# 2020 Cornell Optimization Open Textbook Feedback

## Duality

- An introduction of the topic
- Theory, methodology, and/or algorithmic discussions
- Double check indexes in the dual problem. LHS of the dual problem constraint should be aji.
- Equations in the “constructing the dual” subsection should be aligned properly.
- Please add more details to the KKT Conditions section.
- Remove colon in the subsection title

- At least one numerical example
- A section to discuss and/or illustrate the applications
- A conclusion section
- References
- Lecture notes may not be a credible reference. Please find the original source.

## Simplex algorithm

- An introduction of the topic
- Theory, methodology, and/or algorithmic discussions
- The symbol i in the second expression in dictionary functions, ranges from 1 to m.

- At least one numerical example
- A section to discuss and/or illustrate the applications
- A conclusion section
- References 1. Please be consistent with referencing style.

## Computational complexity

- An introduction of the topic
- Theory, methodology, and/or algorithmic discussions
- Please introduce the Big-oh notation in this section.

- At least one numerical example
- Examples of combinatorial optimization is suggested.

- A section to discuss and/or illustrate the applications
- The applications mentioned need to be discussed further.

- A conclusion section
- References.

## Network flow problem

- An introduction of the topic
- Theory, methodology, and/or algorithmic discussions.
- At least one numerical example
- There is NO need to include code. Simply mention how the problem was coded along with details on the LP solver used.
- The subsection title style should be consistent.

- A section to discuss and/or illustrate the application
- A conclusion section
- References

## Interior-point method for LP

- An introduction of the topic
- Fix typos “where A ε R”
- Please type “minimize” and “subject to” in formal optimization problem form throughout the whole page.

- Theory, methodology, and/or algorithmic discussions
- At least one numerical example
- The numerical example does not use any Newton’s method iterations that are presented in the above section. Please consider using a complicated example that actually uses Newton’s iterations.
- Please type the maximization problem in LaTex form.

- A section to discuss and/or illustrate the applications
- Please double check typos and extra spaces.

- A conclusion section
- References

## Optimization with absolute values

- An introduction of the topic
- Add few sentences on how absolute values convert optimization problem into a nonlinear optimization problem.

- Theory, methodology, and/or algorithmic discussions
- Please add more details to absolute values in nonlinear optimization. (very important!)

- At least one numerical example
- A section to discuss and/or illustrate the applications
- Inline equations at the beginning of this section are not formatted properly. Please fix the notation for expected return throughout the section.

- A conclusion section
- References

## Matrix game (LP for game theory)

- An introduction of the topic
- Theory, methodology, and/or algorithmic discussions
- aij are not defined in this section.

- At least one numerical example
- Interesting example, very well explained.

- A section to discuss and/or illustrate the applications
- A conclusion section
- References
- Please consider linking the references by using this as Wiki template, https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization

## Quasi-Newton methods

- An introduction of the topic
- Theory, methodology, and/or algorithmic discussions
- Please ensure that few spaces are kept between the equations and equation numbers.
- Step 6 of DFP algorithm should use the same variable M as in equation 1.14.

- At least one numerical example
- A section to discuss and/or illustrate the applications
- A conclusion section
- References

## Markov decision process

- An introduction of the topic
- Please fix typos such as “discreet”.

- Theory, methodology, and/or algorithmic discussions
- If abbreviations are defined like MDP, use the abbreviations throughout the Wiki.

- At least one numerical example
- A section to discuss and/or illustrate the applications
- A conclusion section
- References
- Please consider linking the references by using this as Wiki template, https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization

## Eight step procedures

- An introduction of the topic
- Theory, methodology, and/or algorithmic discussions
- At least one numerical example
- Please be consistent in the formatting of mathematical notations and equations.

- A section to discuss and/or illustrate the applications
- A conclusion section
- References
- Lecture notes may not be a credible reference. Please find the original source.

## Facility location problem

- An introduction of the topic
- Theory, methodology, and/or algorithmic discussions
- At least one numerical example
- Mention how the formulated problem is coded and solved. No need to provide GAMS code.

- A section to discuss and/or illustrate the applications
- A conclusion section
- References
- Please consider linking the references by using this as Wiki template, https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization

## Set covering problem

- An introduction of the topic
- Theory, methodology, and/or algorithmic discussions
- Use proper math notations for “greater than equal to”.

