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

2021 Cornell Optimization Open Textbook Feedback

2021-12-19T21:50:03Z

Aw843cornell: /* Wing shape Optimization */

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

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

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

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

* Theory, methodology, and/or algorithmic discussions
# Rephrase “Cut the relevant information and conditions in the portfolio optimization, as well as the final requirements into the relevant variables, constraints and linear functions of the linear programming problem.”
* At least one numerical example
# Fix misspelling “dolling decision variables”.
* A conclusion section
# Need some commas here (second sentence hard to read).
* References
# Remove white space between end of sentences and reference numbers.

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

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

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

== [[Adam]] ==

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

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

* Theory, methodology, and/or algorithmic discussions

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

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

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

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

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

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

== [[Unit commitment problem]] ==

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

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

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

* At least one numerical example
# A numerical example is simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments). There is an Application section where you discuss the applications.
* A conclusion section
# These variables should be defined before the conclusion section, they are out of place here.
* References
# Include hyperlinks to references if possible.

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

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

== [[AdaGrad|Adagrad]] ==
== [[McCormick envelopes|McCormick Envelopes]] ==

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

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

* At least one numerical example

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

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

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

2021 Cornell Optimization Open Textbook Feedback

2021-12-19T21:49:19Z

Aw843cornell: /* Portfolio Optimization */

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

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

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

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

* Theory, methodology, and/or algorithmic discussions
# Rephrase “Cut the relevant information and conditions in the portfolio optimization, as well as the final requirements into the relevant variables, constraints and linear functions of the linear programming problem.”
* At least one numerical example
# Fix misspelling “dolling decision variables”.
* A conclusion section
# Need some commas here (second sentence hard to read).
* References
# Remove white space between end of sentences and reference numbers.

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

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

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

== [[Adam]] ==

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

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

* Theory, methodology, and/or algorithmic discussions

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

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

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

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

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

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

== [[Unit commitment problem]] ==

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

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

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

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

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

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

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

== [[AdaGrad|Adagrad]] ==
== [[McCormick envelopes|McCormick Envelopes]] ==

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

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

* At least one numerical example

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

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

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

2021 Cornell Optimization Open Textbook Feedback

2021-12-19T04:21:26Z

Aw843cornell: /* Wing shape Optimization */

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

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

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

* A conclusion section
* References

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

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section

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

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

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

* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section

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

* Author list

* An introduction of the topic

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

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

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

* Author list:
* An introduction of the topic

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

* A section to discuss and/or illustrate the applications

* A conclusion section

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

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

* Author list

* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section:

* References

== [[Adam]] ==

* Author list
* An introduction of the topic

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

* A section to discuss and/or illustrate the applications

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

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

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

* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

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

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

* Author list
* An introduction of the topic

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

* A section to discuss and/or illustrate the applications

* A conclusion section

* References
# Incorrect reference style.

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

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

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

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

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

* Author list

* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example
* A section to discuss and/or illustrate the applications
* A conclusion section
* References
== [[Outer-approximation (OA)|Outer-approximation]] ==

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

== [[Unit commitment problem]] ==

* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example
# Fix typo “while minimize” to “while minimizing”.
* A section to discuss and/or illustrate the applications:

* A conclusion section
* References

== [[Frank-Wolfe]] ==

* Author list:
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

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

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

* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions
# Avoid pronouns such as “we” (all sections).
* At least one numerical example:

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

* A conclusion section
* References
== [[Piecewise linear approximation|Piecewise Linear Approximation]]==

* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example
* A section to discuss and/or illustrate the applications

* A conclusion section

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

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

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

* Author list:
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

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

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

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

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

# References not properly formatted

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

* Author list
* Sections
* An introduction of the topic

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

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

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

* Author list:
* An introduction of the topic
* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

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

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

* A section to discuss and/or illustrate the applications

* A conclusion section:

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

2021 Cornell Optimization Open Textbook Feedback

2021-12-19T04:19:42Z

Aw843cornell: /* Wing shape Optimization */

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

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

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

* A conclusion section
* References

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

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section

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

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

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

* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section

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

* Author list

* An introduction of the topic

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

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

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

* Author list:
* An introduction of the topic

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

* A section to discuss and/or illustrate the applications

* A conclusion section

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

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

* Author list

* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section:

* References

== [[Adam]] ==

* Author list
* An introduction of the topic

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

* A section to discuss and/or illustrate the applications

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

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

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

* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

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

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

* Author list
* An introduction of the topic

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

* A section to discuss and/or illustrate the applications

* A conclusion section

* References
# Incorrect reference style.

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

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

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

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

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

* Author list

* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example
* A section to discuss and/or illustrate the applications
* A conclusion section
* References
== [[Outer-approximation (OA)|Outer-approximation]] ==

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

== [[Unit commitment problem]] ==

* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example
# Fix typo “while minimize” to “while minimizing”.
* A section to discuss and/or illustrate the applications:

* A conclusion section
* References

== [[Frank-Wolfe]] ==

* Author list:
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

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

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

* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions
# Avoid pronouns such as “we” (all sections).
* At least one numerical example:

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

* A conclusion section
* References
== [[Piecewise linear approximation|Piecewise Linear Approximation]]==

* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example
* A section to discuss and/or illustrate the applications

* A conclusion section

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

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

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

* Author list:
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

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

* A conclusion section
# These variables should be defined before the conclusion section, they are out of place here.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

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

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

# References not properly formatted

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

* Author list
* Sections
* An introduction of the topic

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

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

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

* Author list:
* An introduction of the topic
* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

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

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

* A section to discuss and/or illustrate the applications

* A conclusion section:

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

2021 Cornell Optimization Open Textbook Feedback

2021-12-19T02:08:23Z

Aw843cornell: /* Piecewise Linear Approximation */

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

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

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

* A conclusion section
* References

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

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section

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

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

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

* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section

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

* Author list

* An introduction of the topic

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

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

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

* Author list:
* An introduction of the topic

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

* A section to discuss and/or illustrate the applications

* A conclusion section

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

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

* Author list

* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section:

* References

== [[Adam]] ==

* Author list
* An introduction of the topic

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

* A section to discuss and/or illustrate the applications

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

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

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

* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

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

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

* Author list
* An introduction of the topic

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

* A section to discuss and/or illustrate the applications

* A conclusion section

* References
# Incorrect reference style.

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

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

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

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

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

* Author list

* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example
* A section to discuss and/or illustrate the applications
* A conclusion section
* References
== [[Outer-approximation (OA)|Outer-approximation]] ==

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

== [[Unit commitment problem]] ==

* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example
# Fix typo “while minimize” to “while minimizing”.
* A section to discuss and/or illustrate the applications:

* A conclusion section
* References

== [[Frank-Wolfe]] ==

* Author list:
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

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

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

* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions
# Avoid pronouns such as “we” (all sections).
* At least one numerical example:

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

* A conclusion section
* References
== [[Piecewise linear approximation|Piecewise Linear Approximation]]==

* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example
* A section to discuss and/or illustrate the applications

* A conclusion section

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

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

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

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

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

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

# References not properly formatted

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

* Author list
* Sections
* An introduction of the topic

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

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

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

* Author list:
* An introduction of the topic
* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

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

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

* A section to discuss and/or illustrate the applications

* A conclusion section:

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

2021 Cornell Optimization Open Textbook Feedback

2021-12-19T01:58:57Z

Aw843cornell: /* Line Search Method */

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

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

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

* A conclusion section
* References

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

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section

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

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

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

* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section

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

* Author list

* An introduction of the topic

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

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

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

* Author list:
* An introduction of the topic

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

* A section to discuss and/or illustrate the applications

* A conclusion section

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

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

* Author list

* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section:

* References

== [[Adam]] ==

* Author list
* An introduction of the topic

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

* A section to discuss and/or illustrate the applications

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

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

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

* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

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

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

* Author list
* An introduction of the topic

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

* A section to discuss and/or illustrate the applications

* A conclusion section

* References
# Incorrect reference style.

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

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

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

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

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

* Author list

* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example
* A section to discuss and/or illustrate the applications
* A conclusion section
* References
== [[Outer-approximation (OA)|Outer-approximation]] ==

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

== [[Unit commitment problem]] ==

* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example
# Fix typo “while minimize” to “while minimizing”.
* A section to discuss and/or illustrate the applications:

* A conclusion section
* References

== [[Frank-Wolfe]] ==

* Author list:
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

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

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

* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions
# Avoid pronouns such as “we” (all sections).
* At least one numerical example:

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

* A conclusion section
* References
== [[Piecewise linear approximation|Piecewise Linear Approximation]]==

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

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

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

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

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

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

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

# References not properly formatted

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

* Author list
* Sections
* An introduction of the topic

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

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

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

* Author list:
* An introduction of the topic
* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

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

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

* A section to discuss and/or illustrate the applications

* A conclusion section:

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

2021 Cornell Optimization Open Textbook Feedback

2021-12-19T01:45:21Z

Aw843cornell: /* Unit commitment problem */

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

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

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

* A conclusion section
* References

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

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section

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

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

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

* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section

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

* Author list

* An introduction of the topic

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

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

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

* Author list:
* An introduction of the topic

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

* A section to discuss and/or illustrate the applications

* A conclusion section

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

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

* Author list

* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section:

* References

== [[Adam]] ==

* Author list
* An introduction of the topic

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

* A section to discuss and/or illustrate the applications

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

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

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

* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

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

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

* Author list
* An introduction of the topic

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

* A section to discuss and/or illustrate the applications

* A conclusion section

* References
# Incorrect reference style.

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

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

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

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

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

* Author list

* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example
* A section to discuss and/or illustrate the applications
* A conclusion section
* References
== [[Outer-approximation (OA)|Outer-approximation]] ==

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

== [[Unit commitment problem]] ==

* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example
# Fix typo “while minimize” to “while minimizing”.
* A section to discuss and/or illustrate the applications:

* A conclusion section
* References

== [[Frank-Wolfe]] ==

* Author list:
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

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

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

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

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

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

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

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

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

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

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

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

# References not properly formatted

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

* Author list
* Sections
* An introduction of the topic

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

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

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

* Author list:
* An introduction of the topic
* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

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

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

* A section to discuss and/or illustrate the applications

* A conclusion section:

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

2021 Cornell Optimization Open Textbook Feedback

2021-12-19T01:26:29Z

Aw843cornell: /* Stochastic Dynamic programming */

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

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

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

* A conclusion section
* References

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

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section

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

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

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

* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section

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

* Author list

* An introduction of the topic

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

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

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

* Author list:
* An introduction of the topic

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

* A section to discuss and/or illustrate the applications

* A conclusion section

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

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

* Author list

* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section:

* References

== [[Adam]] ==

* Author list
* An introduction of the topic

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

* A section to discuss and/or illustrate the applications

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

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

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

* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

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

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

* Author list
* An introduction of the topic

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

* A section to discuss and/or illustrate the applications

* A conclusion section

* References
# Incorrect reference style.

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

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

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

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

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

* Author list

* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example
* A section to discuss and/or illustrate the applications
* A conclusion section
* References
== [[Outer-approximation (OA)|Outer-approximation]] ==

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

== [[Unit commitment problem]] ==

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

== [[Frank-Wolfe]] ==

* Author list:
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

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

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

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

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

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

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

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

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

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

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

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

# References not properly formatted

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

* Author list
* Sections
* An introduction of the topic

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

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

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

* Author list:
* An introduction of the topic
* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

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

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

* A section to discuss and/or illustrate the applications

* A conclusion section:

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

2021 Cornell Optimization Open Textbook Feedback

2021-12-17T23:51:50Z

Aw843cornell: /* Adam */

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

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

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section

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

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

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

* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section

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

* Author list

* An introduction of the topic

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

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

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

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

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

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

== [[Conjugate gradient methods]] ==

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

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

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

== [[Adam]] ==

* Author list
* An introduction of the topic

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

* A section to discuss and/or illustrate the applications

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

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

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

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

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

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

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

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

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

== [[Momentum]] ==

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

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

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

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

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

== [[Unit commitment problem]] ==

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

== [[Frank-Wolfe]] ==

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

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

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

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

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

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

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

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

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

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

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

== [[AdaGrad|Adagrad]] ==

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

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

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

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

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

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

2021 Cornell Optimization Open Textbook Feedback

2021-12-17T22:25:23Z

Aw843cornell: /* Portfolio Optimization */

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

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

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section

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

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

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

* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section

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

* Author list

* An introduction of the topic

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

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

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

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

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

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

== [[Conjugate gradient methods]] ==

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

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

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

== [[Adam]] ==

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

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

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

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

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

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

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

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

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

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

== [[Momentum]] ==

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

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

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

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

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

== [[Unit commitment problem]] ==

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

== [[Frank-Wolfe]] ==

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

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

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

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

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

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

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

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

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

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

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

== [[AdaGrad|Adagrad]] ==

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

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

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

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

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

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

2021 Cornell Optimization Open Textbook Feedback

2021-12-17T21:48:54Z

Aw843cornell: /* Disjunctive Inequalities */

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

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

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section

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

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

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

* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section

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

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

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

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

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

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

== [[Conjugate gradient methods]] ==

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

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

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

== [[Adam]] ==

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

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

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

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

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

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

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

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

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

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

== [[Momentum]] ==

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

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

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

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

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

== [[Unit commitment problem]] ==

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

== [[Frank-Wolfe]] ==

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

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

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

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

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

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

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

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

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

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

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

== [[AdaGrad|Adagrad]] ==

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

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

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

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

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

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

2021 Cornell Optimization Open Textbook Feedback

2021-12-17T21:37:03Z

Aw843cornell: /* Disjunctive Inequalities */

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

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

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

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

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

* Author list
* An introduction of the topic

* Theory, methodology, and/or algorithmic discussions

* At least one numerical example

* A section to discuss and/or illustrate the applications

* A conclusion section

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

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

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

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

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

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

== [[Conjugate gradient methods]] ==

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

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

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

== [[Adam]] ==

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

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

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

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

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

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

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

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

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

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

== [[Momentum]] ==

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

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

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

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

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

== [[Unit commitment problem]] ==

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

== [[Frank-Wolfe]] ==

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

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

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

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

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

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

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

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

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

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

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

== [[AdaGrad|Adagrad]] ==

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

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

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

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

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

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

2021 Cornell Optimization Open Textbook Feedback

2021-12-05T21:16:30Z

Aw843cornell: /* Wing shape Optimization */

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

== [[Conjugate gradient methods]] ==

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

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

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

== [[Adam]] ==

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

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

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

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

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

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

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

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

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

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

== [[Momentum]] ==

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

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

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

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

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

== [[Unit commitment problem]] ==

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

== [[Frank-Wolfe]] ==

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

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

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

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

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

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

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

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

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

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

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

== [[AdaGrad|Adagrad]] ==

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

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

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

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

2021 Cornell Optimization Open Textbook Feedback

2021-12-05T21:15:38Z

Aw843cornell: /* Wing shape Optimization */

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

== [[Conjugate gradient methods]] ==

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

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

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

== [[Adam]] ==

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

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

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

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

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

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

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

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

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

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

== [[Momentum]] ==

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

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

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

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

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

== [[Unit commitment problem]] ==

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

== [[Frank-Wolfe]] ==

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

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

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

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

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

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

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

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

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

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

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

== [[AdaGrad|Adagrad]] ==

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

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

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

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

2021 Cornell Optimization Open Textbook Feedback

2021-12-05T21:04:29Z

Aw843cornell: /* Disjunctive Inequalities */

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

== [[Conjugate gradient methods]] ==

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

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

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

== [[Adam]] ==

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

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

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

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

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

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

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

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

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

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

== [[Momentum]] ==

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

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

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

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

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

== [[Unit commitment problem]] ==

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

== [[Frank-Wolfe]] ==

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

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

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

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

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

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

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

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

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

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

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

== [[AdaGrad|Adagrad]] ==

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

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

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

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

2021 Cornell Optimization Open Textbook Feedback

2021-12-05T21:04:07Z

Aw843cornell: /* Disjunctive Inequalities */

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

== [[Conjugate gradient methods]] ==

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

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

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

== [[Adam]] ==

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

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

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

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

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

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

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

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

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

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

== [[Momentum]] ==

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

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

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

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

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

== [[Unit commitment problem]] ==

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

== [[Frank-Wolfe]] ==

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

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

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

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

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

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

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

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

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

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

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

== [[AdaGrad|Adagrad]] ==

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

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

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

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

2021 Cornell Optimization Open Textbook Feedback

2021-12-05T20:57:10Z

Aw843cornell: /* Unit commitment problem */

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

== [[Conjugate gradient methods]] ==

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

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

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

== [[Adam]] ==

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

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

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

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

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

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

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

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

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

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

== [[Momentum]] ==

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

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

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

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

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

== [[Unit commitment problem]] ==

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

== [[Frank-Wolfe]] ==

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

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

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

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

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

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

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

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

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

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

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

== [[AdaGrad|Adagrad]] ==

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

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

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

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

2021 Cornell Optimization Open Textbook Feedback

2021-12-05T20:53:17Z

Aw843cornell: /* Wing shape Optimization */

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

== [[Conjugate gradient methods]] ==

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

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

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

== [[Adam]] ==

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

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

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

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

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

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

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

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

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

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

== [[Momentum]] ==

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

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

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

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

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

== [[Unit commitment problem]] ==

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

== [[Frank-Wolfe]] ==

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

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

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

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

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

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

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

== [[Wing shape optimization|Wing shape Optimization]] ==

* Author list: Remove cornell ID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# The introduction is missing several references (e.g., “software packages like computational fluid dynamics..”, sentences containing things that aren’t common knowledge, performance claims, etc.)
# Avoid discussion involving finer details of subject methods in this section.
# In the titles, please change the font from bold to normal to have consistent formatting in the site. Same applies to box of content!
* Theory, methodology, and/or algorithmic discussions
# Properly cite the CFD package, don’t just include a link.
# Properly label the figure with a figure number.
# Consider removing white space between isolated sentences to improve readability.
* At least one numerical example
# If you’ve already defined an abbreviation (CFD), there is no need to define it again. Just use the abbreviation.
# Avoid pronouns such as “we” or “they”.
# Phrases like “under the following” need to be followed by a colon.
# Properly label the figure with a figure number and consider making them larger to improve visibility. Call the reader's attention to the figures in text by referencing the figure number.
# “As seen in the video below” is stated yet there are only images present and it may be initially unclear to the reader which figure is being referenced here.
# Avoid inserting inline citations like “[4] introduces an..” as it is a bit informal when you don’t explicitly name the subject.
# Don’t just cite the reference when discussing the problem formulation, explicitly write the model formulation and solution process using LaTex or equation visual editor.
# Your team should ideally create a numerical example independently. If you take a numerical example directly from a textbook, you will need to get explicit permission from the textbook author in writing and share that written permission with me.
# A numerical example is simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments). There is an Application section where you discuss the applications.
# The Numerical Example section needs a "step-by-step" calculation process and a clear presentation of each step's results. (again, similar to the way of solving an HW problem).
* A section to discuss and/or illustrate the applications
# Some characters are randomly capitalized in this section.
* A conclusion section
# These variables should be defined before the conclusion section, they are out of place here. Also, please use normal text when explaining variables except for the variable symbol.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Interior-point method for NLP|Interior point method for NLP]] ==

* An introduction of the topic:
* Theory, methodology, and/or algorithmic discussions
# Primal-Dual formulation and comparison to the Barrier Method is not discussed.
# Include brief discussion about big O convergence rates.
# Need discussion about the concept of “central path” and the notion of self concordance
# Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
# Graphs and images are incorrectly formatted to the page. Consider proper alignment with respect to the text body.
# Use explicitly typed Latex equations instead of images to represent math programs and equations.
# Fix typo “optimisation”.
# Use LaTex code or equation editor to display all equations and variables (e.g., “xi ”, “μ”, etc.).
* At least one numerical example:
# There are formatting issues with figures 2,3. Please make sure to embed them within their respective sections.
* A section to discuss and/or illustrate the applications
* A conclusion section
# Minor character code typos in the conclusion.
# Also, please add more discussion in this section. Future research directions is a good start.
# There is a box "􏰐"
* References

== [[AdaGrad|Adagrad]] ==

* An introduction of the topic:
* Theory, methodology, and/or algorithmic discussions
# Include discussion on its variants (most important is AdaDelta).
# Include disadvantages of Adagrad, since this provides motivation for the discussion on the variants and improvements of Adagrad
# Include comparisons to other popular optimizers (particularly important is comparisons to regular SGD and Adam)
# Different convergence rates are possible depending on the setting where Adagrad is used, but this is not mentioned on the page currently. As such the regret bound section should be more thoroughly explained.
* At least one numerical example
# In the first sentence, “..take the following numerical example” should be followed by a colon.
# Fix typo “trayectory”.
* A section to discuss and/or illustrate the applications
# This section is too short; include specific applications in which input features are sparse and Adagrad excels.
# Add reference to the claim “Mainly, it is a good choice for deep learning models with sparse input features”.
* A conclusion section
* References

# Too few references overall, you should aggregate information from multiple sources (even if the base algorithm itself comes from a singular paper)

== [[McCormick envelopes|McCormick Envelopes]] ==

* Author list: OK but I suggest removing NetID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# First sentence is hard to read. Please consider keeping sentences below 25-30 words.
# No references provided. Please cite all sources.
# Figure 1 is provided in the middle between two sections. Please include in the introduction section.
* Theory, methodology, and/or algorithmic discussions
# References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# When using mathematical expressions and symbols, please use the equation editor. (e.g., x*y, exy + y, sin (x+y) - x2)
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# For the sample GAMS code, please place it in a code box
* A section to discuss and/or illustrate the applications
# Having a list is not enough. Please explain at least three applications in a few sentences each.
# This section should be at least a paragraph to discuss relevant applications. Each application should be explicitly linked to the page topic. A few keywords do not meet the requirement at all.
* A conclusion section:
* References
# References are not expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please follow the standard reference style - the current format is incorrect.

