Aspects of Semidefinite Programming Interior Point Algorithms and Selected Applications

Semidefinite programming has been described as linear programming for the year 2000. It is an exciting new branch of mathematical programming, due to important applications in control theory, combinatorial optimization and other fields. Moreover, the successful interior point algorithms for linear programming can be extended to semidefinite programming.
In this monograph the basic theory of interior point algorithms is explained. This includes the latest results on the properties of the central path as well as the analysis of the most important classes of algorithms. Several "classic" applications of semidefinite programming are also described in detail. These include the Lovász theta function and the MAX-CUT approximation algorithm by Goemans and Williamson.
Audience: Researchers or graduate students in optimization or related fields, who wish to learn more about the theory and applications of semidefinite programming.

Theory and Algorithms.- Duality, Optimality, and Degeneracy.- The Central Path.- Self-Dual Embeddings.- The Primal Logarithmic Barrier Method.- Primal-Dual Affine-Scaling Methods.- Primal-Dual Path-Following Methods.- Primal-Dual Potential Reduction Methods.- Selected Applications.- Convex Quadratic Approximation.- The Lovász ?-Function.- Graph Coulouring and the Max-K-Cut Problem.- The Stability Number of a Graph and Standard Quadratic Optimization.- The Satisfiability Problem.