Tue/Thu, 3:00-4:30pm, Towne 321
Shuo Han
Office hour: Wed, 2:00-4:00pm, Moore 317
Andreea Alexandru
Office hour: Tue, 12:30-2:30pm, GRASP conference room (4th floor of Levine, next to the elevators)
Yicheng Lin (Grader)
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.
Working knowledge of linear algebra. Exposure to real analysis and probability. Familiarity with MATLAB. Undergraduates need permission from instructor.
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 |
The required text for the course is
The following additional references may also be useful: