Aspects of Semidefinite Programming: Interior Point Algorithms and Selected Applications

Aspects of Semidefinite Programming: Interior Point Algorithms and Selected Applications

Hardback Applied Optimization

By (author) Etienne de Klerk

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  • Publisher: Kluwer Academic Publishers
  • Format: Hardback | 288 pages
  • Dimensions: 173mm x 237mm x 22mm | 603g
  • Publication date: 31 March 2002
  • Publication City/Country: Dordrecht, Netherlands
  • ISBN 10: 1402005474
  • ISBN 13: 9781402005473
  • Edition statement: 2002 ed.
  • Illustrations note: biography

Product description

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 Lovasz 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

Acknowledgments. List of notation. 1. Introduction. Part I: Theory and Algorithms. 2. Duality, Optimality, and Degeneracy. 3. The Central Path. 4. Self-Dual Embeddings. 5. The Primal Logarithmic Barrier Method. 6. Primal-Dual Affine-Scaling Methods. 7. Primal-Dual Path-Following Methods. 8. Primal-Dual Potential Reduction Methods. Part II: Applications. 9. Convex Quadratic Approximation. 10. The Lovasz upsilon-Function. 11. Graph Colouring and the Max-Kappa-Cut Problem. 12. The Stability Number of a Graph. 13. The Satisfiability Problem. Appendices. References. Index.