Convex Optimization I

Textbook and optional references

The textbook is Convex Optimization, available online, or in hard copy form at the Stanford Bookstore.

Several texts can serve as auxiliary or reference texts:

• Bertsekas, Nedic, and Ozdaglar, Convex Analysis and Optimization
• Ben-Tal and Nemirovski, Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications
• Nesterov, Introductory Lectures on Convex Optimization: A Basic Course
• Ruszczynski, Nonlinear Optimization
• Borwein & Lewis, Convex Analysis and Nonlinear Optimization

Prerequisites

Good knowledge of linear algebra (as in EE263). Exposure to numerical computing, optimization, and application fields helpful but not required; theengineering applications will be kept basic and simple.

Description

Concentrates on recognizing and solving convex optimization problems that arise in engineering. Convex sets, functions, and optimization problems. Basics of convex analysis. Least-squares, linear and quadratic programs, semidefinite programming, minimax, extremal volume, and other problems. Optimality conditions, duality theory, theorems of alternative, and applications. Interior-point methods. Applications to signal processing, control, digital and analog circuit design, computational geometry, statistics, and mechanical engineering.

Course objectives

• to give students the tools and training to recognize convex optimization problems that arise in engineering
• to present the basic theory of such problems, concentrating on results that are useful in computation
• to give students a thorough understanding of how such problems are solved, and some experience in solving them
• to give students the background required to use the methods in their own research or engineering work

Lecture Slides

Professor Stephen Boyd, Stanford University, Spring Quarter 2008–09

1. Introduction
2. Convex sets
3. Convex functions
4. Convex optimization problems
5. Duality
6. Approximation and fitting
7. Statistical estimation
8. Geometric problems
9. Numerical linear algebra background
10. Unconstrained minimization
11. Equality constrained minimization
12. Interior-point methods
13. Conclusions

Additional lecture slides:

1. Convex optimization examples
2. Stochastic programming
3. Chance constrained optimization
4. Filter design and equalization
5. Disciplined convex programming and CVX

Lecture Videos

Professor Stephen Boyd, Stanford University, Winter Quarter 2007–08

Lecture	Slides
Jan 8	1-1 to 1-15	Flash	iTunes
Jan 10	2-1 to 2-23	Flash	iTunes
Jan 15	3-1 to 3-18	Flash	iTunes
Jan 17	3-17 to 3-31	Flash	iTunes
Jan 22	4-1 to 4-19	Flash	iTunes
Jan 24	4-19 to 4-34	Flash	iTunes
Jan 29	4-35 to 5-1	Flash	iTunes
Jan 31	5-1 to 5-17	Flash	iTunes
Feb 5	5-17 to 5-30	Flash	iTunes
Feb 7	6-1 to 6-20	Flash	iTunes
Feb 12	7-1 to 7-14	Flash	iTunes
Feb 14	7-11 to 8-8	Flash	iTunes
Feb 19	8-8 to 9-7	Flash	iTunes
Feb 21	9-8 to 9-14	Flash	iTunes
Feb 26	10-1 to 10-23	Flash	iTunes
Feb 28	10-24 to 11-10	Flash	iTunes
Mar 4	11-6 to 12-4	Flash	iTunes
Mar 6	12-4 to 12-17	Flash	iTunes
Mar 11	12-18 to 13-6	Flash	iTunes