2021 Cornell Optimization Open Textbook Feedback

2021-12-05T20:52:13Z

Aw843cornell: /* Wing shape Optimization */

== [[Lagrangean duality|Lagrangian duality]] ==
* Author list, sections and TOC
# Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.
# Remove cornell ID from Author list
* An introduction of the topic
# This section includes sentences on constructing the dual problem and is referred to as Lagrangian relaxation (LR). This is incorrect, please fix the definition of LR.
# Definitions of LR and its relation to duality should be double checked and re-written.
# Only one reference is present in this section. Please add more relevant references by expanding this section.
# Consider merging the “introduction” and “history” sections.
# In the titles, please change the font from bold to normal to have consistent formatting in the site.
* Theory, methodology, and/or algorithmic discussions
# The Lagrangian variables associated with equality constraints h(x) are unbounded but the Lagrangian dual problem states them as non-negative. Please fix the same.
# Also to construct a dual, we do not change minimization to maximization directly. We observed such things in the examples in lecture notes due to simplification. The lagrangian dual problem would be minimize (,).
# Adding to the previous point, the Lagrangian is a lower bound on the original objective; the solution to the primal and dual or only equivalent if the duality gap is 0. You reference this in one section, but this is after your statement “Hence, solving the dual problem, which is a function of the Lagrangian multipliers (𝜆*) yields the same solution as the primal problem, which is a function of the original variables (x*). “. Please clarify the specific conditions that must hold for the solution of the dual to be equal to the primal’s.
# You refer to the “Complementary Slackness Theorem”, but don’t actually write the mathematical representation of complementary slackness. Please fix this. Also consider including the derivation of the complementary slackness condition, as it is both easy and short. Boyd is a good reference for this.
# Last step of the “process” subsection also needs updating according to the previous comments.
# The inline notations should also be typed using LaTex.
# Please use the LaTex code or equation editor for min, s.t., etc.
* At least one numerical example
# Only one dual variable is associated with each constraint. The numerical example uses two for the first and second constraint which is unnecessary. Please update it accordingly for both constraints. This particular example will only have two dual variables instead of the five dual variables used currently.
# All consecutive steps need to be updated since the dual variables would be updated.
# After substitution the nonlinear function should be further simplified. The current expression reads like a highly nonlinear function but can be easily simplified.
# Similar to the comments in the methodology section, inverting minimize to maximize is incorrect. Please update the dual objective function and domain of dual variables accordingly.
# Please use the LaTex code or equation editor for min, s.t., etc.
* A section to discuss and/or illustrate the applications
# Bullet points could be used to state the last four real-world examples that explain the physical meaning of the primal and dual problems.
# Add references for the last set of applications.
* A conclusion section
# This section contains a few typos. Please fix the same.
* References
# Some citations' hyperlinks are displaying.

== [[Disjunctive inequalities|Disjunctive Inequalities]] ==

* Author list
# Missing course section and semester
# Remove cornell ID
* An introduction of the topic
# No citations are present in this section.
# “mixed-integer programming (MIP)” should be used instead of “multiple integer programming (MIP)”. Please fix this error.
* Theory, methodology, and/or algorithmic discussions
# The abbreviation MILP is not previously defined. Please fix this issue.
# You consistently use the negative sign instead of the NOT operator for y (-y instead of ¬y).
# Some inconsistencies with the spacing of variables, constraints, etc., under the “General” section that need to be fixed.
# Typo in “This is shown below by M1, M2, y1, and y1:” where y1 needs to be changed to y2. Why use two different Big-M variables here? Elsewhere in the Wiki you only use one so this could lead to confusion with a general audience. Also if this was taken from the lecture notes then it needs to be cited.
* At least one numerical example
# Please reformulate and solve a complete numerical example rather than just reformulating a general example. Demonstrate the use of Big-M and Convex Hull formulation in an optimization problem that provides details such as individual steps in the problem solving process and final results.
# Add space between vee (V) operator and brackets in first line of Latex
# Please format variables correctly, for example, use <math>x_1</math> instead of x1.
* A section to discuss and/or illustrate the applications
# Please format the equations appropriately either by using latex code or the visual editor. These images are NOT acceptable!
* A conclusion section
# There is no conclusion presented in this section at all.
* References
# The included references have NOT been used anywhere in the Wiki. Add references for sentences that are not common knowledge and please link them appropriately with the text in Wiki. If the figures used here were not original works, you must also cite them.
# There are many papers on this topic. A simple Google (Scholar) search could provide you with sufficient references to cite.
# Many important references of this topic are missing.
# Please consider linking the references as demonstrated in the Wiki tutorial on Canvas and in this template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

==[[Stochastic programming|Stochastic Programming]] ==

* Author list: Remove cornell IDs
* An introduction of the topic
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
# This section only includes two sentences on Stochastic programming (SP), while the rest gives examples of uncertainty. Please discuss the need for SP in the presence of uncertainty. Also, discussion on robust optimization and its limitations should be removed since it is out of place.
* Theory, methodology, and/or algorithmic discussions
# Please avoid direct inline linkbacks to Wikipedia.
# The symbol “xi” in the methodology subsection should be explained.
* At least one numerical example
# Copying a numerical example "entirely" from a textbook is inappropriate. Your team should come up with a "numerical" case.
# No specific application context is needed for a numerical example.
# The inline notations (`x1`, `s1`) should also be typed using LaTex.
# Label all tables with a table number for better readability.
# Properly format the solution table with the label attached rather than the following sentence. The solution table looks different from the others, please fix this for consistency.
* A section to discuss and/or illustrate the applications;
# I suggest eliminating citing the last name of the first author (i.e. Zhou et al.)
* A conclusion section
* References
# URLs of some citations are not properly formatted (not showing the hyperlinks).

== [[Exponential transformation|Exponential Transformation]] ==

* Author list
# Missing course section
# Remove cornell ID
* An introduction of the topic
# Please expand the introduction.
# Please aim for a maximum average sentence length of ~25 words. Last sentence with 51 words is hard to read.
# Second Sentence: please change the word “they” as it could make the meaning ambiguous
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
# If you use abbreviations, please introduce them (e.g. NLP,MINLP)
* Theory, methodology, and/or algorithmic discussions
# Please explain the transformation in words along with equations
# Terms like posynomial should be described in detail.
# Please move the numerical example to the section below
# The “(eq 1)” is not needed here.
# Please expand this section.
* At least one numerical example
# In the third equation of the numerical example, it is confusing to have coefficients after numbers. Some readers may read it as an exponent.
# Last equation in this section after “further linearization” is incorrect. This equation cannot be further linearized, please fix this.
# Please explain the steps in the numerical examples in detail. The step-by-step solution should be provided.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# Missing part of text: “Proof of convexity of with positive definite test of Hessian…”
# Applications are not numerical examples. Please refer to this link for example of applications: [[Duality|https://optimization.cbe.cornell.edu/index.php?title=Duality]]
# Citation 7 is missing in current applications
# The section current applications is redundant
# Please use the LaTex code or equation editor for min, s.t., etc.
# Under current applications, do not just use a hyperlink to describe an application. Actually describe it. And properly inline citation style should be used instead of the hyperlink.
# The convexification application of MINLP can be further simplified for binary variables. Please refer to the lecture slides for more information.
* A conclusion section
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
* References
# Please consider linking the references by using this as Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Citation 7 is missing in current applications

== [[Sparse Reconstruction with Compressed Sensing|Sparse reconstruction with Compressed Sensing]] ==
This Wiki needs a significant rewrite. Please go through the comments for details.

* An introduction of the topic
# The introduction section should include information about the problem and its implications presented briefly. Please use full sentences to write this Wiki. You may use tools like Grammarly to check sentence formation and grammar.
# This section includes several typos like “sub modual”. Please fix them throughout the wiki and delete them if not required.
# Many abbreviations are used before previously defining them. Please define these abbreviations before using them in the text.
# This section is incomprehensible in its current form. Please rewrite with proper comprehension.
# Equations and math symbols need proper reformatting. The current version reads like text (along with equations) copy-pasted from a specific source. All mathematical symbols and equations should be formatted via LaTex - this is a learning objective of the Wiki assignment. You can find some useful links on converting your equations/symbols into LaTex code here: (https://optimization.cbe.cornell.edu/index.php?title=Help:Contents).
# Try to place the figure at the top of the Wiki between the main text.
# Avoid pronouns such as “we”.
# I suggest the use of more formal abstract illustrations.
* Theory, methodology, and/or algorithmic discussions
# Equations and symbols need proper reformatting.
# Lemmas and theorems are not expected for this Wiki. Sparse reconstruction is a straightforward concept but is unnecessarily complicated here. Please refer to other Wiki examples to get an idea of what the Wiki should convey.
# All equations need to be better formatted.

* At least one numerical example
# Numerical example is missing.
# Every iteration should be clearly presented, and solved "step-by-step".
* A section to discuss and/or illustrate the applications
# Having a list is not enough. Please explain at least three applications in a few sentences each.
* A conclusion section
# Conclusion section is missing.
* References
# The current reference list is not correctly formatted. References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Portfolio optimization|Portfolio Optimization]] ==

* Author list
# Remove cornell id
* An introduction of the topic
# The introductory sentence should be rephrased. The action of minimizing the risks does not inherently maximize the gains, rather PO aims to maximize gains whilst minimizing risks.
# Amount of whitespace can be reduced by changing the orientation of Figure 1 and the sentences in this section.
# Define terms such as risk, return, portfolio, etc., when you introduce them. Assume that the reader may not know much about finance. This goes for all other sections as well.
* Theory, methodology, and/or algorithmic discussions
# A brief mention of modern portfolio theory (i.e.. Markowitz) would be appropriate in this section.
# Several grammatical errors here involving sentence structure and clarity. Some questionable semantics (e.g., “The portfolio optimization mainly assumes two directions.”) and syntax (phrases such as “.. is as follows” should be followed by a colon). Misuse of commas and missing commas in this section. Two sentences introducing E(rp) and w should be combined into one.
# Use LaTex to distinguish variables written within a sentence, such as m and n.
# Rephrase “Cut the relevant information and conditions in the portfolio optimization, as well as the final requirements into the relevant variables, constraints and linear functions of the linear programming problem.”
# An explanation of a few common constraints would be helpful, rather than just including a table.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Solving the numerical example by GAMS is inappropriate. Please provide detailed step-by-step calculation results.
# All tables need to be labeled.
# Include figure number in label for consistency.
# Fix misspelling “dolling decision variables”.
# Use LaTex for all variables, equations, and constraints here.
# Example 2 table is hard to read, so making it bigger would help.
# Remove the “Using excel as the solver” part from the sentence before the solution discussion.
# Some grammatical errors here (phrases such as “.. is as follows” should be followed by a colon).
* A section to discuss and/or illustrate the applications
# Rephrase “Portfolio optimization can be used to screen investment projects that meet investors, rationally allocate investment amounts, etc.”
# Not sure “relevant” is the correct word choice here.
# You need more specific examples with the utility of portfolio optimization, this section is quite general as is. Some more detail and focus on real-world applications in the financial industry that relate to retirement planning, financial security, economic stability, etc., would be helpful.
* A conclusion section
# Need some commas here.
# The sentence “Linear programming has been around since the 1940’s and has such a wide base of applications” is not necessary.
* References
# Please consider linking the references as demonstrated in the Wiki tutorial on Canvas and in this template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove white space between end of sentences and reference numbers.

== [[Chance-constraint method|Chance constraint method]] ==

* Author list:
* An introduction of the topic
# Please consider correcting a few grammatical errors: “pre-planned for”, “god”, “certain levels of feasibility is guaranteed in what are”, and “Performance of a system”
# In “Chance-constraint”, it is capitalized randomly throughout the introduction. Please correct.
# Please use technical language to briefly introduce chance-constrained programming. Words like “acts of god”, “cost of doing business” are not appropriate for a technical Wiki.
* Theory, methodology, and/or algorithmic discussions
# Please add a citation to the first sentence.
# Xi is an uncertainty/randomness variable. It is better to use clear language.
# Please use the mathematical editor for adding explanations in the text. Using “ x is a decision variable” is hard to read. Same for f(x) and others.
# Theory is insufficient. Please expand and explain different approaches.
# Please add pros and cons explicitly as a list.
# Explain the physical meaning for examples of chance constraints along with all the notations used.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please remove this example as it is directly from this book. The example should be purely numerical without any background.
# Please use the equation editor for min, st., etc.
# Please use the mathematical editor for adding explanations in the text. Using “ x is a decision variable” is hard to read. Same for f(x) and others.
# Please change the table format so as not to confuse the reader.
# Multiple instances of [Chart to be added] are missing.
# Example is incomplete.
# Avoid pronouns such as “we”.
* A section to discuss and/or illustrate the applications
# Please connect several grammatical and spelling errors: “real life application”, Energy creation, particularly in renewable sources, have high variabilities”, and others
# “Zhao, Xue, Cao, and Zhang”. No need to list all authors within the article. Provide a reference is sufficient. If authors must be mentioned, (Zhao et al.) should be ok.
* A conclusion section
# Uniqueness and universality earlier are not clear to me. If they are not discussed earlier in the application, it would be better not to introduce new discussions in the conclusion.
# If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
* References
# References seem to vary in format. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Bayesian Optimization]] ==
* Section titles should not be "bold". Please double check using source editor on the section titles.
* Contents: Subheadings for EI and the algorithm should not be bolded, Random words should not be capitalized.
* Author list: Remove cornell ID, Please check names
* Introduction
# The introduction is too general and not substantial enough. For example, simply saying BayesOpt is useful when the objective function is unknown obscures exactly HOW it is useful (namely, computational efficiency in applications where ground truth sampling is expensive). Discussion on applications should be moved to a separate section.
# Machine learning rarely includes black-box functions to be optimized. Bayesian optimization is almost never used for optimizing ML loss functions but can instead be used for hyperparameter optimization. Please update such claims in this section.
* Theory, methodology, and/or algorithmic discussions
# Captions need reformatting.
# Consider italicizing keywords rather than bolding.
# Please add a citation to the first sentence.
# Discussion on acquisition functions should include comparisons, tradeoffs, and reasons to use one over the other. Should also note that expected improvement is the most widely used in practice, and explain.
# Avoid pronouns such as “we”.
# Please write equations in the Wiki instead of attaching images for equations.
# Acquisition function figure could be made larger and clearer to improve readability.
* At least one numerical example
# Any references to functions or methods in code ‘e.g. fmin’ should be properly formatted as code-stylized text.
# Please use the equation editor for min, st., etc.
# Avoid including a figure of the code for this example and explicitly describe the steps to the modeling and solution process instead.
# Avoid pronouns such as “our” and “we”.
* A section to discuss and/or illustrate the applications
* A conclusion section
# Please do not use brackets to enclose lists.
# Some claims here should be supported by references. Please cite each source after its sentence.
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Try to avoid references to “pop” machine learning blogs where anyone can be an author. (e.g. towardsdatascience)
# All references are URLs. Please cite publications and literature.
# A simple Google Scholar search would give you many references.

Notes on grammar: Needs some work. Several instances where colons are inappropriately inserted mid sentence or in subheadings. Explanations are not terse. Several instances of switching between personal and impersonal style of writing, which is distracting.

== [[Conjugate gradient methods]] ==

* Author list: Remove cornell ID
* Introduction
# All inline notations (e.g., `x`, `A`) should be typed using LaTex.
* Theory, methodology, and/or algorithmic discussions
# All equations need to be better formatted.
# Is Gauss-Newton no longer referenced?
# Theorems listed in the first section should be accompanied with high level explanation, not just a list of the theorems themselves. The page should read like an article, with proper flow.
# Please indent equation blocks.
# Please properly format pseudocode.
* At least one numerical example
# Steps should be accompanied with explanation, or reference to the corresponding step in the pseudocode.
# Please properly format in a more organized manner, aligning equations appropriately and demarcating steps appropriately.
* A section to discuss and/or illustrate the applications
# Consider including 2 additional examples of applications
* A conclusion section
# Consider adding future research directions
* References
# Reference primary sources rather than Wikipedia
# Too few references.
# More references should be added. A simple Google Scholar search would give you many references.

== [[Geometric programming|Geometric Programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Examples of applications in this section use the same reference. Please cite their individual sources.
* Theory, methodology, and/or algorithmic discussions
# The symbol denoting the domain in the definition of a monomial is unclear. Please clarify it or fix this if it is incorrect.
# Definition of posynomial refers to section 2.1 which is missing from the Wiki (sections are not numbered in the main text).
# In the generalized posynomial subsection, bullet points do not tell us why h(x) is posynomial. Either provide reasons or simply state that h(x) is posynomial. Also explain why h3 is a generalized posynomial.
# Additional theory on the feasibility analysis could be provided in this section.
* At least one numerical example
# In the transformation example, the last two constraints could also be simplified by applying a natural logarithm on both sides. Please update them as well.
* A section to discuss and/or illustrate the applications
# The figure in this section needs to be labeled.
# The figure needs to be resized and perhaps aligned to the center.
* A conclusion section:
# Please avoid vague language such as: “This makes”.
# Please avoid opinionated statements: “one of the best ways”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# This Wiki has very few references. A quick Google Scholar search may provide relevant references.

