2021 Cornell Optimization Open Textbook Feedback

Lagrangian duality

• Author list, sections and TOC

1. Section titles should not be "bold". Please double check using source editor and avoid HTML formatting on the section titles.
2. Remove cornell ID from Author list

• An introduction of the topic

1. 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.
2. Definitions of LR and its relation to duality should be double checked and re-written.
3. Only one reference is present in this section. Please add more relevant references by expanding this section.
4. Consider merging the “introduction” and “history” sections.
5. In the titles, please change the font from bold to normal to have consistent formatting in the site.

• Theory, methodology, and/or algorithmic discussions

1. 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.
2. 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 (,).
3. 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.
4. 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.
5. Last step of the “process” subsection also needs updating according to the previous comments.
6. The inline notations should also be typed using LaTex.
7. Please use the LaTex code or equation editor for min, s.t., etc.

• At least one numerical example

1. 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.
2. All consecutive steps need to be updated since the dual variables would be updated.
3. After substitution the nonlinear function should be further simplified. The current expression reads like a highly nonlinear function but can be easily simplified.
4. 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.
5. Please use the LaTex code or equation editor for min, s.t., etc.

• A section to discuss and/or illustrate the applications

1. Bullet points could be used to state the last four real-world examples that explain the physical meaning of the primal and dual problems.
2. Add references for the last set of applications.

• A conclusion section

1. This section contains a few typos. Please fix the same.

• References

1. Some citations' hyperlinks are displaying.

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

• An introduction of the topic

1. 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;

1. I suggest eliminating citing the last name of the first author (i.e. Zhou et al.)

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

• Author list

• An introduction of the topic

• Theory, methodology, and/or algorithmic discussions

1. 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

1. Fix misspelling “dolling decision variables”.

• A section to discuss and/or illustrate the applications

• A conclusion section

1. Need some commas here (second sentence hard to read).

• References

1. Remove white space between end of sentences and reference numbers.

Chance constraint method

• Author list:
• An introduction of the topic

• Theory, methodology, and/or algorithmic discussions

1. 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

1. Discussion on applications should be moved to a separate section.

• Theory, methodology, and/or algorithmic discussions

1. Captions need reformatting.
2. Consider italicizing keywords rather than bolding.
3. Please add a citation to the first sentence.
4. Avoid pronouns such as “we”.
5. Acquisition function figure could be made larger and clearer to improve readability.

• At least one numerical example

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

• References

1. 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

Conjugate gradient methods

• Theory, methodology, and/or algorithmic discussions

1. All equations need to be better formatted.
2. Please indent equation blocks.
3. Please properly format pseudocode.

• A conclusion section

1. Consider adding future research directions

Geometric Programming

• Author list

1. Remove cornell ID

• An introduction of the topic

1. Examples of applications in this section use the same reference. Please cite their individual sources.

• Theory, methodology, and/or algorithmic discussions

1. The symbol denoting the domain in the definition of a monomial is unclear. Please clarify it or fix this if it is incorrect.
2. Definition of posynomial refers to section 2.1 which is missing from the Wiki (sections are not numbered in the main text).
3. 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.
4. Additional theory on the feasibility analysis could be provided in this section.

• At least one numerical example

1. 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

1. The figure in this section needs to be labeled.
2. The figure needs to be resized and perhaps aligned to the center.  

• A conclusion section:

1. Please avoid vague language such as: “This makes”.
2. Please avoid opinionated statements: “one of the best ways”.

• References

1. 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
2. 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

1. 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* algorithm

• Author list
• An introduction of the topic:

1. Please consider correcting a few grammatical errors: “Optimal path”, “cross country”, missing period at end of first paragraph, other random capitalizations, etc.
2. There are no citations in the introduction. Please cite every source.

• Theory, methodology, and/or algorithmic discussions

1. Please add the mathematical description of the algorithm. (Insufficient)
2. 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

1. 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 Problem

• An introduction of the topic

1. 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

1. 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.
2. 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.
3. 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.
4. 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.
5. Use LaTex code or equation editor to display all equations and variables in this section and all other sections as well.
6. Check grammar in this section. For example, phrases like “are as follows” need to be followed by a colon and not a period.
7. Consider rewriting the assumptions as a list in this section.