- At least one numerical example
- Since Table 3 provides information on aij required to formulate the constraints, Table 2 serves no purpose and should be removed from the Wiki. Table 3 can be directly generated from Table 1.
- The numerical example is solved manually without using greedy method nor LP solution method. Please solve this example both by the presented greedy algorithm and the newly added LP-based method and finally compare solutions.
- Please leave some space between equation and equation number.

- A section to discuss and/or illustrate the applications
- A conclusion section
- References

## Quadratic assignment problem

- An introduction of the topic
- Theory, methodology, and/or algorithmic discussions
- Discuss dynamic programming and cutting plane solution techniques briefly.

- At least one numerical example
- A section to discuss and/or illustrate the applications
- Please format the equation for definition of yij in the hospital layout subsection.

- A conclusion section
- References

## Newsvendor problem

- An introduction of the topic
- Theory, methodology, and/or algorithmic discussions
- A math programming formulation of the optimization problem with objective function and constraints is expected for the formulation. Please add any variant of the newsvendor problem along with some operational constraints.
- A mathematical presentation of the solution technique is expected. Please consider any distribution for R and present a solution technique for that specific problem.

- At least one numerical example
- A section to discuss and/or illustrate the applications
- A conclusion section
- References

## Mixed-integer cuts

- 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
- MILP and their solution techniques involving cuts are extremely versatile. Yet, only two sentences are added to describe their applications. Please discuss their applications, preferably real-world applications, in brief. Example Wikis provided on the website could be used as a reference to do so.

- A conclusion section
- References

## Column generation algorithms

- 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

## Heuristic algorithms

- 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
- Reference

## Branch and cut

- An introduction of the topic
- Theory, methodology, and/or algorithmic discussions
- Equation in most infeasible branching section is not properly formatted, please fix the same.
- Step 2 appears abruptly in the algorithm and does not explain much. Please add more information regarding the same.
- Step 5 contains latex code terms that are not properly formatted. Please fix the same.
- Fix typos: e.g., repeated “for the current”, men Problem can viewed as partially” ..

- At least one numerical example
- A section to discuss and/or illustrate the applications
- A conclusion section
- References

## Mixed-integer linear fractional programming (MILFP)

- An introduction of the topic
- The abbreviation MINFP is not previously defined. Please fix the same.

- Theory, methodology, and/or algorithmic discussions
- The symbol Q used for objective is often used to denote the set of real numbers. Please simple use a standard Q notation rather than a special form of Q. Same goes for objective function R.

- At least one numerical example
- Please provide comparison between solutions obtained with presented solution technique and MINLP solver for the numerical example for verification of global minimum.
- Please check the index notation in Mass Balance Constraints.
- Please check the typo “obje” in Maximizing Unit NPV.
- Please check other typos as “continous”, “each fractional objective functions, which are shown as below”,”typical algorithm that aim”

- A section to discuss and/or illustrate the applications
- A conclusion section
- References
- Please consider linking the citations to references in the reference list by using this as Wiki template, rather than using website links. https://optimization.cbe.cornell.edu/index.php?title=Quantum_computing_for_optimization

## Convex generalized disjunctive programming (GDP)

- An introduction of the topic
- Please refrain from using abbreviations without defining them first.
- References missing for solvers.

- Theory, methodology, and/or algorithmic discussions
- Please format yP in the text correctly.
- Verify all sentences in the NLP subproblem for a fixed yP subsection, some words seem to be missing.
- Mention few more sentences on the hull reformulation and present the reformulated MINLP problem if possible.
- Fix typos: “So with said”, “dijunctive”, “solve this both”, ..

- At least one numerical example
- Source of the figures can be cited by mentioning the name of the paper or using the same referencing style like the previous sections rather than link to the actual paper.

- A section to discuss and/or illustrate the applications
- Please relabel the figure by order of appearance.

- A conclusion section
- References
- Reference # 6 has all uppercase letters. Please use a consistent style for all references.

## Fuzzy programming

- An introduction of the topic”
- Please fix the typo: “also know as”

- Theory, methodology, and/or algorithmic discussions
- Very well written.
- Discussion on converting piecewise linear membership functions into MILP constraints could be added for further understanding.
- Some minor typos exist: “ a cold set and an hot set”, “"more hot"”,

- At least one numerical example
- Significant whitespace present between problem formulations and text. Try to reduce this whitespace.
- Please fix minor typos: “real word”, “Each firm has their own”

- A section to discuss and/or illustrate the applications
- Applications of fuzzy programming are quite versatile. Please discuss few of the mentioned applications briefly. The provided example Wikis can be used as a reference to write this section.

