Lectures

Tue/Thu, 3:00-4:30pm, Towne 321

Instructor

Shuo Han
Office hour: Wed, 2:00-4:00pm, Moore 317

Teaching Assistant

Andreea Alexandru
Office hour: Tue, 12:30-2:30pm, GRASP conference room (4th floor of Levine, next to the elevators)

Yicheng Lin (Grader)

Course Description

This course concentrates on recognizing and solving convex optimization problems that arise in engineering. Topics include: convex sets, functions, and optimization problems. Basis of convex analysis. Linear, quadratic, geometric, and semidefinite programming. Optimality conditions, duality theory, theorems of alternative, and applications. Interior-point methods, ellipsoid algorithm and barrier methods, self-concordance. Applications to signal processing, control, digital and analog circuit design, computation geometry, statistics, and mechanical engineering.

Prerequisites

Working knowledge of linear algebra. Exposure to real analysis and probability. Familiarity with MATLAB. Undergraduates need permission from instructor.

Schedule

Date Topic Reading Homework
Week 1
1/12
Introduction Chapter 1
Appendix A
Sign up for Piazza
Week 2
1/17, 1/19
Convex sets Chapter 2 Homework 1 (due: 1/26)
Week 3
1/24, 1/26
Convex functions Chapter 3 Homework 2 (due: 2/2)
Week 4
1/31, 2/2
Convex optimization problems Chapter 4 Homework 3 (due: 2/14)
Week 5
2/7, 2/9
Convex optimization problems
Duality
Chapter 4, 5 Homework 4 (TBD)
Week 6
2/14, 2/16
Duality Chapter 5 Homework 5 (due: 2/23)
Week 7
2/21, 2/23
Unconstrained minimization Chapter 9 Homework 6 (due: 3/2)
Week 8
2/28, 3/2
Equality constrained minimization Chapter 10 Homework 7 (due: 3/16)
Spring break
Week 9
3/14, 3/16
Inequality constrained minimization
Interior-point methods
Chapter 11 Homework 8 (due: 3/23)
Week 10
3/21, 3/23
Application: Approximation and fitting Chapter 6 Homework 9 (due: 4/2)
Week 11
3/28, 4/2
Application: Statistical estimation Chapter 7 Homework 10 (due: 4/6)
Week 12
4/4, 4/6
Application: Geometric problems Chapter 8 Homework 11 (due: 4/13)
Week 13
4/11, 4/13
Advanced topic: Convex relaxation TBA Homework 12 (due: 4/20)
Week 14
4/18, 4/20
Advanced topic (time permitting) TBA No homework
Week 15
4/25
Conclusions N/A Final exam

Grading

Course Policy

Course Text and References

The required text for the course is

The following additional references may also be useful: