I taught this course in Spring, 2009 at Lehigh University. Feel free to use any of the material you find here, just drop me an email so that I know.

Course contents

  • Theory of cone optimization (SDP, SOCP)
  • Interior-point methods, implementation details
  • Special problem structures
  • Applications (combinatorial optimization, truss design, robust optimization)

Lecture slides

  1. Introduction
  2. Basics
  3. Special cases
  4. Duality
  5. Optimality
  6. Central path
  7. Newton system
  8. Neighbourhoods
  9. SOCP
  10. Software
  11. Input formats
  12. Preprocessing

Homework assignments

Assignment 1

Assignment 2

Assignment 3

Assignment 4



Takehome final

Suggested reading

Handbook of Semidefinite Programming - Theory, Algorithms, and Applications by Henry Wolkowicz, Romesh Saigal, Lieven Vandenberghe, eds. Published by Kluwer Academic Publishers. ISBN: 0-792-37771-0
Downloadable from Michael J. Todd's website in PS format.

Aspects of Semidefinite Programming: Interior Point Algorithms and Selected Applications by E. de Klerk, Published by Kluwer Academic Publishers. ISBN: 1-4020-0547-4

The PhD thesis of Jos Sturm: Primal dual interior point approach to semidefinite programming, Tilburg University, The Netherlands


The websites of Mike Todd, Pablo Parrilo and Christoph Helmberg.