== [[Adam]] ==

* Author list
* An introduction of the topic
# Some grammatical errors here, mostly related to the need for commas in certain places (e.g., “Before Adam..”).
# Some minor errors with parts of speech throughout the section, need to revisit phrases such as “which has broader scope in future for”, etc.
# Try splitting up some of the longer sentences in this section, a couple are hard to read.
# Avoid definitive statements about Adam being the best or always better solver, as this is simply not true (the choice of the “best” optimizer is setting-dependent). Use language such as “Research has shown that Adam has demonstrated superior experimental performance over..” and then cite academic references to back this claim.
# What does adam stand for? Introduction is insufficient. Please expand.
* Theory, methodology, and/or algorithmic discussions
# Revise grammar here, noticing some missing commas and uncapitalized word after period.
# Rephrase “second one is to update the old position with the updated position”.
# Use LaTex code or equation editor to display all equations and variables in this section, and actual subscripts instead of “m_t”, etc.
# Avoid inserting inline citations after words like “According to..” or “This article..” as it is a bit informal. This could be rephrased or changed to something like “According to author,^[2] …” with author name inserted.
# Remove white space before the period in RMSP discussion.
# Please provide a pseudocode.
# Please use list the two methods here “Adam is a combination of two gradient descent methods which are explained below”
# Please expand the theory section significantly. Theoretical convergence properties should be discussed, even if briefly.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
* A section to discuss and/or illustrate the applications
# Same comment as before, consider replacing inline citations after words like “According to..”.
* A conclusion section
* References
# References should be properly formatted, not just hyperlinks. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Try to avoid references to blogs and use peer-reviewed academic references instead.
# Too few references.
# More references should be added. A simple Google Scholar search would give you many references.

== [[A-star algorithm|a* algorithm]] ==

* Author list: Remove cornell ID
* Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.
* An introduction of the topic:
# Weird spacing between paragraphs. Please fix this issue.
# In the titles, please change the font from bold to normal to have consistent formatting in the site.
# Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.
# There are no citations in the introduction. Please cite every source.
* Theory, methodology, and/or algorithmic discussions
# Please add the mathematical description of the algorithm.
# Reference style varies in sentences. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please fix grammatical and spelling errors as (“from current position to the goal”, “There are a lot of discussions”, etc). Also, many hyphens are missing as “non playable”.
# In algorithms, it is a standard to add high-level description (i.e. pseudocode or flowchart). Please incorporate it.
# Use LaTex code or equation editor to display all equations and variables in this section (e.g., “f(n)...”, “h(n)..”, etc.). This goes for other sections as well.
* At least one numerical example
# The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.
# Instead of writing things like “The above image..”, label each figure and use the figure number to refer to it in text.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# No references in the applications. Please cite every source
# Preferably, add at least an additional application.
* A conclusion section
# Conclusion should summarize descriptions. Please modify it to provide a summary.
# Please pay attention to the length and structure of sentences here and in the full page. First sentence is hard to read.
* References
# References seem to vary in format and are not linked correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Incorrect reference style. Please follow the example and use the template.

== [[Job shop scheduling|Job-Shop Scheduling Problem]] ==

* An introduction of the topic
# The current introduction to the jobshop scheduling problem has only two sentences in addition to the parameter description. Introduction typically contains information about the problem, its importance in the real-world, and some information about the solution techniques and their types to solve the problem. Please add some information that covers the above.
* Theory, methodology, and/or algorithmic discussions
# It is unclear whether the assumptions stated in this section are required to apply the following solution techniques. Please clarify the same. Also use complete sentences to state them.
# The branch and bounds method described in this section only discusses the solution technique for problems with one machines. However, branch and bound is a general technique that can be applied to any MILP problems with varying scales. Please update the “methods” section to be as general as possible.
# Since this Wiki focuses on jobshop scheduling, at least two methods are expected. Branch and bound is a general MILP technique, so, it is recommended to add a tailored technique that can only solve specific jobshop scheduling problems. Solving the numerical example with this technique is not necessary.
# Reference to the branch and bound technique described in this section is a “youtube” video. Please add references in literature that describe this method in detail. The method used in this video is highly tailored for a single machine application. This is also an incorrect way to cite a reference. Please keep this section as general as possible.
# Use LaTex code or equation editor to display all equations and variables in this section and all other sections as well.
# Check grammar in this section. For example, phrases like “are as follows” need to be followed by a colon and not a period.
# Consider rewriting the assumptions as a list in this section.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# The example used in this section is exactly the same as the one in the youtube video. Please use a modification of this example or choose another example/method to demonstrate the solution technique. Your team should ideally create a numerical example independently. If you take a numerical example directly from a particular source, you will need to get explicit permission from the textbook author in writing and share that written permission with the instructors.
# The figure in this section is not numbered when all others are. Relabel this figure for consistency and its number to refer to it in-text.
# A numerical example should be simply "numerical" and does not need any application context (similar to those numerical problems in HW assignments).
* A section to discuss and/or illustrate the applications
# This section should only focus on real-world applications of the jobshop scheduling problem. But currently, this section includes additional information on solution techniques/complexity that is appropriate for the Introduction section. Please discuss the applications of the problem in this section.
* A conclusion section
# The meaning of “Operations applications” is unclear. Please explain or update if necessary.
# The current conclusion section does not properly summarize the problem. Please refer to other Wiki examples for an idea to update the section accordingly.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please reference media sources like reference 5 appropriately.
# A simple Google Scholar search would give you many "formal" references.

== [[Optimization in game theory]] ==

* Author list: remove cornell IDs.
* An introduction of the topic
# References are not linked. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
* Theory, methodology, and/or algorithmic discussions
# Why only a subsection on "Nash Equilibrium" is included in "Theory" section? Please re-format.
# Please edit references.
# Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm.
# Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.
* At least one numerical example
# Please organize the last part in a more readable format. Questions may be in bold and numbered, answers are more direct, etc.
# Remember to cite all images and tables.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps.
* A section to discuss and/or illustrate the applications
# Very good, link the reference and cite all sources.
* A conclusion section
# Please add more summarizing especially from theory sentences and avoid long sentences.
* References
# Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Reference primary sources rather than Wikipedia
# Incorrect reference style. Please correct.

== [[Trust-region methods]] ==

* Author list:
# Remove cornell IDs. Author is also spelled incorrectly.
# Add the course section.
* An introduction of the topic
# References are not linked. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Use LaTex code or equation editor to display all equations and variables (e.g., “xk”, “f`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “we”. This goes for all other sections as well.
* Theory, methodology, and/or algorithmic discussions
# Organization of ideas in this section needs work.
# You have not defined explicitly why the Cauchy point is important to compute beyond a vague allusion to performance improvements, which is also wrong (it is useful because of its guarantees for convergence, not performance) It is also misspelled.
# Each approach should have accompanying explanation and motivation for why it is being discussed. It is not enough to outline the algorithm.
# Please make sure symbols are properly subscripted and superscripted (e.g. “pk” should be “p_k”
# Please format the algorithm in proper algorithmic pseudocode format.
# Little to no discussion on global convergence guarantees
# Please include discussion about the advantages and disadvantages of the algorithm
# Fix typo “couchy point”.
* At least one numerical example
# Any code functions (uminfunc) should have proper text formatting.
# The graph needs a better caption explaining how the axes are labeled and what data points are being shown.
# Please increase the quality of the figure. It is hard to see the red line.
# Add citation to “The Rosenbrock function is a non-convex function, introduced by Howard H. Rosenbrock in 1960, which is often used as a performance test problem for optimization algorithms.”
* A section to discuss and/or illustrate the applications
# The content in this section as it is currently does NOT describe applications, but rather different approaches within the trust region methodology. Please provide specific applications (e.g. TRPO in reinforcement learning).
* A conclusion section
# Please add more summary, future research directions for example is a good start.
* References
# Incorrect reference style.
# Please consider having the references as this Wiki template, <nowiki>https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization</nowiki>
# More references should be added. A simple Google Scholar search would give you many references.

*There are numerous misspellings, grammatical errors, and incorrect claims. Please fix these.

== [[Momentum]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Apart from an explanation on momentum, it is necessary to briefly point out the limitations of SGD and why momentum could help with these limitations. Please update it accordingly.
# Remove bold on “Momentum”.
# Place references after the period at the end of each sentence. This goes for all the sections in the wiki.
* Theory, methodology, and/or algorithmic discussions
# Equation formatting is very poor and should be formalized.
# It is important to use technical language for this Wiki. Although a layman’s explanation is appreciated, it would be better to skip using words like “zig zagging”. Try to explain all concepts in a technical language with few simplifications but NOT vice versa.
# The definition of the update rule for SGD with momentum looks incorrect, specifically the first expression. Please fix it and also explain all the parameters used.
# Use LaTex code or equation editor to display all equations and variables (e.g., “W”, “V`”, etc.) in this section and all other sections as well.
# Avoid pronouns such as “you”.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step". Since writing all iterations is not feasible, at least present a few iterations for both cases.
# Please try to label the plots that explains what each line color means.
# Starting point for SGD with momentum is different in explanation and the table. Please fix the same.
* A section to discuss and/or illustrate the applications
# Please use correct terminology like “optimizing non-convex functions” and not “training non-convex models”.
# Adam, Adadelta, and RMSprop are variants of SGD that already use momentum. Please double check the writing and update if necessary.
* A conclusion section
# Please refrain from using words like “zig zag” effects.
* References
# Almost all references used are URLs. Please try to add journal/conference articles or books for references, instead of directly citing the URLs. Please check the list below and run a quick Google (Scholar) search to identify relevant literature.

== [[Stochastic dynamic programming|Stochastic Dynamic programming]] ==

* Author list
# Remove cornell ID
* An introduction of the topic
# Discussion on applications should be moved to a separate section.
* Theory, methodology, and/or algorithmic discussions
# Remove the grey box background of equations.
* At least one numerical example
* A section to discuss and/or illustrate the applications
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Outer-approximation (OA)|Outer-approximation]] ==

* An introduction of the topic
# See formatting guideline below
# Avoid opinionated statements such as “MINLP problems are usually the hardest to solve”.
# Rearrange the text such that the MINLP formulation is in the theory section and keep the introduction in words only.
* Theory, methodology, and/or algorithmic discussions
# Consider left aligning equations and optimization problem formulations by the “=”. See [[Stochastic programming|https://optimization.cbe.cornell.edu/index.php?title=Stochastic_programming]] for an example
# The sentence “The Outer-Approximation (OA) algorithm was first proposed by Duran and and Grossmann in 1986 to solve MINLP problems.” needs a reference.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# “Minimize” and “subject to” should be “min” and “s.t.” in MathType
* A section to discuss and/or illustrate the applications
# Does not explicitly point out why OA is applicable (and/or preferred) in these applications, rather than other MINLP approaches (show that the problem formulations are amenable to a solution approach through OA)
# The sentence “... an active research area and there exists a vast number of applications in fields such as engineering, computational chemistry, and finance.” needs references.
# Place GAMS code in a single code box or remove it.
# Consider reformatting to make steps more readable. Inserting spaces and breaking down steps would help.
* A conclusion section
# Too short. Consider discussion on future research direction and discussion on uncertainty
# Please review abbreviations throughout the page. Why is MINLP redefined here? “Outer-Approximation is a well known efficient approach for solving convex mixed-integer nonlinear programs (MINLP)”.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Remove "Template:Reflist"

== [[Unit commitment problem]] ==

* Author list
* An introduction of the topic
# Please expand the introduction and avoid discussions of examples or specific applications in this section.
# The sentence “Nonlinear, Non-convex programming optimization problem.” doesn’t make sense by itself and Non-convex shouldn’t be capitalized.
* Theory, methodology, and/or algorithmic discussions
# Figure/image format should be revised to better display the content.
# Uppercase characters are used randomly (e.g., “non-convex transmission Constraints”) . Please follow correct language conventions for sentence structure.
# Avoid inserting inline citations after words like “written in matrix form as equation [3]..” or “presented in [3]...” as it is a bit informal when you don’t explicitly name the subject. Also these two sentences are grammatically incorrect and appear to be missing an ending period and comma, respectively.
# Don’t say “written in matrix form as equation..” and just cite the reference, actually write out the equation.
# Properly label the figure in this section with a figure number and improve visibility by making it larger.
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Label the figures in this section properly with figure numbers.
# Fix typo “while minimize” to “while minimizing”.
# Avoid pronouns such as “we”.
# Use the equation editor when typing equations.
* A section to discuss and/or illustrate the applications:
# I suggest changing the order of the subtitles here. For example, Single-Period Unit Commitment.
* A conclusion section
* References

== [[Frank-Wolfe]] ==

* Author list:
* An introduction of the topic
# I suggest highlighting disadvantages along with advantages.
* Theory, methodology, and/or algorithmic discussions
# “[n x 1] matrix” please use the equation editor to express mathematical descriptions and symbols (p,b, etc)
* At least one numerical example
# Every iteration should be clearly presented, and solved "step-by-step".
# Please show at least a few iterations. Even for smaller examples if needed. Report the final solution.
# Please use the LaTex code or equation editor for min and include s.t., etc.
# Please ensure that the example : (1) is NOT directly taken from a book, and (2) a step-by-step solution should be provided, showing every intermediate steps. For your example, please explicitly state that the derivative is taken etc.
* A section to discuss and/or illustrate the applications:
* A conclusion section
# Same as the introduction. Pros and cons should be evaluated together!
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Line search methods|Line Search Method]] ==

* Author list
* An introduction of the topic
# Expand the introduction and avoid discussion on some of the specific steps in the solution process.
# Provide references here.
* Theory, methodology, and/or algorithmic discussions
# The phrase “are as follows” in the steepest descent method discussion needs to be followed by a colon.
# Rephrase “has a nice convergence theory” and cite a reference for this claim.
# Avoid pronouns such as “we”.
# Add citation after “.. proposed by Phillip Wolfe in 1969.”
# Figure 1 is between two sections. Please fix this issue.
* At least one numerical example:
# Add some space between iterations or subsection break
* A section to discuss and/or illustrate the applications:
# Too few references in this section.
# Last paragraph makes some claims without references.
* A conclusion section
* References
# References should be properly formatted. Refer to the link below for an example: [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# More references should be added. A simple Google Scholar search would give you many references.

== [[Piecewise linear approximation|Piecewise Linear Approximation]]==

* Author list
* An introduction of the topic
# The content of this section is good, but there are some issues with sentence clarity and some other grammatical errors. Please revisit this section and make changes accordingly.
* Theory, methodology, and/or algorithmic discussions
# Fix typo “to force the x’ values become associated with”.
* At least one numerical example
* A section to discuss and/or illustrate the applications
# Please aim for a maximum average sentence length of ~25 words. Some of these longer sentences are hard to read.
* A conclusion section
# Expand the conclusion section to be longer than one sentence. The conclusion section to include a brief summary of what was discussed above, an emphasis on it’s significance, and a brief discussion of future extensions and research direction if applicable.
* References
# Include hyperlinks to sources when possible.

== [[Mathematical programming with equilibrium constraints|Mathematical Programming with Equilibrium constraints]] ==

* An introduction of the topic
# This section includes several terms like variational inequalities, constraint qualifications that were not discussed in the class. Please add a sentence to explain them before using them.
* Theory, methodology, and/or algorithmic discussions
# The meaning of parameter vector x is unclear. Please add more information or update if necessary.
# Equations and symbols in the PIPA subsection are not formatted correctly. Please use the same formatting for all equations, so they read as mathematical equations and not text. This goes for all other sections as well.
# Use equations instead of images to represent math programs and equations in the Implicit Descent and SQP subsection.
# Apart from the steps for each solution technique, please also add a few sentences that describe each method.
* At least one numerical example
# Please define the terms like NCP, MP before abbreviating them. Also try not to unnecessarily abbreviate simple terms.
# Equations should be typed by LaTex. Images for equations are unacceptable.
# GAMS code is strongly discouraged. Please solve the problem "step-by-step".
# The selected numerical example is fine but is directly solved with the MPEC solver in GAMS. Try to solve it manually like the homework/in-class problems step by step using the steps described in the previous section by choosing any of the methods.
# Avoid using figures in the equations (subject to etc)
* A section to discuss and/or illustrate the applications
# Add references to “power management, highway pricing, chemical process engineering, and traffic planning.”
* A conclusion section
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# This Wiki contains very few references. Please check the list below and run a quick Google (Scholar) search to identify relevant literature.

== [[Wing shape optimization|Wing shape Optimization]] ==

* Author list: Remove cornell ID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# The introduction is missing several references (e.g., “software packages like computational fluid dynamics..”, sentences containing things that aren’t common knowledge, performance claims, etc.)
# Avoid discussion involving finer details of subject methods in this section.
# In the titles, please change the font from bold to normal to have consistent formatting in the site. Same applies to box of content!
* Theory, methodology, and/or algorithmic discussions
# Properly cite the CFD package, don’t just include a link.
# Properly label the figure with a figure number.
# Consider removing white space between isolated sentences to improve readability.
* At least one numerical example
# If you’ve already defined an abbreviation (CFD), there is no need to define it again. Just use the abbreviation.
# Avoid pronouns such as “we” or “they”.
# Phrases like “under the following” need to be followed by a colon.
# Properly label the figure with a figure number and consider making them larger to improve visibility. Call the reader's attention to the figures in text by referencing the figure number.
# “As seen in the video below” is stated yet there are only images present and it may be initially unclear to the reader which figure is being referenced here.
# Avoid inserting inline citations like “[4] introduces an..” as it is a bit informal when you don’t explicitly name the subject.
# Don’t just cite the reference when discussing the problem formulation, explicitly write the model formulation and solution process using LaTex or equation visual editor.
# Your team should ideally create a numerical example independently. If
you take a numerical example directly from a textbook, you will need to
get explicit permission from the textbook author in writing and share
that written permission with me.
# A numerical example is simply "numerical" and does not need any
application context (similar to those numerical problems in HW
assignments). There is an Application section where you discuss the
applications.
# The Numerical Example section needs a "step-by-step" calculation
process and a clear presentation of each step's results. (again, similar
to the way of solving an HW problem).
* A section to discuss and/or illustrate the applications
# Some characters are randomly capitalized in this section.
* A conclusion section
# These variables should be defined before the conclusion section, they are out of place here. Also, please use normal text when explaining variables except for the variable symbol.
* References
# Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]

== [[Interior-point method for NLP|Interior point method for NLP]] ==

* An introduction of the topic:
* Theory, methodology, and/or algorithmic discussions
# Primal-Dual formulation and comparison to the Barrier Method is not discussed.
# Include brief discussion about big O convergence rates.
# Need discussion about the concept of “central path” and the notion of self concordance
# Please consider proper formatting of the algorithm as pseudocode. Algorithms also must be accompanied with high level summary and discussion on its most important high level ideas.
# Graphs and images are incorrectly formatted to the page. Consider proper alignment with respect to the text body.
# Use explicitly typed Latex equations instead of images to represent math programs and equations.
# Fix typo “optimisation”.
# Use LaTex code or equation editor to display all equations and variables (e.g., “xi ”, “μ”, etc.).
* At least one numerical example:
# There are formatting issues with figures 2,3. Please make sure to embed them within their respective sections.
* A section to discuss and/or illustrate the applications
* A conclusion section
# Minor character code typos in the conclusion.
# Also, please add more discussion in this section. Future research directions is a good start.
# There is a box "􏰐"
* References

== [[AdaGrad|Adagrad]] ==

* An introduction of the topic:
* Theory, methodology, and/or algorithmic discussions
# Include discussion on its variants (most important is AdaDelta).
# Include disadvantages of Adagrad, since this provides motivation for the discussion on the variants and improvements of Adagrad
# Include comparisons to other popular optimizers (particularly important is comparisons to regular SGD and Adam)
# Different convergence rates are possible depending on the setting where Adagrad is used, but this is not mentioned on the page currently. As such the regret bound section should be more thoroughly explained.
* At least one numerical example
# In the first sentence, “..take the following numerical example” should be followed by a colon.
# Fix typo “trayectory”.
* A section to discuss and/or illustrate the applications
# This section is too short; include specific applications in which input features are sparse and Adagrad excels.
# Add reference to the claim “Mainly, it is a good choice for deep learning models with sparse input features”.
* A conclusion section
* References

# Too few references overall, you should aggregate information from multiple sources (even if the base algorithm itself comes from a singular paper)

== [[McCormick envelopes|McCormick Envelopes]] ==

* Author list: OK but I suggest removing NetID
* Sections: Section titles should not be "bold". Please double check using source editor to avoid weird format of the TOC.
* An introduction of the topic
# First sentence is hard to read. Please consider keeping sentences below 25-30 words.
# No references provided. Please cite all sources.
# Figure 1 is provided in the middle between two sections. Please include in the introduction section.
* Theory, methodology, and/or algorithmic discussions
# References are not linked or expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# When using mathematical expressions and symbols, please use the equation editor. (e.g., x*y, exy + y, sin (x+y) - x2)
* At least one numerical example
# Please add a few sentences to show the transition from problem to solution.
# For the sample GAMS code, please place it in a code box
* A section to discuss and/or illustrate the applications
# Having a list is not enough. Please explain at least three applications in a few sentences each.
# This section should be at least a paragraph to discuss relevant applications. Each application should be explicitly linked to the page topic. A few keywords do not meet the requirement at all.
* A conclusion section:
* References
# References are not expressed correctly. Please consider having the references as this Wiki template, [[Quantum computing for optimization|https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization]]
# Please follow the standard reference style - the current format is incorrect.

