# 2021 Cornell Optimization Open Textbook Feedback

## Lagrangian duality

- Author list, sections and TOC
- Section titles should use normal font. Please double check using source editor and avoid HTML formatting on the section titles.
- Remove cornell ID from Author list

- An introduction of the topic
- This section includes sentences on constructing the dual problem and is referred to as Lagrangian relaxation (LR). This is incorrect, please fix the definition of LR.
- Definitions of LR and its relation to duality should be double checked and re-written.
- Only one reference is present in this section. Please add more relevant references by expanding this section.
- Consider merging the “introduction” and “history” sections.
- In the titles, please change the font from bold to normal to have consistent formatting in the site.

- Theory, methodology, and/or algorithmic discussions
- The Lagrangian variables associated with equality constraints h(x) are unbounded but the Lagrangian dual problem states them as non-negative. Please fix the same.
- Also to construct a dual, we do not change minimization to maximization directly. We observed such things in the examples in lecture notes due to simplification. The lagrangian dual problem would be minimize (,).
- Adding to the previous point, the Lagrangian is a lower bound on the original objective; the solution to the primal and dual or only equivalent if the duality gap is 0. You reference this in one section, but this is after your statement “Hence, solving the dual problem, which is a function of the Lagrangian multipliers (𝜆*) yields the same solution as the primal problem, which is a function of the original variables (x*). “. Please clarify the specific conditions that must hold for the solution of the dual to be equal to the primal’s.
- You refer to the “Complementary Slackness Theorem”, but don’t actually write the mathematical representation of complementary slackness. Please fix this. Also consider including the derivation of the complementary slackness condition, as it is both easy and short. Boyd is a good reference for this.
- Last step of the “process” subsection also needs updating according to the previous comments.
- The inline notations should also be typed using LaTex.
- Please use the LaTex code or equation editor for min, s.t., etc.

- At least one numerical example
- Only one dual variable is associated with each constraint. The numerical example uses two for the first and second constraint which is unnecessary. Please update it accordingly for both constraints. This particular example will only have two dual variables instead of the five dual variables used currently.
- All consecutive steps need to be updated since the dual variables would be updated.
- After substitution the nonlinear function should be further simplified. The current expression reads like a highly nonlinear function but can be easily simplified.
- Similar to the comments in the methodology section, inverting minimize to maximize is incorrect. Please update the dual objective function accordingly.
- Please use the LaTex code or equation editor for min, s.t., etc.

- A section to discuss and/or illustrate the applications
- Bullet points could be used to state the last four real-world examples that explain the physical meaning of the primal and dual problems.
- Add references for the last set of applications.

- A conclusion section
- This section contains a few typos. Please fix the same.

- References

## Disjunctive Inequalities

- Author list
- Missing course section and semester
- Remove cornell ID

- An introduction of the topic

- No citations are present in this section.
- “mixed-integer programming (MIP)” should be used instead of “multiple integer programming (MIP)”. Please fix this error.

- Theory, methodology, and/or algorithmic discussions
- The abbreviation MILP is not previously defined. Please fix this issue.
- You consistently use the negative sign instead of the NOT operator for y (-y instead of ¬y).
- Some inconsistencies with the spacing of variables, constraints, etc., under the “General” section that need to be fixed.
- Typo in “This is shown below by M1, M2, y1, and y1:” where y1 needs to be changed to y2. Why use two different Big-M variables here? Elsewhere in the Wiki you only use one so this could lead to confusion with a general audience. Also if this was taken from the lecture notes then it needs to be cited.

- At least one numerical example
- Please reformulate and solve a complete numerical example rather than just reformulating a general example. Demonstrate the use of Big-M and Convex Hull formulation in an optimization problem that provides details such as individual steps in the problem solving process and final results.
- Add space between vee (V) operator and brackets in first line of Latex
- Please format variables correctly, for example, use x1 instead of x1.

