MA 421 Fall 2026 Project

The project is worth 20% of your course grade.
You can form a group of up to three people - everyone in the group will get the same score.

Your project will be graded according to the following three components:

Abstract (10% of project): due on Friday, Nov 6, 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 (60% of project): due on Friday, Dec 4, 11:59pm, in Brightspace (Submit in one single PDE file)

A (roughly) 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 (30% of project): to be held during Dec 14 - Dec 18, in zoom

Sign-up sheet will be posted toward the end of Nov.

The presentation is 10min+Q&A.

All group members must be present and be part of the presentation.

Slides - suitable for screen sharing - should be used. (Scanned hand-written slides are acceptable.)

Anyone in this class can attend any presentations.

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 weight on how interesting, innovative, and technical your project 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.

Choice of 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]);

Schedule of Presentations - TBD