File:Wikicreatetopic.png

2021-09-30T22:00:24Z

Aw843cornell:

Example image for wiki tutorial

Network flow problem

2020-12-13T03:20:39Z

Aw843cornell:

Author: Aaron Wheeler, Chang Wei, Cagla Deniz Bahadir, Ruobing Shui, Ziqiu Zhang (CHEME 6800 Fall 2020)

Steward: Fengqi You, Allen Yang

== Introduction ==
Network flow problems arise in several key instances and applications within society and have become fundamental problems within computer science, operations research, applied mathematics, and engineering. Developments in the approach to tackle these problems resulted in algorithms that became the chief instruments for solving problems related to large-scale systems and industrial logistics. Spurred by early developments in linear programming, the methods for addressing these extensive problems date back several decades and they evolved over time as the use of digital computing became increasingly prevalent in industrial processes. Historically, the first instance of an algorithmic development for the network flow problem came in 1956, with the network simplex method formulated by George Dantzig.[1] A variation of the simplex algorithm that revolutionized linear programming, this method leveraged the combinatorial structure inherent to these types of problems and demonstrated incredibly high accuracy.[2] This method and its variations would go on to define the embodiment of the algorithms and models for the various and distinct network flow problems discussed here.

== Theory, Methodology, and Algorithms ==
The network flow problem can be conceptualized as a directed graph which abides by flow capacity and conservation constraints. The vertices in the graph are classified into origins (source <math>X</math>), destinations (sink <math>O</math>), and intermediate points and are collectively referred to as nodes (<math>N</math>). These nodes are different from one another such that <math>N_i \neq X,O,\ldots N_j</math>.[3] The edges in the directed graph are the directional links between nodes and are referred to as arcs (<math>A</math>). These arcs are defined with a specific direction <math>(i, j)</math> that corresponds to the nodes they are connecting. The arcs <math>A\subseteq (i,j)</math> are also defined by a specific flow capacity <math>c(A)>0</math> that cannot be exceeded. The supply and demand of units <math>\Sigma_i u_i=0~for~i\in N</math> are formulated by negative and positive flow notation, and are defined such that sources equate to positive values (supply) and sinks equate to negative values (demand). Intermediate nodes have no net supply or demand. Figure 1 illustrates this general definition of the network.
[[File:Picture1.png|thumb|Figure 1. General Network Flow Problem]]

Additional constraints of the network flow optimization model place limits on the solution and vary significantly based on the specific type of problem being solved. Historically, the classic network flow problems are considered to be the maximum flow problem and the minimum-cost circulation problem, the assignment problem, bipartite matching problem, transportation problem, and the transshipment problem.[2] The approach to these problems become quite specific based upon the problem’s objective function but can be generalized by the following iterative approach: 1. determining the initial basic feasible solution; 2. checking the optimality conditions (i.e. whether the problem is infeasible, unbounded over the feasible region, optimal solution has been found, etc.); and 3. constructing an improved basic feasible solution if the optimal solution has not been determined.[3]
=== General Applications ===

==== The Assignment Problem ====
Various real-life instances of assignment problems exist for optimization, such as assigning a group of people to different tasks, events to halls with different capacities, rewards to a team of contributors, and vacation days to workers. All together, the assignment problem is a bipartite matching problem in the kernel. [3] In a classical setting, two types of objects of equal amount are bijective (i.e. they have one-to-one matching), and this tight constraint ensures a perfect matching. The objective is to minimize the cost or maximize the profit of matching, since different items of two types have distinct affinity. [[File:Assignment.png|thumb|Figure 2. Classic model of assignment problem|alt=|267x267px]]A classic example is as follows: suppose there are <math> n </math> people (set <math> P </math>) to be assigned to <math> n </math> tasks (set <math> T </math>). Every task has to be completed and each task has to be handled by only one person, and <math> c_{ij} </math>, usually given by a table, measures the benefits gained by assigning the person <math> i </math> (in <math> P </math>) to the task <math> j </math> (in <math> T </math>). [4] The natural objective here is to maximize the overall benefits by devising the optimal assignment pattern. A graph of the general assignment problem and a table of preference are depicted as Figure 2 and Table 2.
{| class="wikitable sortable"
|+Table 1. Table of preference
!Benefits
!Task 1
! Task 2
!Task 3
!...
!Task n
|-
!Person 1
|0
|3
|5
|...
|2
|-
!Person 2
|2
|1
|3
|...
|6
|-
!Person 3
|1
|4
|0
|...
|3
|-
!...
|...
|...
|...
|...
|...
|-
!Person n
|0
|2
|3
|...
|3
|}
Figure 2 can be viewed as a network. The nodes represent people and tasks, and the edges represent potential assignments between a person and a task. Each task can be completed by any person. However, the person that actually ends up being assigned to the task will be the lone individual who is best suited to complete. In the end, the edges with positive flow values will be the only ones represented in the finalized assignment. [5]

To approach this problem, the binary variable <math> x_{ij} </math> is defined as whether the person <math> i </math> is assigned to the task <math> j </math>. If so, <math> x_{ij} </math> = 1, and <math> x_{ij} </math> = 0 otherwise.

The concise-form formulation of the problem is as follows [3]:

max <math>z=\sum_{i=1}^n\sum_{j=1}^n c_{ij}x_{ij}</math>

Subject to:

<math>\sum_{j=1}^n x_{ij}=1~~\forall i\in [1,n]
</math>

<math>\sum_{I=1}^n x_{ij}=1~~\forall j\in [1,n]
</math>

<math>x_{ij}=0~or~1~~\forall i,j\in [1,n] </math>

The first constraint captures the requirement of assigning each person to a single task. The second constraint indicates that each task must be done by exactly one person. The objective function sums up the overall benefits of all assignments.

To see the analogy between the assignment problem and the network flow, we can describe each person supplying a flow of 1 unit and each task demanding a flow of 1 unit, with the benefits over all “channels” being maximized. [3]

A potential issue lies in the branching of the network, specifically an instance where a person splits its one unit of flow into multiple tasks and the objective remains maximized. This shortcoming is allowed by the laws that govern the network flow model, but are unfeasible in real-life instances. Fortunately, since the network simplex method only involves addition and subtraction of a single edge while transferring the basis, which is served by the spanning tree of the flow graph, if the supply (the number of people here) and the demand (the number of tasks here) in the constraints are integers, the solved variables will be automatically integers even if it is not explicitly stated in the problem. This is called the integrality of the network problem, and it certainly applies to the assignment problem. [6]

==== The Transportation Problem ====
People first came up with the transportation problem when distributing troops during World War II. [7] Now, it has become a useful model for solving logistics problems, and the objective is usually to minimize the cost of transportation.

Consider the following scenario:

There are 2 chemical plants located in 2 different places: <math> M </math> and <math> N </math>. There are 3 raw material suppliers in other 3 locations: <math> F </math>, <math> G </math>, and <math> H </math>. The amount of materials from a supplier can be arbitrarily divided into two parts and shipped to two factories. Supplier <math> F </math>, <math> G </math>, and <math> H </math> can provide <math> S_1 </math>, <math> S_2 </math>, and <math> S_3 </math> amounts of materials respectively. The chemical plants located at <math> M </math> and <math> N </math> have the material demand of <math> D_1 </math> and <math> D_2 </math> respectively. Each transportation route, from suppliers to chemical plants, is attributed with a specific cost. This model raises the question: to keep the chemical plants running, what is the best way to arrange the material from the suppliers so that the transportation cost could be minimized?
[[File:Transportation problem example.png|thumb|Figure 3. Transportation problem example]]
Several quantities should be defined to help formulate the frame of the solution:

<math>S_{i}
</math> = the amount of material provided at the supplier <math>i
</math>

<math>D_{j}
</math> = the amount of material being consumed at the chemical plant <math>j
</math>

<math>x_{ij}
</math> = the amount of material being transferred from supplier <math>i
</math> to chemical plant <math display="inline">j
</math>

<math>C_{ij}
</math> = the cost of transferring 1 unit of material from supplier <math>i
</math> to chemical plant <math>j
</math>

<math>x_{ij}
</math><math>C_{ij}
</math> = the cost of the material transportation from <math>i
</math> to <math>j
</math>

Here, the amount of material being delivered and being consumed is bound to the supply and demand constraints:

(1): The amount of material shipping from supplier <math>i
</math> cannot exceed the amount of material available at supplier <math>i
</math>.

<math>\sum_j^n x_{ij}\ \leq S_{i} \qquad \forall i\in I=[1,m]
</math>

(2): The amount of material arrived at chemical plant <math>j
</math> should at least fulfill the demand at chemical plant <math>j
</math>.

<math>\sum_i^m x_{ij}\ \geq D_{j} \qquad \forall j\in J=[1,n]
</math>

The objective is to find the minimum cost of transportation, so the cost of each transportation line should be added up, and the total cost should be minimized.

<math>\sum_i^m \sum_j^n x_{ij}\ C_{ij}
</math>

Using the definitions above, the problem can be formulated as such:

min<math> \quad z = \sum_i^m \sum_j^n x_{ij}\ C_{ij}

</math>

<math>s.t. \quad\ \sum_j^n x_{ij}\ \leq S_{i} \qquad \forall i\in I=[1,m]
</math>

<math>\sum_i^m x_{ij}\ \geq D_{j} \qquad \forall j\in J=[1,n]
</math>

However, the problem is not complete at this point because there is no constraint for <math>x_{ij}
</math>, and that means <math>x_{ij}
</math> can be any number, even negative. In order for <math>x_{ij}
</math> to make sense physically, a lower bound of zero is mandatory, which corresponds to the situation where no material was transported from <math>i
</math> to <math>j
</math>. Adding the last constraint will complete this formulation as such:

min<math> \quad z = \sum_i^m \sum_j^n x_{ij}\ C_{ij}

</math>

<math>s.t. \quad\ \sum_j^n x_{ij}\ \leq S_{i} \qquad \forall i\in I=[1,m]
</math>

<math>\sum_i^m x_{ij}\ \geq D_{j} \qquad \forall j\in J=[1,n]
</math>

<math>x_{ij}\ \geq 0
</math>

The problem and the formulation is adapted from Chapter 8 of the book: Applied Mathematical Programming by Bradley, Hax and Magnanti. [3]

==== The Shortest-Path Problem ====
The shortest-path problem can be defined as finding the path that yields the shortest total distance between the origin and the destination. Each possible stop is a node and the paths between these nodes are edges incident to these nodes, where the path distance becomes the weight of the edges. In addition to being the most common and straightforward application for finding the shortest path, this model is also used in various applications depending on the definition of nodes and edges. [3] For example, when each node represents a different object and the edge specifies the cost of replacement, the equipment replacement problem is derived. Moreover, when each node represents a different project and the edge specifies the relative priority, the model becomes a project scheduling problem.
[[File:Shortest-Path.png|thumb|443x443px|Figure 4. General form of shortest-path problem]]
A graph of the general shortest-path problem is depicted as Figure 4:

In the general form of the shortest-path problem, the variable <math> x_{ij} </math> represents whether the edge <math> (i,j) </math> is active (i.e. with a positive flow), and the parameter <math> c_{ij} </math> (e.g. <math> c_{12} </math> = 6) defines the distance of the edge <math> (i,j) </math>. The general problem is formulated as below:

min <math>z=\sum_{i=1}^n \sum_{j=1}^n c_{ij}x_{ij}</math>

Subject to:

<math>\sum_{j=1}^n x_{ij} - \sum_{k=1}^n x_{ki} = \begin{cases} 1 & \text{if }i=s\text{ (source)} \\ 0 & \text{otherwise} \\ -1 & \text{if }i=t \text{ (sink)} \end{cases}</math>

<math>x_{ij}\geq 0~~\forall (i,j)\in E</math>

The first term of the constraint is the total outflow of the node i, and the second term is the total inflow. So, the formulation above could be seen as one unit of flow being supplied by the origin, one unit of flow being demanded by the destination, and no net inflow or outflow at any intermediate nodes. These constraints mandate a flow of one unit, amounting to the active path, from the origin to the destination. Under this constraint, the objective function minimizes the overall path distance from the origin to the destination.

Similarly, the integrality of the network problem applies here, precluding the unreasonable fractioning. With supply and demand both being integer (one here), the edges can only have integer amount of flow in the result solved by simplex method. [6]

In addition, the point-to-point model above can be further extended to other problems. A number of real life scenarios require visiting multiple places from a single starting point. This “Tree Problem” can be modeled by making small adjustments to the original model. In this case, the source node should supply more units of flow and there will be multiple sink nodes demanding one unit of flow. Overall, the objective and the constraint formulation are similar. [4]

==== Maximal Flow Problem ====
This problem describes a situation where the material from a source node is sent to a sink node. The source and sink node are connected through multiple intermediate nodes, and the common optimization goal is to maximize the material sent from the source node to the sink node. [3]

Consider the following scenario:
[[File:Picture2.png|thumb|Figure 5. Maximal flow problem example]]
The given structure is a piping system. The water flows into the system from the source node, passing through the intermediate nodes, and flows out from the sink node. There is no limitation on the amount of water that can be used as the input for the source node. Therefore, the sink node can accept an unlimited amount of water coming into it. The arrows denote the valid channel that water can flow through, and each channel has a known flow capacity. What is the maximum flow that the system can take?

Several quantities should be defined to help formulate the frame of the solution:
[[File:Picture3.png|thumb|Figure 6. For every intermediate node j, there is a group of node i and a group of node k.]]
For any intermediate node <math display="inline">j
</math> in the system, it receives water from adjacent node(s) <math>i
</math>, and sends water to the adjacent node(s) <math display="inline">k

</math>. The node <math>i
</math> and k are relative to the node <math display="inline">j
</math>.

<math>i
</math> = the node(s) that gives water to node <math display="inline">j
</math>

<math display="inline">j
</math> = the intermediate node(s)

<math display="inline">k

</math> = the node(s) that receives the water coming out of node <math display="inline">j
</math>

<math>x_{ij}
</math> = amount of water leaving node <math>i
</math> and entering node <math display="inline">j
</math> (<math>i
</math> and <math display="inline">j
</math> are adjacent nodes)

<math>x_{jk}
</math> = amount of water leaving node <math display="inline">j
</math> and entering node <math display="inline">k

</math> (<math>i
</math> and <math display="inline">k

</math> are adjacent nodes)

For the source and sink node, they have net flow that is non-zero:

<math display="inline">m
</math> = source node

<math display="inline">n
</math> = sink node

<math>x_{in}
</math> = amount of water leaving node <math>i
</math> and entering sink node <math display="inline">n
</math> (<math>i
</math> and <math display="inline">n
</math> are adjacent nodes)

<math>x_{mk}
</math> = amount of water leaving source node <math display="inline">m
</math> and entering node <math display="inline">k

</math> (<math display="inline">m
</math> and <math display="inline">k

</math> are adjacent nodes)

Flow capacity definition is applied to all nodes (including intermediate nodes, the sink, and the source):

<math>C_{ab}
</math> = transport capacity between any two nodes <math display="inline">a
</math> and <math display="inline">b
</math> (<math display="inline">a
</math><math> \neq
</math><math display="inline">b
</math>)

The main constraints for this problem are the transport capacity between each node and the material conservation:

(1): The amount of water flowing from any node <math display="inline">a
</math> to node <math display="inline">b
</math> should not exceed the flow capacity between node <math display="inline">a
</math> to node <math display="inline">b
</math> .

<math>0\leq x_{ab} \leq C_{ab}
</math>

(2): The intermediate node <math display="inline">j
</math> does not hold any water, so the amount of water that flows into node <math display="inline">j
</math> has to exit the node with the exact same amount it entered with.

<math>\sum_i^px_{ij}- \sum_k^r x_{jk} =0
\qquad \begin{cases} \forall i\in I=[1,p] \\ \forall j\in J=[1,q]\\ \forall k\in K=[1,r] \end{cases}
</math>

Overall, the net flow out of the source node has to be the same as the net flow into the sink node. This net flow is the amount that should be maximized.

Using the definitions above:
[[File:Picture4.png|thumb|Figure 7. The imaginary flow connects the sink node to the source node, creating a close loop.]]
min<math> \quad z = \sum_k^r x_{uk}

</math> (or <math>\sum_i^p x_{iv}

</math>)

<math>s.t. \quad\ \sum_i^px_{ij}- \sum_k^r x_{jk} =0
\qquad \begin{cases} \forall i\in I=[1,p] \\ \forall j\in J=[1,q]\\ \forall k\in K=[1,r] \end{cases}
</math>

<math>0\leq x_{ab} \leq C_{ab}
</math>

This expression can be further simplified by introducing an imaginary flow from the sink to the source.