- A section to discuss and/or illustrate the applications
- Please format the equations appropriately either by using latex code or the visual editor, and NOT an image.

- A conclusion section
- 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.
- Please consider linking the references as demonstrated in the Wiki tutorial on Canvas and in this template, https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization

## 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
- 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

## Exponential Transformation

- Author list
- Missing course section
- Remove cornell ID

- An introduction of the topic
- Please expand the introduction.
- Please aim for a maximum average sentence length of ~25 words. Last sentence with 51 words is hard to read.
- Second Sentence: please change the word “they” as it could make the meaning ambiguous
- If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.
- If you use abbreviations, please introduce them (e.g. NLP,MINLP)

- Theory, methodology, and/or algorithmic discussions
- Please explain the transformation in words along with equations
- Terms like posynomial should be described in detail.
- Please move the numerical example to the section below
- The “(eq 1)” is not needed here.
- Please expand this section.

- At least one numerical example
- In the third equation of the numerical example, it is confusing to have coefficients after numbers. Some readers may read it as an exponent.
- Last equation in this section after “further linearization” is incorrect. This equation cannot be further linearized, please fix this.

- A section to discuss and/or illustrate the applications
- Missing part of text: “Proof of convexity of with positive definite test of Hessian…”
- Applications are not numerical examples. Please refer to this link for example of applications: 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, https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization
- Citation 7 is missing in current applications

## Sparse reconstruction with Compressed Sensing

This Wiki needs a significant rewrite. Please go through the comments for details.

- An introduction of the topic
- The introduction section should include information about the problem and its implications presented briefly. Please use full sentences to write this Wiki. You may use tools like Grammarly to check sentence formation and grammar.
- This section includes several typos like “sub modual”. Please fix them throughout the wiki and delete them if not required.
- Many abbreviations are used before previously defining them. Please define these abbreviations before using them in the text.
- This section is incomprehensible in its current form. Please rewrite with proper comprehension.
- Equations and math symbols need proper reformatting. The current version reads like text (along with equations) copy-pasted from a specific source.
- Try to place the figure at the top of the Wiki between the main text.
- Avoid pronouns such as “we”.
- I suggest the use of more formal abstract illustrations.

- Theory, methodology, and/or algorithmic discussions
- Equations and symbols need proper reformatting.
- Lemmas and theorems are not expected for this Wiki. Sparse reconstruction is a straightforward concept but is unnecessarily complicated here. Please refer to other Wiki examples to get an idea of what the Wiki should convey.

- At least one numerical example
- Numerical example is missing.

- A section to discuss and/or illustrate the applications
- Having a list is not enough. Please explain at least three applications in a few sentences each.

- A conclusion section
- Conclusion section is missing.

- References
- The current reference list is not correctly formatted. References should be properly formatted, not just hyperlinks. Refer to the link below for an example: https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization

## Portfolio Optimization

- Author list
- Remove cornell id

- An introduction of the topic
- The introductory sentence should be rephrased. The action of minimizing the risks does not inherently maximize the gains, rather PO aims to maximize gains whilst minimizing risks.
- Amount of whitespace can be reduced by changing the orientation of Figure 1 and the sentences in this section.
- Define terms such as risk, return, portfolio, etc., when you introduce them. Assume that the reader may not know much about finance. This goes for all other sections as well.

- Theory, methodology, and/or algorithmic discussions
- A brief mention of modern portfolio theory (i.e.. Markowitz) would be appropriate in this section.
- Several grammatical errors here involving sentence structure and clarity. Some questionable semantics (e.g., “The portfolio optimization mainly assumes two directions.”) and syntax (phrases such as “.. is as follows” should be followed by a colon). Misuse of commas and missing commas in this section. Two sentences introducing E(rp) and w should be combined into one.
- Use LaTex to distinguish variables written within a sentence, such as m and n.
- Rephrase “Cut the relevant information and conditions in the portfolio optimization, as well as the final requirements into the relevant variables, constraints and linear functions of the linear programming problem.”
- An explanation of a few common constraints would be helpful, rather than just including a table.

