Convex Optimization in Control and Signal Processing

Topics Covered

1. Background Review1 week
2. Convex Sets and Convex Functions2 weeks
3. Convex Optimization Problems1 week
4. Lagrangian Duality1 week
5. Necessary and Sufficient Optimality Conditions1 week
6. Regression, Classification and Clustering Problems1 week
7. ML Estimation, Hypothesis Testing, Optimal Detection1 week
8. Algorithms for Convex Optimization: First Order Methods, Primal-Dual, ADMM2 weeks
9. LMIs and SDP Duality1 week
10. Application of LMIs in Linear Control1 week
11. Constrained Optimal Control, MPC, System Identification1 week

Handouts (Spring 2025)

Homework Sheets

Tests

Software Packages

Textbooks

1. Optimization Models by G.C. Calafiore and L. El Ghaoui. [Link]
2. Convex Optimization by Boyd and Vandenberghe. Freely available. [Link]
3. Algorithms for Convex Optimization by Nisheeth K. Vishnoi. [Link]
4. Potential function approach to proving convergence results. [Link]
5. Optimization III: Convex and Nonlinear Programming by Ben-Tal and Nemirovski. Lecture Notes. [Link]

Datasets are available here.