- A conclusion section
- Add few more sentences to the conclusion section to better summarize the presented theory, methods and examples.

- References
- Links to the cited content is not the right way to cite. Please refer to the example Wikis to use a better (accurate) referencing style.

## Adaptive robust optimization

- An introduction of the topic
- References at the end of the sentence should be placed after the period.

- Theory, methodology, and/or algorithmic discussions
- Try to better explain the first stage and second stage decisions in terms of here and now and wait and see decisions.
- It is claimed that x2(u) is independent of u. Please verify and fix if necessary.
- The text contains “[ref various papers]”. Please add the appropriate references here.
- The abbreviation KKT is not previously defined.

- At least one numerical example
- A section to discuss and/or illustrate the applications
- A conclusion section
- References
- Overall, very well written.

## Stochastic gradient descent

- An introduction of the topic
- Fix this sentence. “Gradient descent picks any random weight …”. The user initializes the weights and not SGD.

- Theory, methodology, and/or algorithmic discussions
- Use j to denote jth data point in step 4 of the SGD algorithm and in Mini-batch gradient descent subsection.
- Citations required for the claims in the “learning rate” subsection.
- Please fix the repeated typo “a local minima is reached”

- At least one numerical example
- Bias in linear regression is a completely separate topic and is relevant for estimators. Please use correct terminology for the unknown parameters of linear regression.
- Fix language used in the dataset subsection of the numerical example.
- Amount of whitespace can be reduced by changing orientation of example dataset by converting it into a table containing 3 rows and 6 columns.
- Backpropagation is a technique used to update weights of a neural network. For the linear regression example, simply gradients w.r.t unknown parameters are computed. Please update the subsection title accordingly.
- Ensure that the readers clearly understand that first the algorithm iterates through each data point and then repeats itself all over again with the updated parameters. This can be done by demonstrating iteration 2 using the next datapoint.
- Add reference for the overfitting comment.

- A section to discuss and/or illustrate the applications
- Mention how SGD is relevant for logistic regression.
- The application section starts with discussing relevance of SGD for deep learning, but no discussion on deep learning/ neural networks is present. Subsection on deep learning and the variants of SGD used for deep learning can be mentioned.
- The abbreviation is SGD, please fix it throughout.

- A conclusion section
- No mention of global minima is present in the entire Wiki. Either add citation for the global minimum statement or remove this claim.
- Fix abbreviations for SGD here as well.

- References
- Fix duplicate reference numbers.
- Some references are not linked to the text in Wiki, please update accordingly.
- Reference # 2 has all uppercase letters. Please use a consistent style for all references.

## RMSProp

- An introduction of the topic
- Few sentences in this section are incoherent. Please use grammatically correct sentences.

- Theory, methodology, and/or algorithmic discussions
- The equation presented in the Artificial neural network subsection is valid for the perceptron and not neural net. Please fix either the title or the equation.
- In the Rprop subsection, the momentum parameter is discussed but not used in any of the corresponding equations.
- Fix typos like PMSprop, Aritifical, in the RMSprop subsection.
- The default value of parameters in the RMSprop subsection is mentioned but their relevance or their calculation is not explained.
- Please check grammar in this section.
- Please avoid using contractions (e.g. doesn’t).
- The use of “Obviously” is advised against

- At least one numerical example
- Please demonstrate the working of RMSprop by actually solving any unconstrained optimization problem. Providing links to other resources for numerical examples renders the purpose of Wiki useless.

- A section to discuss and/or illustrate the applications
- The applications section does not contain any discussion on applications. Please mention a few applications of the widely used RMSprop and discuss them briefly.
- Misspelling for applications.
- Please check grammar in this section.

- A conclusion section
- Formulation of ANN is incorrect terminology. ANNs are trained by RMSprop.
- It is claimed that RMSprop achieves global optimization without any reference. Please provide a reference for the same or update the said claim.

- References
- For reference #1 please find the original source of the images and cite that source, rather than citing an image hosting service.
- Please refer to the example Wikis provided to use proper citation style.

## Adam

- An introduction of the topic
- Theory, methodology, and/or algorithmic discussions
- Key challenges mentioned in the mini-batch SGD are more relevant to the batch SGD. Consider moving these to the corresponding section.

- At least one numerical example
- A section to discuss and/or illustrate the applications
- A conclusion section
- Some minor formatting issues between symbols and text should be fixed.

- References
- Overall, very well written.