• At least one numerical example

1. Every iteration should be clearly presented, and solved "step-by-step".
2. 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.
3. 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.
4. 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

1. 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

1. The meaning of  “Operations applications” is unclear. Please explain or update if necessary.
2. 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

1. 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
2. Please reference media sources like reference 5 appropriately.
3. 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

1. 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

1. Why only a subsection on "Nash Equilibrium" is included in "Theory" section? Please re-format.
2. Please edit references.
3. Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm.  
4. 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

1. Please organize the last part in a more readable format. Questions may be in bold and numbered, answers are more direct, etc.
2. Remember to cite all images and tables.
3. 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

1. Very good, link the reference and cite all sources.

• A conclusion section

1. Please add more summarizing especially from theory sentences and avoid long sentences.

• References

1. Please consider having the references as this Wiki template, https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization
2. Reference primary sources rather than Wikipedia
3. Incorrect reference style. Please correct.

Trust-region methods

• An introduction of the topic
  • Avoid pronouns such as “we”. This goes for all other sections as well.

• Theory, methodology, and/or algorithmic discussions

1. Organization of ideas in this section needs work.
2. 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.
3. Please format the algorithm in proper algorithmic pseudocode format.

• References

1. Incorrect reference style.

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

Momentum

• An introduction of the topic

1. 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.
2. Remove bold on “Momentum”.
3. 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

2. 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.
3. 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.
4. Avoid pronouns such as “you”.

• At least one numerical example

1. 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.
2. Please try to label the plots that explains what each line color means.
3. 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

1. Please use correct terminology like “optimizing non-convex functions” and not “training non-convex models”.

• References

1. 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

• Author list

1. Remove cornell ID

• An introduction of the topic

1. Discussion on applications should be moved to a separate section.

• Theory, methodology, and/or algorithmic discussions

1. 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

1. 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

1. See formatting guideline below
2. Avoid opinionated statements such as “MINLP problems are usually the hardest to solve”.
3. 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

1. Consider left aligning equations and optimization problem formulations by the “=”. See https://optimization.cbe.cornell.edu/index.php?title=Stochastic_programming for an example
2. 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

1. Every iteration should be clearly presented, and solved "step-by-step".
2. “Minimize” and “subject to” should be “min” and “s.t.” in MathType

• A section to discuss and/or illustrate the applications

1. 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)
2. 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.
3. 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.
4. Consider reformatting to make steps more readable. Inserting spaces and breaking down steps would help.

• A conclusion section

1. Too short. Consider discussion on future research direction and discussion on uncertainty
2. 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

1. 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
2. Remove "Template:Reflist"

Unit commitment problem

• Author list
• An introduction of the topic

1. Please expand the introduction and avoid discussions of examples or specific applications in this section.
2. 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

1. Figure/image format should be revised to better display the content.
2. Uppercase characters are used randomly (e.g., “non-convex transmission Constraints”) . Please follow correct language conventions for sentence structure.
3. 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.
4. Don’t say “written in matrix form as equation..” and just cite the reference, actually write out the equation.
5. Properly label the figure in this section with a figure number and improve visibility by making it larger.

• At least one numerical example

1. Every iteration should be clearly presented, and solved "step-by-step".
2. Label the figures in this section properly with figure numbers.
3. Fix typo “while minimize” to “while minimizing”.
4. Avoid pronouns such as “we”.
5. Use the equation editor when typing equations.
6. 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.
7. 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:

1. 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

1. I suggest highlighting disadvantages along with advantages.

• Theory, methodology, and/or algorithmic discussions

1. “[n x 1] matrix” please use the equation editor to express mathematical descriptions and symbols (p,b, etc)

• At least one numerical example

1. Every iteration should be clearly presented, and solved "step-by-step".
2. Please show at least a few iterations. Even for smaller examples if needed. Report the final solution.
3. Please use the LaTex code or equation editor for min and include s.t., etc.
4. 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

1. Same as the introduction. Pros and cons should be evaluated together!

• References

1. 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

Line Search Method

• Author list
• An introduction of the topic

1. Expand the introduction and avoid discussion on some of the specific steps in the solution process.
2. Provide references here.

• Theory, methodology, and/or algorithmic discussions

1. The phrase “are as follows” in the steepest descent method discussion needs to be followed by a colon.
2. Rephrase “has a nice convergence theory” and cite a reference for this claim.
3. Avoid pronouns such as “we”.
4. Add citation after “.. proposed by Phillip Wolfe in 1969.”
5. Figure 1 is between two sections. Please fix this issue.