By introducing this imaginary flow, the piping system is now closed. The mass conservation constraint now also holds for the source and sink node, so they can be treated as the intermediate nodes. The problem can be rewritten as the following:

min<math> \quad z = x_{vu}

</math>

<math>s.t. \quad\ \sum_i^px_{ij}- \sum_k^r x_{jk} =0
\qquad \begin{cases} \forall i\in I=[1,p] \\ \forall j\in J=[1,q+2]\\ \forall k\in K=[1,r] \end{cases}
</math>

<math>0\leq x_{ab} \leq C_{ab}
</math>

The problem and the formulation are derived from an example in Chapter 8 of the book: Applied Mathematical Programming by Bradley, Hax and Magnanti. [3]

=== Algorithms ===

==== Ford–Fulkerson Algorithm ====
A broad range of network flow problems could be reduced to the max-flow problem. The most common way to approach the max-flow problem in polynomial time is the Ford-Fulkerson Algorithm (FFA). FFA is essentially a greedy algorithm and it iteratively finds the augmenting s-t path to increase the value of flow. The pathfinding terminates until there is no s-t path present. Ultimately, the max-flow pattern in the network graph will be returned. [8]

Typically, FFA is applied to flow networks with only one source node s and one sink node t. In addition, the capacity conditions and the conservation conditions, which are two properties defining the flow, must be satisfied.[9] The capacity conditions require that each edge carry a flow that is no more than its capacity, or <math>0\leq f\left ( e \right )\leq c_{e},\: \forall e\in E</math>, where function f returns the flow on a certain edge. The conservation conditions require all nodes except the source and the sink to have a net flow of 0, or ,<math>\sum _{e\, into\, v}f\left ( v \right )= \sum _{e\, out\, of\, v}f\left ( v \right ),\: \forall v\in V\: -\: \left \{ s,\, t \right \}</math>.

FFA introduces the concept of residue graph based on the original graph G to allow backtracking, or pushing backward on edges that are already carrying flow.[9] The residue graph <math>G_{f} </math>is defined as the following:
1. <math>G_{f}</math>has exactly the same node set as G.
2. For each edge <math>e = \left ( v,u \right )</math>with a nonnegative flow <math> f\left ( e \right )</math> in G, <math>G_{f}</math>has the edge e with the capacity <math>c\left ( e \right )_{f} = c_{e} - f\left ( e \right )</math>, and also Gf has the edge <math>e' = \left ( v,u \right )</math> with the capacity <math>c\left ( e' \right )_{f} = f\left ( e \right )</math>.
Note that initially, the <math>G_{f} </math> is identical to G since there is no flow present in <math>G</math>.

The steps of FFA are as below. [10] Essentially, the method repeatedly finds a path with positive flow in the residue graph, and updates the flow graph and residue graph until s and t become disjoint in the residue graph.
1.Set <math>f\left ( e \right ) = 0, \forall e\in E\: in\: G</math> , and create a copy as <math>G_{f}</math>.
2.While there is still a s, t path p in <math>G_{f}</math>:
a.Find <math>c_{f}\left ( p \right ) = min\left ( c_{f}\left ( e \right )\, :\, e\in p \right )</math>
b.For each edge <math>e\in p</math>:
i.<math>f\left ( e \right ) = f\left ( e \right ) + c_{f}\left ( p \right )\: if\: e\in E in G, f\left ( e \right ) = f\left ( e \right ) - c_{f}\left ( p \right )\: if\: e'\in E\: in\: G</math>
ii.<math>c\left ( e \right )= c\left ( e \right ) - c_{f}\left ( p \right ),\:c\left ( e' \right )= c\left ( e' \right ) + c_{f}\left ( p \right )\: in\: G_{f}</math>

An example of running the FFA is as below.
The flow graph <math>G</math> and residue graph<math>G_{f}</math> at the initial phase is depicted in Figure 8, where the number of each edge in the flow graph is the flow units on the edge, whereas it is the updated edge capacity in the residue graph.

[pic8]

In the residue graph, an s-t path can be found in the residue graph tracing the edge s->A->B->t with the flow of two units. After augmenting the path on both graphs, the flow graph and the residue graph look like the Figure 9.

[pic9]

At this stage, there is still s,t-path in the residue graph s->B->A->t with a flow of one unit. After augmenting the path on both graphs, the flow graph and the residue graph look like the Figure 10.

[pic10]

At this stage, there is no more s,t-path in the residue graph, so FFA terminates and the maximum flow can be read from the flow graph as 3 units.

== Numerical Example and Solution ==

A Food Distributor Company is farming and collecting vegetables from farmers to later distribute to the grocery stores. The distributor has specific agreements with different third-party companies to mediate the delivery to the grocery stores. In a particular month, the company has 600 ton vegetables to deliver to the grocery store. They have agreements with two third-party transport companies A and B, which have different tariffs for delivering goods between themselves, the distributor, and the grocery store. They also have limits on transport capacity for each path. These delivery points are numbered as shown below, with path 1 being the transport from the Food Distributor Company to the transport company A. The limits and tariffs for each path can be found in the Table 2 below, and the possible transportation connections between the distributor company, the third-party transporters, and the grocery store are shown in the figure below. The distributor companies cannot hold any amount of food, and any incoming food should be delivered to an end point. The distributor company wants to minimize the overall transport cost of shipping 600 tons of vegetables to the grocery store by choosing the optimal path provided by the transport companies. How should the distributor company map out their path and the amount of vegetables carried on each path to minimize cost overall?
[[File:Wiki example.png|thumb|Figure. 11. Illustration of the network for the food distribution problem.]]
{| class="wikitable"
|+Table 2. Product Limits and Tariffs for each Path
|
|1
|2
|3
|4
|5
|6
|-
|Product limit (ton)
|250
|450
|350
|200
|300
|500
|-
|Tariff ($/ton)
|10
|12.5
|5
|7.5
|10
|20
|}

This question is adapted from one of the exercise questions in chapter 8 of the book: Applied Mathematical Programming by Bradley, Hax and Magnanti [3].

=== Formulation of the Problem ===
The problem can be formulated as below where variables <math>x_1, x_2, x_3,..., x_6</math> denote the tons of vegetables carried in paths 1 to 6. The objective function stated in the first line is to minimize the cost of the operation, which is the summation of the tons of vegetables carried on each path multiplied by the corresponding tariff: <math>\sum_{i=1}^6 x_i t_i</math>.

<math>\begin{array}{lcl} \min z = 10x_1 + 12.5x_2 + 5x_3 + 7.5x_4 + 10x_5 + 20x_6 \\ s.t. \qquad x_5 = x_1 - x_3 + x_4 \\ \ \ \ \quad \qquad x_6 = x_2 + x_3 - x_4 \\ \ \ \ \quad \qquad x_5 + x_6 = 600 \\ \ \ \ \quad \qquad x_1 + x_2 = 600 \\ \ \ \ \quad \qquad x_1 \leq 250 \\ \ \ \ \quad \qquad x_2 \leq 450 \\ \ \ \ \quad \qquad x_3 \leq 350 \\ \ \ \ \quad \qquad x_4 \leq 200 \\ \ \ \ \quad \qquad x_5 \leq 300 \\ \ \ \ \quad \qquad x_6 \leq 500 \\ \ \ \ \quad \qquad x_1, x_2, x_3, x_4, x_5, x_6 \geq 0\\\end{array}

</math>

The second step is to write down the constraints. The first constraint ensures that the net amount present in the Transport Company A, which is the deliveries received from path 1 and path 2 minus the transport to Transport Company B should be delivered to the grocery store with path 5. The second constraint ensures this for the Transport Company B. The third and fourth constraints are ensuring that the total amount of vegetables shipping from the Food Distributor Company and the total amount of vegetables delivered to the grocery store are both 600 tons. The constraints 5 to 10 depict the upper limits of the amount of vegetables that can be carried on paths 1 to 6. The final constraint depicts that all variables are non-negative.

=== Solution of the Problem ===
This problem can be solved using Simplex Algorithm[11] or with the CPLEX Linear Programming solver in GAMS optimization platform. The steps of the solution using the GAMS platform is as follows:

The first step is to list the variables, which are the tons of vegetables that will be transported in routes 1 to 6. The paths can be denoted as<math>x_1, x_2, x_3,..., x_6</math> . The objective function is the overall cost: z.

'''variables x1,x2,x3,x4,x5,x6,z;'''

The second step is to list the equations which are the constraints and the objective function. The objective function is a summation of the amount of vegetables carried in path i, multiplied with the tariff of path i for all i: <math>\sum_{i=1}^6 x_i t_i</math>. The GAMS code for the objective function is written below:

'''obj.. z=e= 10*x1+12.5*x2+5*x3+7.5*x4+10*x5+20*x6;'''

Overall, there are 10 constraints in this problem. The constraints 1, and 2 are equations for the paths 5 and 6. The amount carried in path 5 can be found by summing the amount of vegetables incoming to Transport Company A from path 1 and path 4, minus the amount of vegetables leaving Transport Company A with path 3. This can be attributed to the restriction that barrs the companies from keeping any vegetables and requires them to eventually deliver all the incoming produce. The equality 1 ensures that this constraint holds for path 5 and equation 2 ensures it for path 6. A sample of these constraints is written below for path 5:

'''c1.. x5 =e=x1-x3+x4;'''

Constraint 3 ensures that the sum of vegetables carried in path 1 and path 2 add to the total of 600 tons of vegetables that leave the Food Distributor Company. Likewise, the constraint 4 ensures that the sum amount of food transported in paths 5 and 6 adds up to 600 tons of vegetables that have to be delivered to the grocery store. A sample of these constraints is written below for the total delivery to the grocery store:

'''c3.. x5+x6=e=600;'''

Constraints 5 to 10 should ensure that the amount of food transported in each path should not exceed the maximum capacity depicted in the table. A sample of these constraints is written below for the capacity of path 1:

'''c5.. x1=l=250;'''

After listing the variables, objective function and the constraints, the final step is to call the CPLEX solver and set the type of the optimization problem as '''lp''' (linear programming). In this case the problem will be solved with a Linear Programming algorithm to minimize the objective (cost) function.

The GAMS code yields the results below:

'''x1 = 250, x2 = 350, x3 = 0, x4 = 50, x5 = 300, x6 = 300, z =16250.'''

== Real Life Applications ==
Network problems have many applications in all kinds of areas such as transportation, city design, resource management and financial planning.[6]

There are several special cases of network problems, such as the shortest path problem, minimum cost flow problem, assignment problem and transportation problem.[6] Three application cases will be introduced here.

=== The minimum cost flow problem ===
[[File:Pic8.jpg|thumb|Figure. 12. Illustration of the ship subnetwork.[14]]]
[[File:Pic9.jpg|thumb|Figure. 13. Illustration of cargo subnetwork.[14]]]
Minimum cost flow problems are pervasive in real life, such as deciding how to allocate temporal quay crane in container terminals, and how to make optimal train schedules on the same railroad line.[12]

R. Dewil and his group use MCNFP to assist traffic enforcement.[13] Police patrol “hot spots”, which are areas where crashes occur frequently on highways. R. Dewil studies a method intended to estimate the optimal route of hot spots. He describes the time it takes to move the detector to a certain position as the cost, and the number of patrol cars from one node to next as the flow, in order to minimize the total cost.[13]

=== The assignment problem ===
Dung-Ying Lin studies an assignment problem in which he aims to assign freights to ships and arrange transportation paths along the Northern Sea Route in a manner which yields maximum profit.[14] Within this network composed of a ship subnetwork and a cargo subnetwork( shown as Figure 12 and Figure 13), each node corresponds to a port at a specific time and each arc represents the movement of a ship or a cargo. Other types of assignment problems are faculty scheduling, freight assignment, and so on.

=== The shortest path problem ===
Shortest path problems are also present in many fields, such as transportation, 5G wireless communication, and implantation of the global dynamic routing scheme.[15][16][17]

Qiang Tu and his group studies the constrained reliable shortest path (CRSP) problem for electric vehicles in the urban transportation network. [15] He describes the reliable travel time of path as the objective item, which is made up of planning travel time of path and the reliability item. The group studies the Chicago sketch network consisting of 933 nodes and 2950 links and the Sioux Falls network consisting of 24 nodes and 76 links. The results show that the travelers’ risk attitudes and properties of electric vehicles in the transportation network can have a great influence on the path choice.[15] The study can contribute to the invention of the city navigation system.

== Conclusion ==
Since its inception, the network flow problem has provided humanity with a straightforward and scalable approach for several large-scale challenges and problems. The Simplex algorithm and other computational optimization platforms have made addressing these problems routine, and have greatly expedited efforts for groups concerned with supply-chain and other distribution processes. The formulation of this problem has had several derivations from its original format, but its overall methodology and approach have remained prevalent in several of society’s industrial and commercial processes, even over half a century later. Classical models such as the assignment, transportation, maximal flow, and shortest path problem configurations have found their way into diverse settings, ranging from streamlining oil distribution networks along the gulf coast to arranging optimal scheduling assignments for college students amidst a global pandemic. All in all, the network flow problem and its monumental impact, have made it a fundamental tool for any group that deals with combinatorial data sets. And with the surge in adoption of data-driven models and applications within virtually all industries, the use of the network flow problem approach will only continue to drive innovation and meet consumer demands for the foreseeable future.

== References ==
1. Karp, R. M. (2008). [https://www.sciencedirect.com/science/article/pii/S1572528607000370/ George Dantzig’s impact on the theory of computation]. Discrete Optimization, 5(2), 174-185.

2. Goldberg, A. V. Tardos, Eva, Tarjan, Robert E. (1989). [http://www.cs.cornell.edu/~eva/Network.Flow.Algorithms.pdf/ Network Flow Algorithms, Algorithms and Combinatorics]. 9. 101-164.

3. Bradley, S. P. Hax, A. C., & Magnanti, T. L. (1977). Network Models. [http://web.mit.edu/15.053/www/AMP.htm/ Applied mathematical programming] (p. 259). Reading, MA: Addison-Wesley.

4. Chinneck, J. W. (2006). [https://www.optimization101.org/ Practical optimization: a gentle introduction. Systems and Computer Engineering]. Carleton University, Ottawa. 11.

5. Roy, B. V. Mason, K.(2005). [https://web.stanford.edu/~ashishg/msande111/notes/chapter5.pdf/ Formulation and Analysis of Linear Programs, Chapter 5 Network Flows].

6. Vanderbei, R. J. (2020). [https://www.springer.com/gp/book/9781461476306/ Linear programming: foundations and extensions (Vol. 285)]. Springer Nature.

7. Sobel, J. (2014). [https://econweb.ucsd.edu/~jsobel/172aw02/notes8.pdf/ Linear Programming Notes VIII: The Transportation Problem].

8. Cormen, Thomas H.; Leiserson, Charles E.; Rivest, Ronald L.; Stein, Clifford (2001). "Section 26.2: The Ford–Fulkerson method". Introduction to Algorithms (Second ed.). MIT Press and McGraw–Hill.

9. Jon Kleinberg; Éva Tardos (2006). "Chapter 7: Network Flow". Algorithm Design. Pearson Education.

10. Ford–Fulkerson algorithm. Retrieved December 05, 2020, from https://en.wikipedia.org/wiki/Ford%E2%80%93Fulkerson_algorithm.

11. Hu, G. (2020, November 19). [https://optimization.cbe.cornell.edu/index.php?title=Simplex_algorithm#cite_note-11/ Simplex algorithm]. Retrieved November 22, 2020.

12. Altınel, İ. K., Aras, N., Şuvak, Z., & Taşkın, Z. C. (2019). [https://www.sciencedirect.com/science/article/pii/S0166218X18304815/ Minimum cost noncrossing flow problem on layered networks]. Discrete Applied Mathematics, 261, 2-21.

13. Dewil, R., Vansteenwegen, P., Cattrysse, D., & Van Oudheusden, D. (2015). [https://core.ac.uk/download/pdf/34613916.pdf/ A minimum cost network flow model for the maximum covering and patrol routing problem]. European Journal of Operational Research, 247(1), 27-36.

14. Lin, D. Y., & Chang, Y. T. (2018). [https://www.sciencedirect.com/science/article/pii/S1366554517308037/ Ship routing and freight assignment problem for liner shipping: Application to the Northern Sea Route planning problem]. Transportation Research Part E: Logistics and Transportation Review, 110, 47-70.

15. Tu, Q., Cheng, L., Yuan, T., Cheng, Y., & Li, M. (2020). [https://www.sciencedirect.com/science/article/pii/S095965262031177X/ The Constrained Reliable Shortest Path Problem for Electric Vehicles in the Urban Transportation Network]. Journal of Cleaner Production, 121130.

16. Guo, Y., Li, S., Jiang, W., Zhang, B., & Ma, Y. (2017). [https://dl.acm.org/doi/abs/10.1016/j.phycom.2017.06.010/ Learning automata-based algorithms for solving the stochastic shortest path routing problems in 5G wireless communication]. Physical Communication, 25, 376-385.

17. Haddou, N. B., Ez-Zahraouy, H., & Rachadi, A. (2016). [https://www.infona.pl/resource/bwmeta1.element.elsevier-2eaa73bc-4e22-39aa-89b9-71ef2d7e2d63/ Implantation of the global dynamic routing scheme in scale-free networks under the shortest path strategy]. Physics Letters A, 380(33), 2513-2517.

Network flow problem

2020-12-08T21:27:37Z

Aw843cornell: /* Conclusion */

Author: Aaron Wheeler, Chang Wei, Cagla Deniz Bahadir, Ruobing Shui, Ziqiu Zhang (CHEME 6800 Fall 2020)

Steward: Fengqi You, Allen Yang

== Introduction ==
Network flow problems arise in several key instances and applications within society and have become fundamental problems within computer science, operations research, applied mathematics, and engineering. Developments in the approach to tackle these problems resulted in algorithms that became the chief instruments for solving problems related to large-scale systems and industrial logistics. Spurred by early developments in linear programming, the methods for addressing these extensive problems date back several decades and they evolved over time as the use of digital computing became increasingly prevalent in industrial processes. Historically, the first instance of an algorithmic development for the network flow problem came in 1956, with the network simplex method formulated by George Dantzig.[1] A variation of the simplex algorithm that revolutionized linear programming, this method leveraged the combinatorial structure inherent to these types of problems and demonstrated incredibly high accuracy.[2] This method and its variations would go on to define the embodiment of the algorithms and models for the various and distinct network flow problems discussed here.