- At least one numerical example
- All tables need to be labeled.
- Include figure number in label for consistency.
- Fix misspelling “dolling decision variables”.
- Use LaTex for all variables, equations, and constraints here.
- Example 2 table is hard to read, so making it bigger would help.
- Remove the “Using excel as the solver” part from the sentence before the solution discussion.
- Some grammatical errors here (phrases such as “.. is as follows” should be followed by a colon).

- A section to discuss and/or illustrate the applications
- Rephrase “Portfolio optimization can be used to screen investment projects that meet investors, rationally allocate investment amounts, etc.”
- Not sure “relevant” is the correct word choice here.
- You need more specific examples with the utility of portfolio optimization, this section is quite general as is. Some more detail and focus on real-world applications in the financial industry that relate to retirement planning, financial security, economic stability, etc., would be helpful.

- A conclusion section
- Need some commas here.
- The sentence “Linear programming has been around since the 1940’s and has such a wide base of applications” is not necessary.

- References
- Please consider linking the references as demonstrated in the Wiki tutorial on Canvas and in this template, 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

- Author list:
- An introduction of the topic
- Please consider correcting a few grammatical errors: “pre-planned for”, “god”, “certain levels of feasibility is guaranteed in what are”, and “Performance of a system”
- In “Chance-constraint”, it is capitalized randomly throughout the introduction. Please correct.
- Please use technical language to briefly introduce chance-constrained programming. Words like “acts of god”, “cost of doing business” are not appropriate for a technical Wiki.

- Theory, methodology, and/or algorithmic discussions
- Please add a citation to the first sentence.
- Xi is an uncertainty/randomness variable. It is better to use clear language.
- Please use the mathematical editor for adding explanations in the text. Using “ x is a decision variable” is hard to read. Same for f(x) and others.
- Theory is insufficient. Please expand and explain different approaches.
- Please add pros and cons explicitly as a list.
- Explain the physical meaning for examples of chance constraints along with all the notations used.

- At least one numerical example
- Please use the equation editor for min, st., etc.
- Please use the mathematical editor for adding explanations in the text. Using “ x is a decision variable” is hard to read. Same for f(x) and others.
- Please change the table format so as not to confuse the reader.
- Multiple instances of [Chart to be added] are missing.
- Example is incomplete.
- Avoid pronouns such as “we”.

- A section to discuss and/or illustrate the applications
- Please connect several grammatical and spelling errors: “real life application”, Energy creation, particularly in renewable sources, have high variabilities”, and others
- “Zhao, Xue, Cao, and Zhang”. No need to list all authors within the article. Provide a reference is sufficient. If authors must be mentioned, (Zhao et al.) should be ok.

- A conclusion section
- Uniqueness and universality earlier are not clear to me. If they are not discussed earlier in the application, it would be better not to introduce new discussions in the conclusion.
- If you cite an example on the page, as in the last sentence, please provide a link to move the reader to the section/subsection.

- References
- References seem to vary in format. Please consider having the references as this Wiki template, https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization

## Bayesian Optimization

- Contents: Subheadings for EI and the algorithm should not be bolded, Random words should not be capitalized.
- Author list: Remove cornell ID, Please check names
- Introduction
- The introduction is too general and not substantial enough. For example, simply saying BayesOpt is useful when the objective function is unknown obscures exactly HOW it is useful (namely, computational efficiency in applications where ground truth sampling is expensive). Discussion on applications should be moved to a separate section.
- Machine learning rarely includes black-box functions to be optimized. Bayesian optimization is almost never used for optimizing ML loss functions but can instead be used for hyperparameter optimization. Please update such claims in this section.

