricing problems. Computers & Operations Research 35(5), 1601 { 1612 (2008). Part Special Issue: Algorithms and Computational Methods in Feasibility and Infeasibility<br />
# Rebennack, S., Nahapetyan, A., Pardalos, P.: Bilinear modeling solution approach for_xed charge network ow problems. Optimization Letters 3(3), 347{355 (2009) <br />
# Quesada, Ignacio & Grossmann, Ignacio. (1995). A Global Optimization Algorithm for Linear Fractional and Bilinear Programs. Journal of Global Optimization. 6. 39-76. 10.1007/BF01106605.<br />
# Bagajewicz, 2000<br />
# Haverly, 1978<br />
# Geunes, J., Pardalos, P.: Supply chain optimization, vol. 98. Springer Science & Business Media (2006) <br />
# Co_rin, C., Hijazi, H., Van Hentenryck, P., Lehmann, K.: Primal and dual bounds for optimal transmission switching. Proceedings of the 18th Power Syst. Computation Conf., Wroclaw Poland, PSCC (2014)<br />
# Gemine, Q., Ernst, D., Louveaux, Q., Corn_elusse, B.: Relaxations for multi-period optimal power ow problems with discrete decision variables. Proceedings of the 18th Power Syst. Computation Conf., Wroclaw, Poland, PSCC 2014 (2014)<br />
# Hijazi, H., Corin, C., Van Hentenryck, P.: Convex Quadratic Relaxations for Mixed-Integer Nonlinear Programs in Power Systems. NICTA Technical Report (2014)<br />
# Hijazi, H., Thiebaux, S.: Optimal AC distribution systems reconfiguration. Proceedings of the 18th Power Syst. Computation Conf., Wroclaw, Poland, PSCC 2014 (2014) <br /></div>Asa279https://optimization.cbe.cornell.edu/index.php?title=McCormick_envelopes&diff=3065McCormick envelopes2021-11-17T23:33:00Z<p>Asa279: </p>
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<div>'''Introduction'''<br />
<br />
Optimization of a non-convex function f(x) is challenging since it may have multiple locally optimal points and it can take a significant amount of time or effort to determine if the problem has no solution or if the solution is global. Gradient based solvers are unable to certify optimality1. Different techniques are used to address this challenge depending on the characteristics of the problem. One technique used is convex envelopes2:<br />
<br />
Given a non-convex function f(x), g(x) is a convex envelope of f(x) for X <math>\in</math> S if:<br />
<br />
· g(x) is convex under-estimator of f(x)<br />
<br />
· g(x)>=h(x) for all convex under-estimators h(x)<br />
<br />
'''McCormick Envelopes'''<br />
<br />
In particular, for bilinear (e.g., x*y, x<sup>2</sup>) Non-Linear Programming (NLP) problems3, the McCormick Envelope is a type of convex relaxation used for optimization. <br />
<br />
In case of an NLP, an LP relaxation is derived by replacing each bilinear term with a new variable and adding four sets of constraints. In the case of an MINLP, an MILP relaxation is derived. This strategy is known as McCormick relaxation.<br />
<br />
The LP solution gives a lower bound and any feasible solution gives an upper bound.<br />
<br />
As noted by Scott et al4, McCormick envelopes are attractive due to their recursive nature of their definition, which affords wide applicability and easy implementation computationally. Furthermore, these relaxations are typically stronger than those resulting from convexification or linearization procedures. <br />
<br />
'''Derivation of McCormick Envelopes'''<br />
<br />
<nowiki><math>w=xy \\</math></nowiki><br />
<br />
x^{L}\leq x\leq x^{U} \\<br />
<br />
y^{L}\leq y\leq y^{U} \\<br />
<br />
where \space\ x^{L}, x^{U}, y^{L}, y^{U} are \space\ upper \space\ and \space\ lower \space\ bound \space\ values \space\ for \space\ x \space\ and \space\ y \space\ respectively \\<br />
<br />
a=\left (x-x^{L} \right )\\<br />
<br />
b=\left (y-y^{L} \right )\\<br />
<br />
a * b\geq 0 \\<br />
<br />
a * b=\left ( x-x^{L} \right )\left ( y-y^{L} \right )=xy-x^{L}y-xy^{L}+x^{L}y^{L}\geq 0 \\<br />
<br />
w\geq x^{L}y+xy^{L}-x^{L}y^{L} \\<br />
<br />
\\<br />
<br />
a=\left ( x^{U}-x \right ) \\<br />
<br />
b = \left ( y^{U} -y\right ) \\<br />
<br />
w\geq x^{U}y+xy^{U}-x^{U}y^{U} \\<br />
<br />
\\<br />
<br />
a=\left ( x^{U}-x\right )\\<br />
<br />
b=\left ( y-y^{L} \right )\\<br />
<br />
w\leq x^{U}y+xy^{L}-x^{U}y^{L}\\<br />
<br />
\\<br />
<br />
a=\left ( x-x^{L} \right )\\<br />
<br />
b=\left ( y^{U} \right )-y\\<br />
<br />
w\leq xy^{U}+x^{L}y-x^{L}y^{U}\\<br />
<br />
The<space>underestimators<space>of<space>the<space>function<space>are<space>represented<space>by:\\<br />
<br />
w\geq x^{L}y+xy^{L}-x^{L}y^{L}\\<br />
<br />
w\geq x^{U}y+xy^{U}-x^{U}y^{U}\\<br />
<br />
The<space>overestimators<space>of<space>the<space>function<space>are<space>represented<space>by:\\<br />
<br />
w\geq x^{U}y+xy^{L}-x^{U}y^{L}\\<br />
<br />
w\geq x^{U}y+xy^{L}-x^{L}y^{U}\\<br />
<br />
\end{align*}<br />
<br />
<br />
<br />
<nowiki><math>\textstyle \sum_{j=1}^n \displaystyle c_j x_j^* = \textstyle \sum_{i=1}^m \displaystyle b_i y_i^*</math></nowiki><br />
<br />
<br />
<br />
'''Example: Convex Relaxation''' <br />
<br />
Good bounds are essential to focusing the feasible solution which may be obtained either by inspection or solving the optimization problem to minimize (maximize) x subject to the same constraints as the original problem.<br />
<br />
<br />
<br />
As noted by Hazaji, state-of-the-art global optimization solvers implement bound contraction techniques in order to improve this bounding procedure. Once bound propagation is completed,<br />
<br />
domain partitioning becomes necessary. Spatial branch and bound schemes [6, 7] are among the most effective partitioning methods in global optimization.<br />
<br />
By splitting the domain of a given variable, the solver is able to divide the original domain into two smaller regions, further tightening the convex relaxations of each partition.<br />
<br />
'''Example: Numerical'''<br />
<br />
'''Application'''<br />
<br />
Bilinear expressions are the most common nonconvex components in mathematical formulations modeling problems in: <sup>5</sup><br />
<br />
Chemical engineering 8, 9, 10, 11<br />
<br />
Process network problems12 (Quesada & Grossmann, 1995)<br />
<br />
Water networks13 (Bagajewicz, 2000) <br />
<br />
Pooling and blending14 (Haverly, 1978)<br />
<br />
Supply Chain and Transportation 15, 9, 10, 11<br />
<br />
Energy Systems 16 17 18 19<br />
<br />
'''Conclusion'''<br />
<br />
McCormick Envelopes provide a relaxation technique for bilinear non-convex nonlinear programming problems3. Since non-convex NLP are challenging to solve and may be time or resource intensive, McCormick envelopes are attractive due to their recursive nature of their definition, which affords wide applicability and easy implementation computationally. Furthermore, these relaxations are typically stronger than those resulting from convexification or linearization procedures4.<br />
<br />
'''References'''<br />
<br />