== Theory, Methodology, and Algorithms ==
Qualitatively, the network flow problem can be conceptualized as a directed graph which abides by certain flow capacity constraints at its edges and equates the values entering and exiting its vertices at all points besides terminal source and sink terms. The vertices in this problem are the origins, destinations, and intermediate points and are referred to as ''nodes''. The edges are the directional transportation links between these nodes and are referred to as ''arcs''.[3] Models for network flow problems function as tools for computing the net flow of units along these constrained arcs and between pairs of nodes, and are useful for quantifying logistical interests such as the optimal scheme for the distribution of a product from a plant to its consumer constituents. In this scenario, the product departs from the distribution source (origin) and travels through a network of intermediary transition points such as warehouses and fulfillment centers (nodes), before finally reaching the consumer market (destination). Along this journey, the transportation method along the route (arc) may be subjected to certain restraints such as the allowable amount of product carried between points (capacity constraints). The objective function in this case would be to minimize the cost of shipping the product whilst still meeting a specified demand. This exact circumstance is very common in industrial logistics and was the primary motivation for defining and solving the network flow problem. This case, the transportation problem, was the beginning of a wide assortment of problems defined for network flow by leveraging its combinatorial structure in a special-purpose algorithm.[3]

Historically, the classic network flow problems are considered to be the maximum flow problem and the minimum-cost circulation problem, the assignment problem, bipartite matching problem, transportation problem, and the transshipment problem.[2] The approach to these problems become quite specific based upon the problem’s objective function but can be generalized by the following iterative approach: 1. determining the initial basic feasible solution; 2. checking the optimality conditions; and 3. constructing an improved basic feasible solution if the optimal solution has not been determined.[3]

=== General Applications ===

==== The Assignment Problem ====
Various real-life instances of assignment problems exist for optimization, such as assigning a group of people to different tasks, events to halls with different capacities, rewards to a team of contributors, and vacation days to workers. All together, the assignment problem is a bipartite matching problem in the kernel. [3] In a classical setting, two types of objects of equal amount are bijective (i.e. they have one-to-one matching), and this tight constraint ensures a perfect matching. The objective is to minimize the cost or maximize the profit of matching, since different items of two types have distinct affinity. [[File:Assignment.png|thumb|Figure 1. Classic model of assignment problem|alt=|267x267px]]A classic example is as follows: suppose there are <math> n </math> people (set <math> P </math>) to be assigned to <math> n </math> tasks (set <math> T </math>). Every task has to be completed and each task has to be handled by only one person, and <math> c_{ij} </math>, usually given by a table, measures the benefits gained by assigning the person <math> i </math> (in <math> P </math>) to the task <math> j </math> (in <math> T </math>). [4] The natural objective here is to maximize the overall benefits by devising the optimal assignment pattern. A graph of the general assignment problem and a table of preference are depicted as Figure 1 and Table 1.
{| class="wikitable sortable"
|+Table 1. Table of preference
!Benefits
!Task 1
! Task 2
!Task 3
!...
!Task n
|-
!Person 1
|0
|3
|5
|...
|2
|-
!Person 2
|2
|1
|3
|...
|6
|-
!Person 3
|1
|4
|0
|...
|3
|-
!...
|...
|...
|...
|...
|...
|-
!Person n
|0
|2
|3
|...
|3
|}
Figure 1 can be viewed as a network. The nodes represent people and tasks, and the edges represent potential assignments between a person and a task. Each task can be completed by any person. However, the person that actually ends up being assigned to the task will be the lone individual who is best suited to complete. In the end, the edges with positive flow values will be the only ones represented in the finalized assignment. [5]

To approach this problem, the binary variable <math> x_{ij} </math> is defined as whether the person <math> i </math> is assigned to the task <math> j </math>. If so, <math> x_{ij} </math> = 1, and <math> x_{ij} </math> = 0 otherwise.

The concise-form formulation of the problem is as follows [3]:

max <math>z=\sum_{i=1}^n\sum_{j=1}^n c_{ij}x_{ij}</math>

Subject to:

<math>\sum_{j=1}^n x_{ij}=1~~\forall i\in [1,n]
</math>

<math>\sum_{I=1}^n x_{ij}=1~~\forall j\in [1,n]
</math>

<math>x_{ij}=0~or~1~~\forall i,j\in [1,n] </math>

The first constraint captures the requirement of assigning each person to a single task. The second constraint indicates that each task must be done by exactly one person. The objective function sums up the overall benefits of all assignments.

To see the analogy between the assignment problem and the network flow, we can describe each person supplying a flow of 1 unit and each task demanding a flow of 1 unit, with the benefits over all “channels” being maximized. [3]

A potential issue lies in the branching of the network, specifically an instance where a person splits its one unit of flow into multiple tasks and the objective remains maximized. This shortcoming is allowed by the laws that govern the network flow model, but are unfeasible in real-life instances. Fortunately, since the network simplex method only involves addition and subtraction of a single edge while transferring the basis, which is served by the spanning tree of the flow graph, if the supply (the number of people here) and the demand (the number of tasks here) in the constraints are integers, the solved variables will be automatically integers even if it is not explicitly stated in the problem. This is called the integrality of the network problem, and it certainly applies to the assignment problem. [6]

==== The Transportation Problem ====
People first came up with the transportation problem when distributing troops during World War II. [7] Now, it has become a useful model for solving logistics problems, and the objective is usually to minimize the cost of transportation.

Consider the following scenario:

There are 2 chemical plants located in 2 different places: <math> M </math> and <math> N </math>. There are 3 raw material suppliers in other 3 locations: <math> F </math>, <math> G </math>, and <math> H </math>. The amount of materials from a supplier can be arbitrarily divided into two parts and shipped to two factories. Supplier <math> F </math>, <math> G </math>, and <math> H </math> can provide <math> S_1 </math>, <math> S_2 </math>, and <math> S_3 </math> amounts of materials respectively. The chemical plants located at <math> M </math> and <math> N </math> have the material demand of <math> D_1 </math> and <math> D_2 </math> respectively. Each transportation route, from suppliers to chemical plants, is attributed with a specific cost. This model raises the question: to keep the chemical plants running, what is the best way to arrange the material from the suppliers so that the transportation cost could be minimized?
[[File:Transportation problem example.png|thumb|Figure 2. Transportation problem example]]
Several quantities should be defined to help formulate the frame of the solution:

<math>S_{i}
</math> = the amount of material provided at the supplier <math>i
</math>

<math>D_{j}
</math> = the amount of material being consumed at the chemical plant <math>j
</math>

<math>x_{ij}
</math> = the amount of material being transferred from supplier <math>i
</math> to chemical plant <math display="inline">j
</math>

<math>C_{ij}
</math> = the cost of transferring 1 unit of material from supplier <math>i
</math> to chemical plant <math>j
</math>

<math>x_{ij}
</math><math>C_{ij}
</math> = the cost of the material transportation from <math>i
</math> to <math>j
</math>

Here, the amount of material being delivered and being consumed is bound to the supply and demand constraints:

(1): The amount of material shipping from supplier <math>i
</math> cannot exceed the amount of material available at supplier <math>i
</math>.

<math>\sum_j^n x_{ij}\ \leq S_{i} \qquad \forall i\in I=[1,m]
</math>

(2): The amount of material arrived at chemical plant <math>j
</math> should at least fulfill the demand at chemical plant <math>j
</math>.

<math>\sum_i^m x_{ij}\ \geq D_{j} \qquad \forall j\in J=[1,n]
</math>

The objective is to find the minimum cost of transportation, so the cost of each transportation line should be added up, and the total cost should be minimized.

<math>\sum_i^m \sum_j^n x_{ij}\ C_{ij}
</math>

Using the definitions above, the problem can be formulated as such:

min<math> \quad z = \sum_i^m \sum_j^n x_{ij}\ C_{ij}

</math>

<math>s.t. \quad\ \sum_j^n x_{ij}\ \leq S_{i} \qquad \forall i\in I=[1,m]
</math>

<math>\sum_i^m x_{ij}\ \geq D_{j} \qquad \forall j\in J=[1,n]
</math>

However, the problem is not complete at this point because there is no constraint for <math>x_{ij}
</math>, and that means <math>x_{ij}
</math> can be any number, even negative. In order for <math>x_{ij}
</math> to make sense physically, a lower bound of zero is mandatory, which corresponds to the situation where no material was transported from <math>i
</math> to <math>j
</math>. Adding the last constraint will complete this formulation as such:

min<math> \quad z = \sum_i^m \sum_j^n x_{ij}\ C_{ij}

</math>

<math>s.t. \quad\ \sum_j^n x_{ij}\ \leq S_{i} \qquad \forall i\in I=[1,m]
</math>

<math>\sum_i^m x_{ij}\ \geq D_{j} \qquad \forall j\in J=[1,n]
</math>

<math>x_{ij}\ \geq 0
</math>

The problem and the formulation is adapted from Chapter 8 of the book: Applied Mathematical Programming by Bradley, Hax and Magnanti. [3]

==== The Shortest-Path Problem ====
The shortest-path problem can be defined as finding the path that yields the shortest total distance between the origin and the destination. Each possible stop is a node and the paths between these nodes are edges incident to these nodes, where the path distance becomes the weight of the edges. In addition to being the most common and straightforward application for finding the shortest path, this model is also used in various applications depending on the definition of nodes and edges. [3] For example, when each node represents a different object and the edge specifies the cost of replacement, the equipment replacement problem is derived. Moreover, when each node represents a different project and the edge specifies the relative priority, the model becomes a project scheduling problem.
[[File:Shortest-Path.png|thumb|443x443px|Figure 3. General form of shortest-path problem]]
A graph of the general shortest-path problem is depicted as Figure 2:

In the general form of the shortest-path problem, the variable <math> x_{ij} </math> represents whether the edge <math> (i,j) </math> is active (i.e. with a positive flow), and the parameter <math> c_{ij} </math> (e.g. <math> c_{12} </math> = 6) defines the distance of the edge <math> (i,j) </math>. The general problem is formulated as below:

min <math>z=\sum_{i=1}^n \sum_{j=1}^n c_{ij}x_{ij}</math>

Subject to:

<math>\sum_{j=1}^n x_{ij} - \sum_{k=1}^n x_{ki} = \begin{cases} 1 & \text{if }i=s\text{ (source)} \\ 0 & \text{otherwise} \\ -1 & \text{if }i=t \text{ (sink)} \end{cases}</math>

<math>x_{ij}\geq 0~~\forall (i,j)\in E</math>

The first term of the constraint is the total outflow of the node i, and the second term is the total inflow. So, the formulation above could be seen as one unit of flow being supplied by the origin, one unit of flow being demanded by the destination, and no net inflow or outflow at any intermediate nodes. These constraints mandate a flow of one unit, amounting to the active path, from the origin to the destination. Under this constraint, the objective function minimizes the overall path distance from the origin to the destination.

Similarly, the integrality of the network problem applies here, precluding the unreasonable fractioning. With supply and demand both being integer (one here), the edges can only have integer amount of flow in the result solved by simplex method. [6]

In addition, the point-to-point model above can be further extended to other problems. A number of real life scenarios require visiting multiple places from a single starting point. This “Tree Problem” can be modeled by making small adjustments to the original model. In this case, the source node should supply more units of flow and there will be multiple sink nodes demanding one unit of flow. Overall, the objective and the constraint formulation are similar. [4]

==== Maximal Flow Problem ====
This problem describes a situation where the material from a source node is sent to a sink node. The source and sink node are connected through multiple intermediate nodes, and the common optimization goal is to maximize the material sent from the source node to the sink node. [3]

Consider the following scenario:
[[File:Picture2.png|thumb|Figure 4. Maximal flow problem example]]
The given structure is a piping system. The water flows into the system from the source node, passing through the intermediate nodes, and flows out from the sink node. There is no limitation on the amount of water that can be used as the input for the source node. Therefore, the sink node can accept an unlimited amount of water coming into it. The arrows denote the valid channel that water can flow through, and each channel has a known flow capacity. What is the maximum flow that the system can take?

Several quantities should be defined to help formulate the frame of the solution:
[[File:Picture3.png|thumb|Figure 5. For every intermediate node j, there is a group of node i and a group of node k.]]
For any intermediate node <math display="inline">j
</math> in the system, it receives water from adjacent node(s) <math>i
</math>, and sends water to the adjacent node(s) <math display="inline">k

</math>. The node <math>i
</math> and k are relative to the node <math display="inline">j
</math>.

<math>i
</math> = the node(s) that gives water to node <math display="inline">j
</math>

<math display="inline">j
</math> = the intermediate node(s)

<math display="inline">k

</math> = the node(s) that receives the water coming out of node <math display="inline">j
</math>

<math>x_{ij}
</math> = amount of water leaving node <math>i
</math> and entering node <math display="inline">j
</math> (<math>i
</math> and <math display="inline">j
</math> are adjacent nodes)

<math>x_{jk}
</math> = amount of water leaving node <math display="inline">j
</math> and entering node <math display="inline">k

</math> (<math>i
</math> and <math display="inline">k

</math> are adjacent nodes)

For the source and sink node, they have net flow that is non-zero:

<math display="inline">m
</math> = source node

<math display="inline">n
</math> = sink node

<math>x_{in}
</math> = amount of water leaving node <math>i
</math> and entering sink node <math display="inline">n
</math> (<math>i
</math> and <math display="inline">n
</math> are adjacent nodes)

<math>x_{mk}
</math> = amount of water leaving source node <math display="inline">m
</math> and entering node <math display="inline">k

</math> (<math display="inline">m
</math> and <math display="inline">k

</math> are adjacent nodes)

Flow capacity definition is applied to all nodes (including intermediate nodes, the sink, and the source):

<math>C_{ab}
</math> = transport capacity between any two nodes <math display="inline">a
</math> and <math display="inline">b
</math> (<math display="inline">a
</math><math> \neq
</math><math display="inline">b
</math>)

The main constraints for this problem are the transport capacity between each node and the material conservation:

(1): The amount of water flowing from any node <math display="inline">a
</math> to node <math display="inline">b
</math> should not exceed the flow capacity between node <math display="inline">a
</math> to node <math display="inline">b
</math> .

<math>0\leq x_{ab} \leq C_{ab}
</math>

(2): The intermediate node <math display="inline">j
</math> does not hold any water, so the amount of water that flows into node <math display="inline">j
</math> has to exit the node with the exact same amount it entered with.

<math>\sum_i^px_{ij}- \sum_k^r x_{jk} =0
\qquad \begin{cases} \forall i\in I=[1,p] \\ \forall j\in J=[1,q]\\ \forall k\in K=[1,r] \end{cases}
</math>

Overall, the net flow out of the source node has to be the same as the net flow into the sink node. This net flow is the amount that should be maximized.

Using the definitions above:
[[File:Picture4.png|thumb|Figure 6. The imaginary flow connects the sink node to the source node, creating a close loop.]]
min<math> \quad z = \sum_k^r x_{uk}

</math> (or <math>\sum_i^p x_{iv}

</math>)

<math>s.t. \quad\ \sum_i^px_{ij}- \sum_k^r x_{jk} =0
\qquad \begin{cases} \forall i\in I=[1,p] \\ \forall j\in J=[1,q]\\ \forall k\in K=[1,r] \end{cases}
</math>

<math>0\leq x_{ab} \leq C_{ab}
</math>

This expression can be further simplified by introducing an imaginary flow from the sink to the source.

By introducing this imaginary flow, the piping system is now closed. The mass conservation constraint now also holds for the source and sink node, so they can be treated as the intermediate nodes. The problem can be rewritten as the following:

min<math> \quad z = x_{vu}

</math>

<math>s.t. \quad\ \sum_i^px_{ij}- \sum_k^r x_{jk} =0
\qquad \begin{cases} \forall i\in I=[1,p] \\ \forall j\in J=[1,q+2]\\ \forall k\in K=[1,r] \end{cases}
</math>

<math>0\leq x_{ab} \leq C_{ab}
</math>

The problem and the formulation are derived from an example in Chapter 8 of the book: Applied Mathematical Programming by Bradley, Hax and Magnanti. [3]

=== Algorithms ===

== Numerical Example and Solution ==

A Food Distributor Company is farming and collecting vegetables from farmers to later distribute to the grocery stores. The distributor has specific agreements with different third-party companies to mediate the delivery to the grocery stores. In a particular month, the company has 600 ton vegetables to deliver to the grocery store. They have agreements with two third-party transport companies A and B, which have different tariffs for delivering goods between themselves, the distributor, and the grocery store. They also have limits on transport capacity for each path. These delivery points are numbered as shown below, with path 1 being the transport from the Food Distributor Company to the transport company A. The limits and tariffs for each path can be found in the Table 2 below, and the possible transportation connections between the distributor company, the third-party transporters, and the grocery store are shown in the figure below. The distributor companies cannot hold any amount of food, and any incoming food should be delivered to an end point. The distributor company wants to minimize the overall transport cost of shipping 600 tons of vegetables to the grocery store by choosing the optimal path provided by the transport companies. How should the distributor company map out their path and the amount of vegetables carried on each path to minimize cost overall?
[[File:Wiki example.png|thumb|Figure. 7. Illustration of the network for the food distribution problem.]]
{| class="wikitable"
|+Table 2. Product Limits and Tariffs for each Path
|
|1
|2
|3
|4
|5
|6
|-
|Product limit (ton)
|250
|450
|350
|200
|300
|500
|-
|Tariff ($/ton)
|10
|12.5
|5
|7.5
|10
|20
|}

This question is adapted from one of the exercise questions in chapter 8 of the book: Applied Mathematical Programming by Bradley, Hax and Magnanti [3].

=== Formulation of the Problem ===
The problem can be formulated as below where variables <math>x_1, x_2, x_3,..., x_6</math> denote the tons of vegetables carried in paths 1 to 6. The objective function stated in the first line is to minimize the cost of the operation, which is the summation of the tons of vegetables carried on each path multiplied by the corresponding tariff: <math>\sum_{i=1}^6 x_i t_i</math>.

<math>\begin{array}{lcl} \min z = 10x_1 + 12.5x_2 + 5x_3 + 7.5x_4 + 10x_5 + 20x_6 \\ s.t. \qquad x_5 = x_1 - x_3 + x_4 \\ \ \ \ \quad \qquad x_6 = x_2 + x_3 - x_4 \\ \ \ \ \quad \qquad x_5 + x_6 = 600 \\ \ \ \ \quad \qquad x_1 + x_2 = 600 \\ \ \ \ \quad \qquad x_1 \leq 250 \\ \ \ \ \quad \qquad x_2 \leq 450 \\ \ \ \ \quad \qquad x_3 \leq 350 \\ \ \ \ \quad \qquad x_4 \leq 200 \\ \ \ \ \quad \qquad x_5 \leq 300 \\ \ \ \ \quad \qquad x_6 \leq 500 \\ \ \ \ \quad \qquad x_1, x_2, x_3, x_4, x_5, x_6 \geq 0\\\end{array}

</math>

The second step is to write down the constraints. The first constraint ensures that the net amount present in the Transport Company A, which is the deliveries received from path 1 and path 2 minus the transport to Transport Company B should be delivered to the grocery store with path 5. The second constraint ensures this for the Transport Company B. The third and fourth constraints are ensuring that the total amount of vegetables shipping from the Food Distributor Company and the total amount of vegetables delivered to the grocery store are both 600 tons. The constraints 5 to 10 depict the upper limits of the amount of vegetables that can be carried on paths 1 to 6. The final constraint depicts that all variables are non-negative.

=== Solution of the Problem ===
This problem can be solved using Simplex Algorithm[15] or the GAMS optimization platform. The steps of the solution using the GAMS platform is as follows:

The first step is to list the variables, which are the tons of vegetables that will be transported in routes 1 to 6. The paths can be denoted as<math>x_1, x_2, x_3,..., x_6</math> . The objective function is the overall cost: z.

'''variables x1,x2,x3,x4,x5,x6,z;'''

The second step is to list the equations which are the constraints and the objective function. The objective function is a summation of the amount of vegetables carried in path i, multiplied with the tariff of path i for all i: <math>\sum_{i=1}^6 x_i t_i</math>

Overall, there are 10 constraints in this problem. The constraints c1, and c2 are equations for the paths 5 and 6. The amount carried in path 5 can be found by summing the amount of vegetables incoming to Transport Company A from path 1 and path 4, minus the amount of vegetables leaving Transport Company A with path 3. This can be attributed to the restriction that barrs the companies from keeping any vegetables and requires them to eventually deliver all the incoming produce. The equality c1 ensures that this constraint holds for path 5 and c2 for path 6.

Constraint c3 ensures that the sum of vegetables carried in path 1 and path 2 add to the total of 600 tons of vegetables that leave the Food Distributor Company. Likewise, the constraint c4 ensures that the sum amount of food transported in paths 5 and 6 adds up to 600 tons of vegetables that have to be delivered to the grocery store.

Constraints c5 to c10 show the maximum amount of food that can be transported in each path, as shown in the table.

'''equations obj,c1,c2,c3,c4,c5,c6,c7,c8,c9,c10;'''

'''obj.. z=e= 10*x1+12.5*x2+5*x3+7.5*x4+10*x5+20*x6;'''

'''c1.. x5 =e=x1-x3+x4;'''

'''c2.. x6=e=x2+x3-x4;'''

'''c3.. x5+x6=e=600;'''

'''c4.. x1+x2=e=600;'''

'''c5.. x1=l=250;'''

'''c6.. x2=l=450;'''

'''c7.. x3=l=350;'''

'''c8.. x4=l=200;'''

'''c9.. x5=l=300;'''

'''c10.. x6=l=500;'''

'''x1.lo=0;'''

'''x2.lo=0;'''

'''x3.lo=0;'''

'''x4.lo=0;'''

'''x5.lo=0;'''

'''x6.lo=0;'''

After listing the variables, objective function and the constraints, the final step is to call the solver and define the type of the optimization problem. In this case the problem will be solved with a Linear Programming algorithm to minimize the objective (cost) function.

'''model problem1 /all/ ;'''

'''solve problem1 using lp minimizing z;'''

The GAMS code yields the results below:

'''x1 = 250, x2 = 350, x3 = 0, x4 = 50, x5 = 300, x6 = 300, z =16250.'''

== Real Life Applications ==
Network problems have many applications in all kinds of areas such as transportation, city design, resource management and financial planning.[6]

There are several special cases of network problems, such as the shortest path problem, minimum cost flow problem, assignment problem and transportation problem.[6] Three application cases will be introduced here.

=== The minimum cost flow problem ===
[[File:Pic8.jpg|thumb|Figure. 8. Illustration of the ship subnetwork.[10]]]
[[File:Pic9.jpg|thumb|Figure. 9. Illustration of cargo subnetwork.[10]]]
Minimum cost flow problems are pervasive in real life, such as deciding how to allocate temporal quay crane in container terminals, and how to make optimal train schedules on the same railroad line.[8]

R. Dewil and his group use MCNFP to assist traffic enforcement.[9] Police patrol “hot spots”, which are areas where crashes occur frequently on highways. R. Dewil studies a method intended to estimate the optimal route of hot spots. He describes the time it takes to move the detector to a certain position as the cost, and the number of patrol cars from one node to next as the flow, in order to minimize the total cost.[9]

=== The assignment problem ===
Dung-Ying Lin studies an assignment problem in which he aims to assign freights to ships and arrange transportation paths along the Northern Sea Route in a manner which yields maximum profit.[10] Within this network composed of a ship subnetwork and a cargo subnetwork( shown as Figure 7 and Figure 8), each node corresponds to a port at a specific time and each arc represents the movement of a ship or a cargo. Other types of assignment problems are faculty scheduling, freight assignment, and so on.

=== The shortest path problem ===
Shortest path problems are also present in many fields, such as transportation, 5G wireless communication, and implantation of the global dynamic routing scheme.[11][12][13]

Qiang Tu and his group studies the constrained reliable shortest path (CRSP) problem for electric vehicles in the urban transportation network. [14] He describes the reliable travel time of path as the objective item, which is made up of planning travel time of path and the reliability item. The group studies the Chicago sketch network consisting of 933 nodes and 2950 links and the Sioux Falls network consisting of 24 nodes and 76 links. The results show that the travelers’ risk attitudes and properties of electric vehicles in the transportation network can have a great influence on the path choice.[14] The study can contribute to the invention of the city navigation system.

== Conclusion ==
Since its inception, the network flow problem has provided humanity with a straightforward and scalable approach for several large-scale challenges and problems. The Simplex algorithm and other computational optimization platforms have made addressing these problems routine, and have greatly expedited efforts for groups concerned with supply-chain and other distribution processes. The formulation of this problem has had several derivations from its original format, but its overall methodology and approach have remained prevalent in several of society’s industrial and commercial processes, even over half a century later. Classical models such as the assignment, transportation, maximal flow, and shortest path problem configurations have found their way into diverse settings, ranging from streamlining oil distribution networks along the gulf coast to arranging optimal scheduling assignments for college students amidst a global pandemic. All in all, the network flow problem and its monumental impact, have made it a fundamental tool for any group that deals with combinatorial data sets. And with the surge in adoption of data-driven models and applications within virtually all industries, the use of the network flow problem approach will only continue to drive innovation and meet consumer demands for the foreseeable future.

== References ==
1. Karp, R. M. (2008). George Dantzig’s impact on the theory of computation. Discrete Optimization, 5(2), 174-185.

2. Goldberg, A. V. Tardos, Eva, Tarjan, Robert E. (1989). Network Flow Algorithms, Algorithms and Combinatorics. 9. 101-164.

3. Bradley, S. P. Hax, A. C., & Magnanti, T. L. (1977). Network Models. In Applied mathematical programming (p. 259). Reading, MA: Addison-Wesley.

4. Chinneck, J. W. (2006). Practical optimization: a gentle introduction. Systems and Computer Engineering), Carleton University, Ottawa. http://www.sce.carleton.ca/faculty/chinneck/po.html, 11.

5. Roy, B. V. Mason, K.(2005). Formulation and Analysis of Linear Programs, Chapter 5 Network Flows.

6. Vanderbei, R. J. (2020). Linear programming: foundations and extensions (Vol. 285). Springer Nature.

7. Sobel, J. (2014). Linear Programming Notes VIII: The Transportation Problem.

8. Altınel, İ. K., Aras, N., Şuvak, Z., & Taşkın, Z. C. (2019). Minimum cost noncrossing flow problem on layered networks. Discrete Applied Mathematics, 261, 2-21.

9. Dewil, R., Vansteenwegen, P., Cattrysse, D., & Van Oudheusden, D. (2015). A minimum cost network flow model for the maximum covering and patrol routing problem. European Journal of Operational Research, 247(1), 27-36.

10. Lin, D. Y., & Chang, Y. T. (2018). Ship routing and freight assignment problem for liner shipping: Application to the Northern Sea Route planning problem. Transportation Research Part E: Logistics and Transportation Review, 110, 47-70.

11. Tu, Q., Cheng, L., Yuan, T., Cheng, Y., & Li, M. (2020). The Constrained Reliable Shortest Path Problem for Electric Vehicles in the Urban Transportation Network. Journal of Cleaner Production, 121130.

12. Guo, Y., Li, S., Jiang, W., Zhang, B., & Ma, Y. (2017). Learning automata-based algorithms for solving the stochastic shortest path routing problems in 5G wireless communication. Physical Communication, 25, 376-385.

13. Haddou, N. B., Ez-Zahraouy, H., & Rachadi, A. (2016). Implantation of the global dynamic routing scheme in scale-free networks under the shortest path strategy. Physics Letters A, 380(33), 2513-2517.

14. Tu, Q., Cheng, L., Yuan, T., Cheng, Y., & Li, M. (2020). The Constrained Reliable Shortest Path Problem for Electric Vehicles in the Urban Transportation Network. Journal of Cleaner Production, 121130.

15. Hu, G. (2020, November 19). Simplex algorithm. Retrieved November 22, 2020, from [[Simplex algorithm|https://optimization.cbe.cornell.edu/index.php?title=Simplex_algorithm]].

Network flow problem

2020-12-08T21:23:12Z

Aw843cornell: /* Theory, Methodology, and Algorithms */

Author: Aaron Wheeler, Chang Wei, Cagla Deniz Bahadir, Ruobing Shui, Ziqiu Zhang (CHEME 6800 Fall 2020)

Steward: Fengqi You, Allen Yang

== Introduction ==
Network flow problems arise in several key instances and applications within society and have become fundamental problems within computer science, operations research, applied mathematics, and engineering. Developments in the approach to tackle these problems resulted in algorithms that became the chief instruments for solving problems related to large-scale systems and industrial logistics. Spurred by early developments in linear programming, the methods for addressing these extensive problems date back several decades and they evolved over time as the use of digital computing became increasingly prevalent in industrial processes. Historically, the first instance of an algorithmic development for the network flow problem came in 1956, with the network simplex method formulated by George Dantzig.[1] A variation of the simplex algorithm that revolutionized linear programming, this method leveraged the combinatorial structure inherent to these types of problems and demonstrated incredibly high accuracy.[2] This method and its variations would go on to define the embodiment of the algorithms and models for the various and distinct network flow problems discussed here.

== Theory, Methodology, and Algorithms ==
Qualitatively, the network flow problem can be conceptualized as a directed graph which abides by certain flow capacity constraints at its edges and equates the values entering and exiting its vertices at all points besides terminal source and sink terms. The vertices in this problem are the origins, destinations, and intermediate points and are referred to as ''nodes''. The edges are the directional transportation links between these nodes and are referred to as ''arcs''.[3] Models for network flow problems function as tools for computing the net flow of units along these constrained arcs and between pairs of nodes, and are useful for quantifying logistical interests such as the optimal scheme for the distribution of a product from a plant to its consumer constituents. In this scenario, the product departs from the distribution source (origin) and travels through a network of intermediary transition points such as warehouses and fulfillment centers (nodes), before finally reaching the consumer market (destination). Along this journey, the transportation method along the route (arc) may be subjected to certain restraints such as the allowable amount of product carried between points (capacity constraints). The objective function in this case would be to minimize the cost of shipping the product whilst still meeting a specified demand. This exact circumstance is very common in industrial logistics and was the primary motivation for defining and solving the network flow problem. This case, the transportation problem, was the beginning of a wide assortment of problems defined for network flow by leveraging its combinatorial structure in a special-purpose algorithm.[3]

Historically, the classic network flow problems are considered to be the maximum flow problem and the minimum-cost circulation problem, the assignment problem, bipartite matching problem, transportation problem, and the transshipment problem.[2] The approach to these problems become quite specific based upon the problem’s objective function but can be generalized by the following iterative approach: 1. determining the initial basic feasible solution; 2. checking the optimality conditions; and 3. constructing an improved basic feasible solution if the optimal solution has not been determined.[3]

=== General Applications ===

==== The Assignment Problem ====
Various real-life instances of assignment problems exist for optimization, such as assigning a group of people to different tasks, events to halls with different capacities, rewards to a team of contributors, and vacation days to workers. All together, the assignment problem is a bipartite matching problem in the kernel. [3] In a classical setting, two types of objects of equal amount are bijective (i.e. they have one-to-one matching), and this tight constraint ensures a perfect matching. The objective is to minimize the cost or maximize the profit of matching, since different items of two types have distinct affinity. [[File:Assignment.png|thumb|Figure 1. Classic model of assignment problem|alt=|267x267px]]A classic example is as follows: suppose there are <math> n </math> people (set <math> P </math>) to be assigned to <math> n </math> tasks (set <math> T </math>). Every task has to be completed and each task has to be handled by only one person, and <math> c_{ij} </math>, usually given by a table, measures the benefits gained by assigning the person <math> i </math> (in <math> P </math>) to the task <math> j </math> (in <math> T </math>). [4] The natural objective here is to maximize the overall benefits by devising the optimal assignment pattern. A graph of the general assignment problem and a table of preference are depicted as Figure 1 and Table 1.
{| class="wikitable sortable"
|+Table 1. Table of preference
!Benefits
!Task 1
! Task 2
!Task 3
!...
!Task n
|-
!Person 1
|0
|3
|5
|...
|2
|-
!Person 2
|2
|1
|3
|...
|6
|-
!Person 3
|1
|4
|0
|...
|3
|-
!...
|...
|...
|...
|...
|...
|-
!Person n
|0
|2
|3
|...
|3
|}
Figure 1 can be viewed as a network. The nodes represent people and tasks, and the edges represent potential assignments between a person and a task. Each task can be completed by any person. However, the person that actually ends up being assigned to the task will be the lone individual who is best suited to complete. In the end, the edges with positive flow values will be the only ones represented in the finalized assignment. [5]

To approach this problem, the binary variable <math> x_{ij} </math> is defined as whether the person <math> i </math> is assigned to the task <math> j </math>. If so, <math> x_{ij} </math> = 1, and <math> x_{ij} </math> = 0 otherwise.

The concise-form formulation of the problem is as follows [3]:

max <math>z=\sum_{i=1}^n\sum_{j=1}^n c_{ij}x_{ij}</math>

Subject to:

<math>\sum_{j=1}^n x_{ij}=1~~\forall i\in [1,n]
</math>

<math>\sum_{I=1}^n x_{ij}=1~~\forall j\in [1,n]
</math>

<math>x_{ij}=0~or~1~~\forall i,j\in [1,n] </math>

The first constraint captures the requirement of assigning each person to a single task. The second constraint indicates that each task must be done by exactly one person. The objective function sums up the overall benefits of all assignments.

To see the analogy between the assignment problem and the network flow, we can describe each person supplying a flow of 1 unit and each task demanding a flow of 1 unit, with the benefits over all “channels” being maximized. [3]

A potential issue lies in the branching of the network, specifically an instance where a person splits its one unit of flow into multiple tasks and the objective remains maximized. This shortcoming is allowed by the laws that govern the network flow model, but are unfeasible in real-life instances. Fortunately, since the network simplex method only involves addition and subtraction of a single edge while transferring the basis, which is served by the spanning tree of the flow graph, if the supply (the number of people here) and the demand (the number of tasks here) in the constraints are integers, the solved variables will be automatically integers even if it is not explicitly stated in the problem. This is called the integrality of the network problem, and it certainly applies to the assignment problem. [6]

==== The Transportation Problem ====
People first came up with the transportation problem when distributing troops during World War II. [7] Now, it has become a useful model for solving logistics problems, and the objective is usually to minimize the cost of transportation.

Consider the following scenario:

There are 2 chemical plants located in 2 different places: <math> M </math> and <math> N </math>. There are 3 raw material suppliers in other 3 locations: <math> F </math>, <math> G </math>, and <math> H </math>. The amount of materials from a supplier can be arbitrarily divided into two parts and shipped to two factories. Supplier <math> F </math>, <math> G </math>, and <math> H </math> can provide <math> S_1 </math>, <math> S_2 </math>, and <math> S_3 </math> amounts of materials respectively. The chemical plants located at <math> M </math> and <math> N </math> have the material demand of <math> D_1 </math> and <math> D_2 </math> respectively. Each transportation route, from suppliers to chemical plants, is attributed with a specific cost. This model raises the question: to keep the chemical plants running, what is the best way to arrange the material from the suppliers so that the transportation cost could be minimized?
[[File:Transportation problem example.png|thumb|Figure 2. Transportation problem example]]
Several quantities should be defined to help formulate the frame of the solution:

<math>S_{i}
</math> = the amount of material provided at the supplier <math>i
</math>

<math>D_{j}
</math> = the amount of material being consumed at the chemical plant <math>j
</math>

<math>x_{ij}
</math> = the amount of material being transferred from supplier <math>i
</math> to chemical plant <math display="inline">j
</math>

<math>C_{ij}
</math> = the cost of transferring 1 unit of material from supplier <math>i
</math> to chemical plant <math>j
</math>

<math>x_{ij}
</math><math>C_{ij}
</math> = the cost of the material transportation from <math>i
</math> to <math>j
</math>

Here, the amount of material being delivered and being consumed is bound to the supply and demand constraints:

(1): The amount of material shipping from supplier <math>i
</math> cannot exceed the amount of material available at supplier <math>i
</math>.

<math>\sum_j^n x_{ij}\ \leq S_{i} \qquad \forall i\in I=[1,m]
</math>

(2): The amount of material arrived at chemical plant <math>j
</math> should at least fulfill the demand at chemical plant <math>j
</math>.

<math>\sum_i^m x_{ij}\ \geq D_{j} \qquad \forall j\in J=[1,n]
</math>

The objective is to find the minimum cost of transportation, so the cost of each transportation line should be added up, and the total cost should be minimized.

<math>\sum_i^m \sum_j^n x_{ij}\ C_{ij}
</math>

Using the definitions above, the problem can be formulated as such:

min<math> \quad z = \sum_i^m \sum_j^n x_{ij}\ C_{ij}

</math>

<math>s.t. \quad\ \sum_j^n x_{ij}\ \leq S_{i} \qquad \forall i\in I=[1,m]
</math>

<math>\sum_i^m x_{ij}\ \geq D_{j} \qquad \forall j\in J=[1,n]
</math>

However, the problem is not complete at this point because there is no constraint for <math>x_{ij}
</math>, and that means <math>x_{ij}
</math> can be any number, even negative. In order for <math>x_{ij}
</math> to make sense physically, a lower bound of zero is mandatory, which corresponds to the situation where no material was transported from <math>i
</math> to <math>j
</math>. Adding the last constraint will complete this formulation as such:

min<math> \quad z = \sum_i^m \sum_j^n x_{ij}\ C_{ij}

</math>

<math>s.t. \quad\ \sum_j^n x_{ij}\ \leq S_{i} \qquad \forall i\in I=[1,m]
</math>

<math>\sum_i^m x_{ij}\ \geq D_{j} \qquad \forall j\in J=[1,n]
</math>

<math>x_{ij}\ \geq 0
</math>

The problem and the formulation is adapted from Chapter 8 of the book: Applied Mathematical Programming by Bradley, Hax and Magnanti. [3]

==== The Shortest-Path Problem ====
The shortest-path problem can be defined as finding the path that yields the shortest total distance between the origin and the destination. Each possible stop is a node and the paths between these nodes are edges incident to these nodes, where the path distance becomes the weight of the edges. In addition to being the most common and straightforward application for finding the shortest path, this model is also used in various applications depending on the definition of nodes and edges. [3] For example, when each node represents a different object and the edge specifies the cost of replacement, the equipment replacement problem is derived. Moreover, when each node represents a different project and the edge specifies the relative priority, the model becomes a project scheduling problem.
[[File:Shortest-Path.png|thumb|443x443px|Figure 3. General form of shortest-path problem]]
A graph of the general shortest-path problem is depicted as Figure 2:

In the general form of the shortest-path problem, the variable <math> x_{ij} </math> represents whether the edge <math> (i,j) </math> is active (i.e. with a positive flow), and the parameter <math> c_{ij} </math> (e.g. <math> c_{12} </math> = 6) defines the distance of the edge <math> (i,j) </math>. The general problem is formulated as below:

min <math>z=\sum_{i=1}^n \sum_{j=1}^n c_{ij}x_{ij}</math>

Subject to:

<math>\sum_{j=1}^n x_{ij} - \sum_{k=1}^n x_{ki} = \begin{cases} 1 & \text{if }i=s\text{ (source)} \\ 0 & \text{otherwise} \\ -1 & \text{if }i=t \text{ (sink)} \end{cases}</math>

<math>x_{ij}\geq 0~~\forall (i,j)\in E</math>

The first term of the constraint is the total outflow of the node i, and the second term is the total inflow. So, the formulation above could be seen as one unit of flow being supplied by the origin, one unit of flow being demanded by the destination, and no net inflow or outflow at any intermediate nodes. These constraints mandate a flow of one unit, amounting to the active path, from the origin to the destination. Under this constraint, the objective function minimizes the overall path distance from the origin to the destination.

Similarly, the integrality of the network problem applies here, precluding the unreasonable fractioning. With supply and demand both being integer (one here), the edges can only have integer amount of flow in the result solved by simplex method. [6]

In addition, the point-to-point model above can be further extended to other problems. A number of real life scenarios require visiting multiple places from a single starting point. This “Tree Problem” can be modeled by making small adjustments to the original model. In this case, the source node should supply more units of flow and there will be multiple sink nodes demanding one unit of flow. Overall, the objective and the constraint formulation are similar. [4]

==== Maximal Flow Problem ====
This problem describes a situation where the material from a source node is sent to a sink node. The source and sink node are connected through multiple intermediate nodes, and the common optimization goal is to maximize the material sent from the source node to the sink node. [3]

Consider the following scenario:
[[File:Picture2.png|thumb|Figure 4. Maximal flow problem example]]
The given structure is a piping system. The water flows into the system from the source node, passing through the intermediate nodes, and flows out from the sink node. There is no limitation on the amount of water that can be used as the input for the source node. Therefore, the sink node can accept an unlimited amount of water coming into it. The arrows denote the valid channel that water can flow through, and each channel has a known flow capacity. What is the maximum flow that the system can take?

