2021 Cornell Optimization Open Textbook Feedback

Lagrangian duality

• 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.

• At least one numerical example

1. Please update the dual objective function and domain of dual variables accordingly.

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

1. The inline notations (`x1`, `s1`) should also be typed using LaTex.

Portfolio Optimization

• 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 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

• Theory, methodology, and/or algorithmic discussions

1. Some normal text was expressed as equation.

Bayesian Optimization

• Theory, methodology, and/or algorithmic discussions

1. Acquisition function figure could be made larger and clearer to improve readability.

• 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 (#2 is still incorrectly formatt

Conjugate gradient methods

• Theory, methodology, and/or algorithmic discussions

1. All equations need to be better formatted.
2. Please properly format pseudocode.

• A conclusion section

1. Consider adding future research directions

Adam

• 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.

a* algorithm

• 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.

Job-Shop Scheduling Problem

• Theory, methodology, and/or algorithmic discussions

1. 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

1. Add a mathematical description of the problem and a pseudocode/flowchart for the Lemke-Howson algorithm.  
2. Rephrase “This algorithm utilizes iterated pivoting much like the simplex algorithm used in the simplex algorithm used in linear programming”.
3. Formatting (incomplete).

• References

1. Incorrect reference style.

Trust-region methods

• An introduction of the topic

1. 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. Please format the algorithm in proper algorithmic pseudocode format.

Outer-approximation

• Theory, methodology, and/or algorithmic discussions

1. “Minimize” and “subject to” should be “min” and “s.t.” in MathType (inconsistent formatting)

Unit commitment problem

• At least one numerical example

1. Fix typo “while minimize” to “while minimizing”.

Line Search Method

• Theory, methodology, and/or algorithmic discussions

1. Avoid pronouns such as “we” (all sections).

Wing shape Optimization

• At least one numerical example

1. 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

1. These variables should be defined before the conclusion section, they are out of place here.

• References

1. Include hyperlinks to references if possible.

Interior point method for NLP

• Theory, methodology, and/or algorithmic discussions

1. Need discussion about the concept of “central path” and the notion of self concordance
2. 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.
3. Fix typo “optimisation”.

McCormick Envelopes

• 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

• 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".

• References

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

Branch and Bound for MINLP

• At least one numerical example

1. 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).

1. 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

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