Aspects of Semidefinite Programming: Interior Point Algorithms and Selected Applications

E. Klerk

ISBN 10: 1441952160 / ISBN 13: 9781441952165

Editore: Springer US, 2002

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300 pages. 9.00x6.00x0.70 inches. In Stock.

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Dati bibliografici

• Titolo: Aspects of Semidefinite Programming: Interior Point Algorithms and Selected Applications
• Editore: Springer US
• Data di pubblicazione: 2002
• Lingua: Inglese
• ISBN 10: 1441952160
• ISBN 13: 9781441952165
• Rilegatura: Paperback
• Condizione: Brand New

Descrizione articolo

Riassunto

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.

Contenuti

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 Lovász 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.