- Theory, methodology, and/or algorithmic discussions
- Captions need reformatting.
- Consider italicizing keywords rather than bolding.
- Please add a citation to the first sentence.
- Discussion on acquisition functions should include comparisons, tradeoffs, and reasons to use one over the other. Should also note that expected improvement is the most widely used in practice, and explain.
- Avoid pronouns such as “we”.
- Please write equations in the Wiki instead of attaching images for equations.
- Acquisition function figure could be made larger and clearer to improve readability.

- At least one numerical example
- Any references to functions or methods in code ‘e.g. fmin’ should be properly formatted as code-stylized text.
- Please use the equation editor for min, st., etc.
- Avoid including a figure of the code for this example and explicitly describe the steps to the modeling and solution process instead.
- Avoid pronouns such as “our” and “we”.

- A section to discuss and/or illustrate the applications
- A conclusion section
- Please do not use brackets to enclose lists.
- Some claims here should be supported by references. Please cite each source after its sentence.

- References
- References should be properly formatted, not just hyperlinks. Refer to the link below for an example: https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization
- Try to avoid references to “pop” machine learning blogs where anyone can be an author. (e.g. towardsdatascience)

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

## Conjugate gradient methods

- Author list: Remove cornell ID
- Introduction
- All inline notations (e.g., `x`, `A`) should be typed using LaTex.

- Theory, methodology, and/or algorithmic discussions
- Is Gauss-Newton no longer referenced?
- Theorems listed in the first section should be accompanied with high level explanation, not just a list of the theorems themselves. The page should read like an article, with proper flow.
- Please indent equation blocks.
- Please properly format pseudocode.

- At least one numerical example
- Steps should be accompanied with explanation, or reference to the corresponding step in the pseudocode.

- A section to discuss and/or illustrate the applications
- Consider including 2 additional examples of applications

- A conclusion section
- Consider adding future research directions

- References
- Reference primary sources rather than Wikipedia
- Too few references.

## Geometric Programming

- 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, https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization

## Adam

- Author list
- An introduction of the topic
- Some grammatical errors here, mostly related to the need for commas in certain places (e.g., “Before Adam..”).
- Some minor errors with parts of speech throughout the section, need to revisit phrases such as “which has broader scope in future for”, etc.
- Try splitting up some of the longer sentences in this section, a couple are hard to read.
- Avoid definitive statements about Adam being the best or always better solver, as this is simply not true (the choice of the “best” optimizer is setting-dependent). Use language such as “Research has shown that Adam has demonstrated superior experimental performance over..” and then cite academic references to back this claim.
- What does adam stand for? Introduction is insufficient. Please expand.

- Theory, methodology, and/or algorithmic discussions
- Revise grammar here, noticing some missing commas and uncapitalized word after period.
- Rephrase “second one is to update the old position with the updated position”.
- Use LaTex code or equation editor to display all equations and variables in this section, and actual subscripts instead of “m_t”, etc.
- Avoid inserting inline citations after words like “According to..” or “This article..” as it is a bit informal. This could be rephrased or changed to something like “According to author,^[2] …” with author name inserted.
- Remove white space before the period in RMSP discussion.
- Please provide a pseudocode.
- Please use list the two methods here “Adam is a combination of two gradient descent methods which are explained below”
- Please expand the theory section significantly. Theoretical convergence properties should be discussed, even if briefly.

- At least one numerical example
- 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: https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization
- Try to avoid references to blogs and use peer-reviewed academic references instead.
- Too few references.

## a* algorithm

- Author list:
- Remove cornell ID

- An introduction of the topic:
- In the titles, please change the font from bold to normal to have consistent formatting in the site.
- Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.
- There are no citations in the introduction. Please cite every source.

