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; the engineering 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

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  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