Several quantities should be defined to help formulate the frame of the solution:
[[File:Picture3.png|thumb|Figure 5. For every intermediate node j, there is a group of node i and a group of node k.]]
For any intermediate node <math display="inline">j
</math> in the system, it receives water from adjacent node(s) <math>i
</math>, and sends water to the adjacent node(s) <math display="inline">k

</math>. The node <math>i
</math> and k are relative to the node <math display="inline">j
</math>.

<math>i
</math> = the node(s) that gives water to node <math display="inline">j
</math>

<math display="inline">j
</math> = the intermediate node(s)

<math display="inline">k

</math> = the node(s) that receives the water coming out of node <math display="inline">j
</math>

<math>x_{ij}
</math> = amount of water leaving node <math>i
</math> and entering node <math display="inline">j
</math> (<math>i
</math> and <math display="inline">j
</math> are adjacent nodes)

<math>x_{jk}
</math> = amount of water leaving node <math display="inline">j
</math> and entering node <math display="inline">k

</math> (<math>i
</math> and <math display="inline">k

</math> are adjacent nodes)

For the source and sink node, they have net flow that is non-zero:

<math display="inline">m
</math> = source node

<math display="inline">n
</math> = sink node

<math>x_{in}
</math> = amount of water leaving node <math>i
</math> and entering sink node <math display="inline">n
</math> (<math>i
</math> and <math display="inline">n
</math> are adjacent nodes)

<math>x_{mk}
</math> = amount of water leaving source node <math display="inline">m
</math> and entering node <math display="inline">k

</math> (<math display="inline">m
</math> and <math display="inline">k

</math> are adjacent nodes)

Flow capacity definition is applied to all nodes (including intermediate nodes, the sink, and the source):

<math>C_{ab}
</math> = transport capacity between any two nodes <math display="inline">a
</math> and <math display="inline">b
</math> (<math display="inline">a
</math><math> \neq
</math><math display="inline">b
</math>)

The main constraints for this problem are the transport capacity between each node and the material conservation:

(1): The amount of water flowing from any node <math display="inline">a
</math> to node <math display="inline">b
</math> should not exceed the flow capacity between node <math display="inline">a
</math> to node <math display="inline">b
</math> .

<math>0\leq x_{ab} \leq C_{ab}
</math>

(2): The intermediate node <math display="inline">j
</math> does not hold any water, so the amount of water that flows into node <math display="inline">j
</math> has to exit the node with the exact same amount it entered with.

<math>\sum_i^px_{ij}- \sum_k^r x_{jk} =0
\qquad \begin{cases} \forall i\in I=[1,p] \\ \forall j\in J=[1,q]\\ \forall k\in K=[1,r] \end{cases}
</math>

Overall, the net flow out of the source node has to be the same as the net flow into the sink node. This net flow is the amount that should be maximized.

Using the definitions above:
[[File:Picture4.png|thumb|Figure 6. The imaginary flow connects the sink node to the source node, creating a close loop.]]
min<math> \quad z = \sum_k^r x_{uk}

</math> (or <math>\sum_i^p x_{iv}

</math>)

<math>s.t. \quad\ \sum_i^px_{ij}- \sum_k^r x_{jk} =0
\qquad \begin{cases} \forall i\in I=[1,p] \\ \forall j\in J=[1,q]\\ \forall k\in K=[1,r] \end{cases}
</math>

<math>0\leq x_{ab} \leq C_{ab}
</math>

This expression can be further simplified by introducing an imaginary flow from the sink to the source.

By introducing this imaginary flow, the piping system is now closed. The mass conservation constraint now also holds for the source and sink node, so they can be treated as the intermediate nodes. The problem can be rewritten as the following:

min<math> \quad z = x_{vu}

</math>

<math>s.t. \quad\ \sum_i^px_{ij}- \sum_k^r x_{jk} =0
\qquad \begin{cases} \forall i\in I=[1,p] \\ \forall j\in J=[1,q+2]\\ \forall k\in K=[1,r] \end{cases}
</math>

<math>0\leq x_{ab} \leq C_{ab}
</math>

The problem and the formulation are derived from an example in Chapter 8 of the book: Applied Mathematical Programming by Bradley, Hax and Magnanti. [3]

=== Algorithms ===

== Numerical Example and Solution ==

A Food Distributor Company is farming and collecting vegetables from farmers to later distribute to the grocery stores. The distributor has specific agreements with different third-party companies to mediate the delivery to the grocery stores. In a particular month, the company has 600 ton vegetables to deliver to the grocery store. They have agreements with two third-party transport companies A and B, which have different tariffs for delivering goods between themselves, the distributor, and the grocery store. They also have limits on transport capacity for each path. These delivery points are numbered as shown below, with path 1 being the transport from the Food Distributor Company to the transport company A. The limits and tariffs for each path can be found in the Table 2 below, and the possible transportation connections between the distributor company, the third-party transporters, and the grocery store are shown in the figure below. The distributor companies cannot hold any amount of food, and any incoming food should be delivered to an end point. The distributor company wants to minimize the overall transport cost of shipping 600 tons of vegetables to the grocery store by choosing the optimal path provided by the transport companies. How should the distributor company map out their path and the amount of vegetables carried on each path to minimize cost overall?
[[File:Wiki example.png|thumb|Figure. 7. Illustration of the network for the food distribution problem.]]
{| class="wikitable"
|+Table 2. Product Limits and Tariffs for each Path
|
|1
|2
|3
|4
|5
|6
|-
|Product limit (ton)
|250
|450
|350
|200
|300
|500
|-
|Tariff ($/ton)
|10
|12.5
|5
|7.5
|10
|20
|}

This question is adapted from one of the exercise questions in chapter 8 of the book: Applied Mathematical Programming by Bradley, Hax and Magnanti [3].

=== Formulation of the Problem ===
The problem can be formulated as below where variables <math>x_1, x_2, x_3,..., x_6</math> denote the tons of vegetables carried in paths 1 to 6. The objective function stated in the first line is to minimize the cost of the operation, which is the summation of the tons of vegetables carried on each path multiplied by the corresponding tariff: <math>\sum_{i=1}^6 x_i t_i</math>.

<math>\begin{array}{lcl} \min z = 10x_1 + 12.5x_2 + 5x_3 + 7.5x_4 + 10x_5 + 20x_6 \\ s.t. \qquad x_5 = x_1 - x_3 + x_4 \\ \ \ \ \quad \qquad x_6 = x_2 + x_3 - x_4 \\ \ \ \ \quad \qquad x_5 + x_6 = 600 \\ \ \ \ \quad \qquad x_1 + x_2 = 600 \\ \ \ \ \quad \qquad x_1 \leq 250 \\ \ \ \ \quad \qquad x_2 \leq 450 \\ \ \ \ \quad \qquad x_3 \leq 350 \\ \ \ \ \quad \qquad x_4 \leq 200 \\ \ \ \ \quad \qquad x_5 \leq 300 \\ \ \ \ \quad \qquad x_6 \leq 500 \\ \ \ \ \quad \qquad x_1, x_2, x_3, x_4, x_5, x_6 \geq 0\\\end{array}

</math>

The second step is to write down the constraints. The first constraint ensures that the net amount present in the Transport Company A, which is the deliveries received from path 1 and path 2 minus the transport to Transport Company B should be delivered to the grocery store with path 5. The second constraint ensures this for the Transport Company B. The third and fourth constraints are ensuring that the total amount of vegetables shipping from the Food Distributor Company and the total amount of vegetables delivered to the grocery store are both 600 tons. The constraints 5 to 10 depict the upper limits of the amount of vegetables that can be carried on paths 1 to 6. The final constraint depicts that all variables are non-negative.

=== Solution of the Problem ===
This problem can be solved using Simplex Algorithm[15] or the GAMS optimization platform. The steps of the solution using the GAMS platform is as follows:

The first step is to list the variables, which are the tons of vegetables that will be transported in routes 1 to 6. The paths can be denoted as<math>x_1, x_2, x_3,..., x_6</math> . The objective function is the overall cost: z.

'''variables x1,x2,x3,x4,x5,x6,z;'''

The second step is to list the equations which are the constraints and the objective function. The objective function is a summation of the amount of vegetables carried in path i, multiplied with the tariff of path i for all i: <math>\sum_{i=1}^6 x_i t_i</math>

Overall, there are 10 constraints in this problem. The constraints c1, and c2 are equations for the paths 5 and 6. The amount carried in path 5 can be found by summing the amount of vegetables incoming to Transport Company A from path 1 and path 4, minus the amount of vegetables leaving Transport Company A with path 3. This can be attributed to the restriction that barrs the companies from keeping any vegetables and requires them to eventually deliver all the incoming produce. The equality c1 ensures that this constraint holds for path 5 and c2 for path 6.

Constraint c3 ensures that the sum of vegetables carried in path 1 and path 2 add to the total of 600 tons of vegetables that leave the Food Distributor Company. Likewise, the constraint c4 ensures that the sum amount of food transported in paths 5 and 6 adds up to 600 tons of vegetables that have to be delivered to the grocery store.

Constraints c5 to c10 show the maximum amount of food that can be transported in each path, as shown in the table.

'''equations obj,c1,c2,c3,c4,c5,c6,c7,c8,c9,c10;'''

'''obj.. z=e= 10*x1+12.5*x2+5*x3+7.5*x4+10*x5+20*x6;'''

'''c1.. x5 =e=x1-x3+x4;'''

'''c2.. x6=e=x2+x3-x4;'''

'''c3.. x5+x6=e=600;'''

'''c4.. x1+x2=e=600;'''

'''c5.. x1=l=250;'''

'''c6.. x2=l=450;'''

'''c7.. x3=l=350;'''

'''c8.. x4=l=200;'''

'''c9.. x5=l=300;'''

'''c10.. x6=l=500;'''

'''x1.lo=0;'''

'''x2.lo=0;'''

'''x3.lo=0;'''

'''x4.lo=0;'''

'''x5.lo=0;'''

'''x6.lo=0;'''

After listing the variables, objective function and the constraints, the final step is to call the solver and define the type of the optimization problem. In this case the problem will be solved with a Linear Programming algorithm to minimize the objective (cost) function.

'''model problem1 /all/ ;'''

'''solve problem1 using lp minimizing z;'''

The GAMS code yields the results below:

'''x1 = 250, x2 = 350, x3 = 0, x4 = 50, x5 = 300, x6 = 300, z =16250.'''

== Real Life Applications ==
Network problems have many applications in all kinds of areas such as transportation, city design, resource management and financial planning.[6]

There are several special cases of network problems, such as the shortest path problem, minimum cost flow problem, assignment problem and transportation problem.[6] Three application cases will be introduced here.

=== The minimum cost flow problem ===
[[File:Pic8.jpg|thumb|Figure. 8. Illustration of the ship subnetwork.[10]]]
[[File:Pic9.jpg|thumb|Figure. 9. Illustration of cargo subnetwork.[10]]]
Minimum cost flow problems are pervasive in real life, such as deciding how to allocate temporal quay crane in container terminals, and how to make optimal train schedules on the same railroad line.[8]

R. Dewil and his group use MCNFP to assist traffic enforcement.[9] Police patrol “hot spots”, which are areas where crashes occur frequently on highways. R. Dewil studies a method intended to estimate the optimal route of hot spots. He describes the time it takes to move the detector to a certain position as the cost, and the number of patrol cars from one node to next as the flow, in order to minimize the total cost.[9]

=== The assignment problem ===
Dung-Ying Lin studies an assignment problem in which he aims to assign freights to ships and arrange transportation paths along the Northern Sea Route in a manner which yields maximum profit.[10] Within this network composed of a ship subnetwork and a cargo subnetwork( shown as Figure 7 and Figure 8), each node corresponds to a port at a specific time and each arc represents the movement of a ship or a cargo. Other types of assignment problems are faculty scheduling, freight assignment, and so on.

=== The shortest path problem ===
Shortest path problems are also present in many fields, such as transportation, 5G wireless communication, and implantation of the global dynamic routing scheme.[11][12][13]

Qiang Tu and his group studies the constrained reliable shortest path (CRSP) problem for electric vehicles in the urban transportation network. [14] He describes the reliable travel time of path as the objective item, which is made up of planning travel time of path and the reliability item. The group studies the Chicago sketch network consisting of 933 nodes and 2950 links and the Sioux Falls network consisting of 24 nodes and 76 links. The results show that the travelers’ risk attitudes and properties of electric vehicles in the transportation network can have a great influence on the path choice.[14] The study can contribute to the invention of the city navigation system.

== Conclusion ==
Since its inception, the network flow problem has provided humanity with a straightforward and scalable approach for several large-scale challenges and problems. The Simplex algorithm and other computational optimization platforms have made addressing these problems routine, and have greatly expedited efforts for groups concerned with supply-chain and other distribution processes. The modelling of this problem has had several derivations from its original format, but its methodology and approach have remained prevalent in several of society’s industrial and commercial processes, even over half a century later. Classical models such as the assignment, transportation, maximal flow, and shortest path problem configurations have found their way into diverse settings, ranging from streamlining oil distribution networks along the gulf coast, to arranging optimal scheduling assignments for college students amidst a global pandemic. All in all, the network flow problem and it’s monumental impact, have made it a fundamental tool for any group that deals with combinatorial data sets. And with the surge in adoption of data-driven models and applications within virtually all industries, the use of the network flow problem approach will only continue to drive innovation and meet consumer demands for the foreseeable future.

== References ==
1. Karp, R. M. (2008). George Dantzig’s impact on the theory of computation. Discrete Optimization, 5(2), 174-185.

2. Goldberg, A. V. Tardos, Eva, Tarjan, Robert E. (1989). Network Flow Algorithms, Algorithms and Combinatorics. 9. 101-164.

3. Bradley, S. P. Hax, A. C., & Magnanti, T. L. (1977). Network Models. In Applied mathematical programming (p. 259). Reading, MA: Addison-Wesley.

4. Chinneck, J. W. (2006). Practical optimization: a gentle introduction. Systems and Computer Engineering), Carleton University, Ottawa. http://www.sce.carleton.ca/faculty/chinneck/po.html, 11.

5. Roy, B. V. Mason, K.(2005). Formulation and Analysis of Linear Programs, Chapter 5 Network Flows.

6. Vanderbei, R. J. (2020). Linear programming: foundations and extensions (Vol. 285). Springer Nature.

7. Sobel, J. (2014). Linear Programming Notes VIII: The Transportation Problem.

8. Altınel, İ. K., Aras, N., Şuvak, Z., & Taşkın, Z. C. (2019). Minimum cost noncrossing flow problem on layered networks. Discrete Applied Mathematics, 261, 2-21.

9. Dewil, R., Vansteenwegen, P., Cattrysse, D., & Van Oudheusden, D. (2015). A minimum cost network flow model for the maximum covering and patrol routing problem. European Journal of Operational Research, 247(1), 27-36.

10. Lin, D. Y., & Chang, Y. T. (2018). Ship routing and freight assignment problem for liner shipping: Application to the Northern Sea Route planning problem. Transportation Research Part E: Logistics and Transportation Review, 110, 47-70.

11. Tu, Q., Cheng, L., Yuan, T., Cheng, Y., & Li, M. (2020). The Constrained Reliable Shortest Path Problem for Electric Vehicles in the Urban Transportation Network. Journal of Cleaner Production, 121130.

12. Guo, Y., Li, S., Jiang, W., Zhang, B., & Ma, Y. (2017). Learning automata-based algorithms for solving the stochastic shortest path routing problems in 5G wireless communication. Physical Communication, 25, 376-385.

13. Haddou, N. B., Ez-Zahraouy, H., & Rachadi, A. (2016). Implantation of the global dynamic routing scheme in scale-free networks under the shortest path strategy. Physics Letters A, 380(33), 2513-2517.

14. Tu, Q., Cheng, L., Yuan, T., Cheng, Y., & Li, M. (2020). The Constrained Reliable Shortest Path Problem for Electric Vehicles in the Urban Transportation Network. Journal of Cleaner Production, 121130.

15. Hu, G. (2020, November 19). Simplex algorithm. Retrieved November 22, 2020, from [[Simplex algorithm|https://optimization.cbe.cornell.edu/index.php?title=Simplex_algorithm]].

Network flow problem

2020-11-24T18:15:37Z

Aw843cornell: /* References */ and conclusion

Network flow problem

2020-11-21T03:03:55Z

Aw843cornell: first paste

Author: Ruobing Shui (CHEME 6800 Fall 2020)

Steward: Allen Yang, Fengqi You

Introduction:

Network flow problems arise in several key instances and applications within society and have become fundamental problems within computer science, operations research, applied mathematics, and engineering. Developments in the approach to tackle these problems resulted in algorithms that became the chief instruments for solving problems related to large-scale systems and industrial logistics. Spurred by early developments in linear programming, the methods for addressing these extensive problems date back several decades and they evolved over time as the use of digital computing became increasingly prevalent in industrial processes. Historically, the first instance of an algorithmic development for the network flow problem came in 1956, with the network simplex method formulated by George Dantzig [ref]. A variation of the simplex algorithm that revolutionized linear programming, this method leveraged the combinatorial structure inherent to these types of problems and demonstrated incredibly high accuracy [ref]. This method and its variations would go on to define the embodiment of the algorithms and models for the various and distinct network flow problems discussed here.

Theory:

Qualitatively, the network flow problem can be conceptualized as a directed graph which abides by certain flow capacity constraints at its edges and equates the values entering and exiting its vertices at all points besides terminal source and sink terms. The vertices in this problem are the origins, destinations, and intermediate points and are referred to as nodes. The edges are the directional transportation links between these nodes and are referred to as arcs [ref]. Models for network flow problems function as tools for computing the net flow of units along these constrained arcs and between pairs of nodes, and are useful for quantifying logistical interests such as the optimal scheme for the distribution of a product from a plant to it’s consumer constituents. In this scenario, the product departs from the distribution source (origin) and travels through a network of intermediary transition points such as warehouses and fulfillment centers (nodes), before finally reaching the consumer market (destination). Along this journey, the transportation method along the route (arc) may be subjected to certain restraints such as the allowable amount of product carried between points (capacity constraints). The objective function in this case would be to minimize the cost of shipping the product whilst still meeting a specified demand. This exact circumstance is very common in industrial logistics and was the primary motivation for defining and solving the network flow problem [ref]. This case, the transportation problem, was the beginning of a wide assortment of problems defined for network flow by leveraging it’s combinatorial structure in a special-purpose algorithm.

Historically, the classic network flow problems are considered to be the maximum flow problem and the minimum-cost circulation problem, the assignment problem, bipartite matching problem, transportation problem, and the transshipment problem [ref]. The approach to these problems become quite specific based upon the problem’s objective function but can be generalized by the following iterative approach: 1. determining the initial basic feasible solution; 2. checking the optimality conditions (i.e. whether the problem is infeasible, unbounded over the feasible region, optimal solution has been found, etc.); and 3. constructing an improved basic feasible solution if the optimal solution has not been determined [ref].