- Theory, methodology, and/or algorithmic discussions
- Please add the mathematical description of the algorithm.
- Reference style varies in sentences. Please consider having the references as this Wiki template, https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization
- Please fix grammatical and spelling errors as (“from current position to the goal”, “There are a lot of discussions”, etc). Also, many hyphens are missing as “non playable”.
- In algorithms, it is a standard to add high-level description (i.e. pseudocode or flowchart). Please incorporate it.
- Use LaTex code or equation editor to display all equations and variables in this section (e.g., “f(n)...”, “h(n)..”, etc.). This goes for other sections as well.

- At least one numerical example
- The numerical example does not show the full computations the algorithm performs. Please show the computation on a smaller example.
- Instead of writing things like “The above image..”, label each figure and use the figure number to refer to it in text.

- A section to discuss and/or illustrate the applications
- No references in the applications. Please cite every source
- Preferably, add at least an additional application.

- A conclusion section
- Conclusion should summarize descriptions. Please modify it to provide a summary.
- Please pay attention to the length and structure of sentences here and in the full page. First sentence is hard to read.

- References
- References seem to vary in format and are not linked correctly. Please consider having the references as this Wiki template, https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization

## Job-Shop Scheduling Problem

- An introduction of the topic
- The current introduction to the jobshop scheduling problem has only two sentences in addition to the parameter description. Introduction typically contains information about the problem, its importance in the real-world, and some information about the solution techniques and their types to solve the problem. Please add some information that covers the above.

- Theory, methodology, and/or algorithmic discussions
- It is unclear whether the assumptions stated in this section are required to apply the following solution techniques. Please clarify the same. Also use complete sentences to state them.
- The branch and bounds method described in this section only discusses the solution technique for problems with one machines. However, branch and bound is a general technique that can be applied to any MILP problems with varying scales. Please update the “methods” section to be as general as possible.
- Since this Wiki focuses on jobshop scheduling, at least two methods are expected. Branch and bound is a general MILP technique, so, it is recommended to add a tailored technique that can only solve specific jobshop scheduling problems. Solving the numerical example with this technique is not necessary.
- Reference to the branch and bound technique described in this section is a “youtube” video. Please add references in literature that describe this method in detail. The method used in this video is highly tailored for a single machine application. This is also an incorrect way to cite a reference. Please keep this section as general as possible.
- Use LaTex code or equation editor to display all equations and variables in this section and all other sections as well.
- Check grammar in this section. For example, phrases like “are as follows” need to be followed by a colon and not a period.
- Consider rewriting the assumptions as a list in this section.

- At least one numerical example
- The example used in this section is exactly the same as the one in the youtube video. Please use a modification of this example or choose another example/method to demonstrate the solution technique.
- The figure in this section is not numbered when all others are. Relabel this figure for consistency and its number to refer to it in-text.

- A section to discuss and/or illustrate the applications
- This section should only focus on real-world applications of the jobshop scheduling problem. But currently, this section includes additional information on solution techniques/complexity that is appropriate for the Introduction section. Please discuss the applications of the problem in this section.

- A conclusion section
- The meaning of “Operations applications” is unclear. Please explain or update if necessary.
- The current conclusion section does not properly summarize the problem. Please refer to other Wiki examples for an idea to update the section accordingly.

- References
- Include hyperlinks to references if possible. Please consider having the references appear as in this Wiki template, https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization
- Please reference media sources like reference 5 appropriately.

## 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, https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization

- Theory, methodology, and/or algorithmic discussions
- Please edit references.
- Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm.
- Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.

- At least one numerical example
- Please organize the last part in a more readable format. Questions may be in bold and numbered, answers are more direct, etc.
- Remember to cite all images and tables.

- A section to discuss and/or illustrate the applications
- Very good, link the reference and cite all sources.

- A conclusion section
- Please add more summarizing especially from theory sentences and avoid long sentences.

