MA 421 Fall 2025 Project

The maximum score of the project is 200 points, about three homework's weight. This will give you a sense of the amount of work for this I am expecting. You can form a group of up to three people - everyone in the group will get the same score. The project consists of the following three components.

Abstract (50 pts): due on Friday, Nov 14, 11:59pm, in Brightspace (Submit in one single PDE file)

A short paragraph (1/3 to half a page) about your problem description, formulation, and intended solution method.
(The purpose of the abstract is for you to start early and not wait till the last minute.)

Report (100 pts): due on Friday, Dec 5, 11:59pm, in Brightspace (Submit in one single PDE file)

A 4- to 5-page report, typed. It should consist of

problem motivation and description;

solution method which include both a mathematical formulation and a genuine/meaningful example of a computer solution;
(i.e. try to give an example that is difficult to solve by hand.)

conclusion/outlook/what's next for this problem.

list of references.

Presentation (50 pts): to be held Dec 8 - Dec 19, in zoom

The presentation is 10min in zoom. Sign-up sheet will be posted toward the end of Nov.
Slides should be used. (Hand-written slides are acceptable.)

Evaluation criteria:

The project will be evaluated based on mathematical accuracy and how you can effectively apply the ideas/techniques of linear and nonlinear programming (learned in this class) in solving the problem of your choice. I will also give some weight to how interesting and technical your question is. But this can also depend on how you present your problem motivation and solution method. As usual, the clarity of the report and presentation play an important role.

Suggested Topics:

There should be no lack of possible problems related to linear and nonlinear programming. I am not expecting you to tackle a brand new problem. I just want you to explore somewhat on your own and demonstrate what interests you most, in relation to the topics covered in this class. Most (or all the) topics covered in class has many interesting extensions, many of which probably I am not aware of. So you are welcome to explore those also.

The following are some more specific suggestions. (They are in fact some topics that I would like to cover in class, in the "unlikely" event that schedule allows.) You should be able to find the listed references freely online, or from Purdue Library Search.

Support vector machine and various approximation and classification algorithms
(Book: Convex Optimization, by Boyd and Vandenberghe, Part II;
Book: Introduction to Applied Linear Algebra Vectors, Matrices, and Least Squares, by Boyd and Vandenberghe, Part III.
These two references contain a lot of materials/examples/applications. The latter is tailored more towards undergraduate level.)

Compressed sensing
(Paper: Making Do with Less: An Introduction to Compressed Sensing, by Kurt Bryan and Tanya Leise.)

Game theory ([V Chapter 11], [C Chapter 15])
(I am still hoping to "squeeze in" some of this materials in class.)

Properties and computation related to polytopes/polyhedrons ([C Chapter 16, 18]);