Course Website

All slides, program files, and homework assignments will be posted in the Owl Space at http://owlspace.rice.edu.

General announcement

Scope: Convex optimization problems arise in communication, system theory, VLSI, CAD, finance, inventory, network optimization, learning, computer vision, statistics, etc. Various new solvers are now available and have made solving convex problems ever easier. Nevertheless, problems are often unrecognized as convex and, therefore, remain unsolved. This course is designed to be an exposure to convex optimization problems, their solution techniques and applications.

Topics covered: optimization fundations, convex sets and functions, convex optimization problems (QP, SOCP, SDP, etc.), duality, a subset of algorithms, and applications from

• CAAM, CS, EE, and BioEng: compressed sensing, statistical learning, image processing, computer vision, etc.


• Business: robust portfolio selection, etc.


• Statistics: robust regression, data fitting, etc.

Prerequisites: Linear algebra. Some knowledge in MATLAB programming helps. No previous background in optimization is required.

Textbook: “Convex Optimization” by S.Boyd and L.Vendenberghe
Available both in print and online at www.stanford.edu/~boyd/cvxbook/

Course workload: approx. 5 homework sets, a few MATLAB programming assignments, 1 final take-home project

Credits: 3 credit hours

Instructor: Wotao Yin
Office Hour: 10:00-10:50 a.m. Tuesday and Thursday
Course webpage: www.caam.rice.edu/~wy1/CAAM554
Slides and homework: owlspace.rice.edu

Syllabus

15 weeks.

A variety of applications will be discussed throughout the lectures.

Lectures 1-3: Introduction to optimization
Lectures 4-6: Recognizing problem structure convex sets and convex functions
Lectures 7-8: Formulations of convex optimization problems
Lectures 9-11: Duality theory
Lecture 12-15: Introduction to convex optimization algorithms
Lectures 16-17: MATLAB programming basic and tricks
Lecture 18: Group project proposals
Lectures 19-25: Convex optimization algorithms
Lectures 27-29: Student project presentations

Lecture slides

1. Introduction