- References
- Please consider having the references as this Wiki template, https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization
- Reference primary sources rather than Wikipedia

## 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, 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”.

- Organization of ideas in this section needs work.
- At least one numerical example
- Any code functions (uminfunc) should have proper text formatting.
- The graph needs a better caption explaining how the axes are labeled and what data points are being shown.
- Please increase the quality of the figure. It is hard to see the red line.
- Add citation to “The Rosenbrock function is a non-convex function, introduced by Howard H. Rosenbrock in 1960, which is often used as a performance test problem for optimization algorithms.”

- A section to discuss and/or illustrate the applications
- The content in this section as it is currently does NOT describe applications, but rather different approaches within the trust region methodology. Please provide specific applications (e.g. TRPO in reinforcement learning).

- A conclusion section
- Please add more summary, future research directions for example is a good start.

- References
- Please consider having the references as this Wiki template, https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization

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
- It is important to use technical language for this Wiki. Although a layman’s explanation is appreciated, it would be better to skip using words like “zig zagging”. Try to explain all concepts in a technical language with few simplifications but NOT vice versa.
- The definition of the update rule for SGD with momentum looks incorrect, specifically the first expression. Please fix it and also explain all the parameters used.
- Use LaTex code or equation editor to display all equations and variables (e.g., “W”, “V`”, etc.) in this section and all other sections as well.
- Avoid pronouns such as “you”.

- At least one numerical example
- Please try to label the plots that explains what each line color means.

- A section to discuss and/or illustrate the applications
- Please use correct terminology like “optimizing non-convex functions” and not “training non-convex models”.
- Adam, Adadelta, and RMSprop are variants of SGD that already use momentum. Please double check the writing and update if necessary.

- A conclusion section
- Please refrain from using words like “zig zag” effects.

- References
- Almost all references used are URLs. Please try to add journal/conference articles or books for references, instead of directly citing the URLs.

## Stochastic Dynamic programming

- 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
- 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, https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization

## 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 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
- “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.
- 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

## 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
- 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
- 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
- Please show at least a few iterations. Even for smaller examples if needed. Report the final solution.
- Please use the LaTex code or equation editor for min and include s.t., etc.

- A section to discuss and/or illustrate the applications:
- A conclusion section
- Same as the introduction. Pros and cons should be evaluated together!

- References

## 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: https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization

## 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

- 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.
- 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

## Wing shape Optimization

- Author list
- Remove cornell ID

- An introduction of the topic
- The introduction is missing several references (e.g., “software packages like computational fluid dynamics..”, sentences containing things that aren’t common knowledge, performance claims, etc.)
- Avoid discussion involving finer details of subject methods in this section.
- In the titles, please change the font from bold to normal to have consistent formatting in the site. Same applies to box of content!

- Theory, methodology, and/or algorithmic discussions
- Properly cite the CFD package, don’t just include a link.
- Properly label the figure with a figure number.
- Consider removing white space between isolated sentences to improve readability.

- At least one numerical example
- If you’ve already defined an abbreviation (CFD), there is no need to define it again. Just use the abbreviation.
- Avoid pronouns such as “we” or “they”.
- Phrases like “under the following” need to be followed by a colon.
- Properly label the figure with a figure number and consider making them larger to improve visibility. Call the reader's attention to the figures in text by referencing the figure number.
- “As seen in the video below” is stated yet there are only images present and it may be initially unclear to the reader which figure is being referenced here.
- Avoid inserting inline citations like “[4] introduces an..” as it is a bit informal when you don’t explicitly name the subject.
- Don’t just cite the reference when discussing the problem formulation, explicitly write the model formulation and solution process using LaTex or equation visual editor.

- A section to discuss and/or illustrate the applications
- Some characters are randomly capitalized in this section.

- A conclusion section
- These variables should be defined before the conclusion section, they are out of place here. Also, please use normal text when explaining variables except for the variable symbol.

- References

## 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.

- References

## 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

- Author list: OK but I suggest removing NetID
- 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, 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.

- A conclusion section:
- References
- References are not expressed correctly. Please consider having the references as this Wiki template, https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization