CS 7301: Convex Optimization

Fall 2021

An introduction to convex optimization for Ph.D. students.

Where: ECSN 2.112
When: TR, 11:30am-12:45pm

Instructor: Nicholas Ruozzi
Office Hours: T 12:45pm-2:00pm and by appointment online.

TA: TBD
Office Hours: TBD

Grading: problem sets (100%)

Recommended Prerequisites: Mathematical sophistication, e.g., multivariate calculus, linear algebra, probability and statistics, etc.

Week	Dates	Topic	Readings
1	Aug. 24 & 26	Introduction & Calculus Review Convex Sets and Functions	Boyd Appendix A Boyd 2.1-2.3, 3.1-3.2
2	Aug. 31 & Sept. 2	Gradient Descent Convex Optimization	Boyd 9.1-9.3 Boyd 4.1-4.3
3	Sept. 7 & 9	Projected Gradient Duality and Lagrange Multipliers	Boyd 5
4	Sept. 14 & 16	Constraint Qualification and KKT Second Order Methods	Boyd 5
5	Sept. 21 & 23	Second Order Methods ML Applications	Boyd 3.3, 9.5, 10.1-10.2
6	Sept. 28 & 30	Linear Algebra Review Positive Semidefinite Matrices	Boyd A.5
7	Oct. 5 & 7	Singular Value Decomposition Matrix Factorizations	Boyd A.5.4 CUR Decompositions
8	Oct. 12 & 14	More Matrix Factorizations Alternating Projection
10	Oct. 19 & 21	Proximal Gradient
11	Oct. 26 & 28	Submodular Functions	Submodular Function Notes, Ch. 1 - 3
12	Nov. 2 & 4	Convergence Accelerated Gradient
13	Nov. 9 & 11	Alternating Directions Method of Multipliers Majorization	ADMM Notes

All problem sets will be available on eLearning and are to be turned in there. See the homework guidelines below for homework policies.

There is no required textbook, but the following books may serve as useful references for different parts of the course.

• Convex Optimization by Stephen Boyd and Lieven Vandenberghe (online) .
• Convex Optimization Theory by Dimitri P. Bertsekas

I expect you to try solving each problem set on your own. However, if you get stuck on a problem, I encourage you to collaborate with other students in the class, subject to the following rules:

1. You may discuss a problem with any student in this class, and work together on solving it. This can involve brainstorming and verbally discussing the problem, going together through possible solutions, but should not involve one student telling another a complete solution.
2. Once you solve the homework, you must write up your solutions on your own, without looking at other people's write-ups or giving your write-up to others.
3. In your solution for each problem, you must write down the names of any person with whom you discussed it. This will not affect your grade.
4. Do not consult solution manuals or other people's solutions from similar courses - ask the course staff, we are here to help!

Late homework will NOT be accepted except in extreme circumstances or those permitted by university policy (e.g., a religious holiday). All such exceptions MUST be cleared in advance of the due date.

UT Dallas Course Policies and Procedures

For a complete list of UTD policies and procedures, see here.