Csc5160: Combinatorial Optimization and Approximation Algorithms Topic: Semidefinite Programming 22.1 Semidefinite Programming Problem

In this lecture, we provide another class of relaxations, called Semidefinite Programming Relaxation. These serve as relaxations for several NP-hard problems, in particular, for problems that can be expressed as strict quadratic programs. The relaxed problems, together with techniques like randomized rounding, give good approximation algorithms to hard combinatorial problems. We will illustrate the use of semidefinite programming by deriving a 0.87856-approximation algorithm for two problems: the Maximum Cut problem and the MAX-2-SAT problem. Some materials come from [1]. Reader can refer to that for more details.