# Castro, Pedro. "A Tighter Piecewise McCormick Relaxation for Bilinear Problems." (n.d.): n. pag. 3 June 2014. Web. 6 June 2015. <<nowiki>http://minlp.cheme.cmu.edu/2014/papers/castro.pdf</nowiki><br />
# You, F (2021). Notes for a lecture on Mixed Integer Non-Linear Programming (MINLP). Archives for SYSEN 5800 Computational Optimization (2021FA), Cornell University, Ithaca, NY.<br />
# Dombrowski, J. (2015, June 7). Northwestern University Open Text Book on Process Optimization, McCormick Envelopes Retrieved from <nowiki>https://optimization.mccormick.northwestern.edu/index.php/McCormick_envelopes</nowiki><br />
# Scott, J. K. Stuber, M. D. & Barton, P. I. (2011). Generalized McCormick Relaxations. Journal of Global Optimization, Vol. 51, Issue 4, 569-606 doi: 10.1007/s10898-011-9664-7 <br />
# Hijazi, H., Perspective Envelopes for Bilinear Functions, unpublished manuscript, The Australian National University, Canberra, Australia 4841.pdf<br />
# Androulakis, I., Maranas, C., Floudas, C.: alphabb: A global optimization method for general constrained nonconvex problems. Journal of Global Optimization 7(4), 337{363 (1995)<br />
# Smith, E., Pantelides, C.: A symbolic reformulation/spatial branch-and-bound algorithm for the global optimisation of nonconvex fMINLPsg. Computers & Chemical Engineering 23(4), 457 { 478 (1999) <br />
# Geunes, J., Pardalos, P.: Supply chain optimization, vol. 98. Springer Science & BusinessMedia (2006)<br />
# Nahapetyan, A.: Bilinear programming: applications in the supply chain management bilinear programming: Applications in the supply chain management. In: C.A. Floudas, P.M. Pardalos (eds.) Encyclopedia of Optimization, pp. 282{288. Springer US (2009)<br />
# Nahapetyan, A.G., Pardalos, P.M.: A bilinear reduction based algorithm for solving capacitated multi-item dynamic pricing problems. Computers & Operations Research 35(5), 1601 { 1612 (2008). Part Special Issue: Algorithms and Computational Methods in Feasibility and Infeasibility<br />
# Rebennack, S., Nahapetyan, A., Pardalos, P.: Bilinear modeling solution approach for_xed charge network ow problems. Optimization Letters 3(3), 347{355 (2009) <br />
# Quesada, Ignacio & Grossmann, Ignacio. (1995). A Global Optimization Algorithm for Linear Fractional and Bilinear Programs. Journal of Global Optimization. 6. 39-76. 10.1007/BF01106605.<br />
# Bagajewicz, 2000<br />
# Haverly, 1978<br />
# Geunes, J., Pardalos, P.: Supply chain optimization, vol. 98. Springer Science & Business Media (2006) <br />
# Co_rin, C., Hijazi, H., Van Hentenryck, P., Lehmann, K.: Primal and dual bounds for optimal transmission switching. Proceedings of the 18th Power Syst. Computation Conf., Wroclaw Poland, PSCC (2014)<br />
# Gemine, Q., Ernst, D., Louveaux, Q., Corn_elusse, B.: Relaxations for multi-period optimal power ow problems with discrete decision variables. Proceedings of the 18th Power Syst. Computation Conf., Wroclaw, Poland, PSCC 2014 (2014)<br />
# Hijazi, H., Corin, C., Van Hentenryck, P.: Convex Quadratic Relaxations for Mixed-Integer Nonlinear Programs in Power Systems. NICTA Technical Report (2014)<br />
# Hijazi, H., Thiebaux, S.: Optimal AC distribution systems reconfiguration. Proceedings of the 18th Power Syst. Computation Conf., Wroclaw, Poland, PSCC 2014 (2014) <br /></div>Asa279https://optimization.cbe.cornell.edu/index.php?title=User:ANPReina57&diff=737User:ANPReina572020-10-02T04:14:18Z<p>Asa279: Blanked the page</p>
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