• At least one numerical example:

1. Add some space between iterations or subsection break

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

1. Too few references in this section.
2. Last paragraph makes some claims without references.

• A conclusion section
• References

1. 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
2. More references should be added. A simple Google Scholar search would give you many references.

Piecewise Linear Approximation

• Author list
• An introduction of the topic

1. 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

1. Fix typo “to force the x’ values become associated with”.

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

1. Please aim for a maximum average sentence length of ~25 words. Some of these longer sentences are hard to read.

• A conclusion section

1. 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

1. Include hyperlinks to sources when possible.

Mathematical Programming with Equilibrium constraints

• An introduction of the topic

1. 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

1. The meaning of parameter vector x is unclear. Please add more information or update if necessary.
2. 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.
3. Use equations instead of images to represent math programs and equations in the Implicit Descent and SQP subsection.
4. Apart from the steps for each solution technique, please also add a few sentences that describe each method.

• At least one numerical example

1. Please define the terms like NCP, MP before abbreviating them. Also try not to unnecessarily abbreviate simple terms.
2. Equations should be typed by LaTex. Images for equations are unacceptable.
3. GAMS code is strongly discouraged. Please solve the problem "step-by-step".
4. 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.
5. Avoid using figures in the equations (subject to etc)

• A section to discuss and/or illustrate the applications

1. Add references to “power management, highway pricing, chemical process engineering, and traffic planning.”

• A conclusion section
• References

1. 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
2. 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

• 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

1. 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.)
2. Avoid discussion involving finer details of subject methods in this section.
3. 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

1. Properly cite the CFD package, don’t just include a link.
2. Properly label the figure with a figure number.
3. Consider removing white space between isolated sentences to improve readability.

• At least one numerical example

1. If you’ve already defined an abbreviation (CFD), there is no need to define it again. Just use the abbreviation.
2. Avoid pronouns such as “we” or “they”.
3. Phrases like “under the following” need to be followed by a colon.
4. 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.
5. “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.
6. Avoid inserting inline citations like “[4] introduces an..”  as it is a bit informal when you don’t explicitly name the subject.
7. 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.
8. 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.
9. 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.
10. 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

1. Some characters are randomly capitalized in this section.

• A conclusion section

1. 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

1. 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

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

• At least one numerical example

1. In the first sentence, “..take the following numerical example” should be followed by a colon.

• A section to discuss and/or illustrate the applications

1. This section is too short; include specific applications in which input features are sparse and Adagrad excels.

• References

1. References not properly formatted

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

1. First sentence is hard to read. Please consider keeping sentences below 25-30 words.
2. No references provided. Please cite all sources.
3. Figure 1 is provided in the middle between two sections. Please include in the introduction section.

• Theory, methodology, and/or algorithmic discussions

1. 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
2. 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

1. Please add a few sentences to show the transition from problem to solution.
2. The solution technique should be clearly presented, and solved "step-by-step".
3. GAMS code is unnecessary. Please provide detailed step-by-step calculation results.

• A section to discuss and/or illustrate the applications

1. Having a list is not enough. Please explain at least three applications in a few sentences each.
2. 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

1. 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
2. Please follow the standard reference style - the current format is incorrect.

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

1. Please cite sources appropriately: 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
2. 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.
3. An illustration might be useful here.

• Theory, methodology, and/or algorithmic discussions

1. 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.
2. Use linked citations please as the Wiki template above.
3. 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.
4. Step 2 is missing yet it is referenced in the text multiple times. Please address this in addition to the above comment.
5. An illustration might be useful here as well.
6. Please explain what a Gomory Cut is. If the topic is available on optimization.cb.cornell.edu, you can link it.
7. The current equations seem to be simple text written in Italics. All mathematical symbols and equations should be formatted via LaTex.
8. Please format the math programs with equations and notations using formulations in lecture notes as templates.

• At least one numerical example

1. Please add a few sentences to show the transition from problem to solution.
2. 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).
3. 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: (https://optimization.cbe.cornell.edu/index.php?title=Help:Contents). Again, any formatting issue will incur a "compound" penalty in the grading.
4. 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.
5. Make sure your example is not taken from a book as that is strictly disallowed.

• A section to discuss and/or illustrate the applications

1. 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.
2. 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:

1. 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.
2. Please use summarizing sentences to describe earlier sections instead of introducing new concepts/discussion.

• References

1. Too few references overall, you should aggregate information from multiple sources. A quick Google scholar search could provide relevant references.
2. 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
3. Please follow the standard reference style - the current format is incorrect.