Aspects of Semidefinite Programming: Interior Point Algorithms and Selected Applications

Etienne de Klerk (auth.)9781402005473, 1402005474

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.

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Table of contents :
Introduction….Pages 1-18
Duality, Optimality, and Degeneracy….Pages 21-39
The Central Path….Pages 41-59
Self-Dual Embeddings….Pages 61-73
The Primal Logarithmic Barrier Method….Pages 75-93
Primal-Dual Affine-Scaling Methods….Pages 95-113
Primal-Dual Path-Following Methods….Pages 115-131
Primal-Dual Potential Reduction Methods….Pages 133-146
Convex Quadratic Approximation….Pages 149-155
The Lovász ϑ-Function….Pages 157-167
Graph Coulouring and the Max- K -Cut Problem….Pages 169-185
The Stability Number of a Graph and Standard Quadratic Optimization….Pages 187-209
The Satisfiability Problem….Pages 211-228