Semidefinite programming and combinatorial optimization

Abstract

Semidefinite programs have recently turned out to be a powerful tool for approximating integer problems. To survey the development in this area over the last few years, the following topics are addressed in some detail. First, we investigate ways to derive semidefinite programs from discrete optimization problems. The duality theory for semidefinite programs is the key to understand algorithms to solve them. The relevant duality results are therefore summarized. The second part of the paper deals with the approximation of integer problems both in a theoretical setting, and from a computational point of view.