Wolkowicz / Saigal / Vandenberghe Handbook of Semidefinite Programming

Theory, Algorithms, and Applications
2000
ISBN: 978-1-4615-4381-7
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 27, 654 Seiten, eBook

Reihe: International Series in Operations Research Management Science

Semidefinite programming (SDP) is one of the most exciting and active research areas in optimization. It has and continues to attract researchers with very diverse backgrounds, including experts in convex programming, linear algebra, numerical optimization, combinatorial optimization, control theory, and statistics. This tremendous research activity has been prompted by the discovery of important applications in combinatorial optimization and control theory, the development of efficient interior-point algorithms for solving SDP problems, and the depth and elegance of the underlying optimization theory.
The offers an advanced and broad overview of the current state of the field. It contains nineteen chapters written by the leading experts on the subject. The chapters are organized in three parts: Theory, Algorithms, and Applications and Extensions.

Zielgruppe

Research

Autoren/Hrsg.

Wolkowicz, Henry

Saigal, Romesh

Vandenberghe, Lieven

Inhaltsverzeichnis

Contributing Authors. List of Figures. List of Tables. Preface. 1. Introduction; H. Wolkowicz, et al. Part I: Theory. 2. Convex Analysis on Symmetric Matrices; F. Jarre. 3. The Geometry of Semidefinite Programming; G. Pataki. 4. Duality and Optimality Conditions; A. Shapiro, K. Scheinberg. 5. Self-Dual Embeddings; E. de Klerk, et al. 6. Robustness; A. Ben-Tal, et al. 7. Error Analysis; Zhiquan Luo, J. Sturm. Part II: Algorithms. 8. Symmetric Cones, Potential Reduction Methods; F. Alizadeh, S. Schmieta. 9. Potential Reduction and Primal-Dual Methods; L. Tuncel. 10. Path-Following Methods; R. Monteiro, M. Todd. 11. Bundle Methods and Eigenvalue Functions; C. Helmberg, F. Oustry. Part III: Applications and Extensions. 12. Combinatorial Optimization; M. Goemans, F. Rendl. 13. Nonconvex Quadratic Optimization; Y. Nesterov, et al. 14. SDP in Systems and Control Theory; V. Balakrishnan, Fan Wang. 15. Structural Design; A. Ben-Tal, A. Nemirovski. 16. Moment Problems and Semidefinite Optimization; D. Bertsimas, J. Sethuraman. 17. Design of Experiments in Statistics; V. Fedorov, J. Lee. 18. Matrix Completion Problems; A. Alfakih, H. Wolkowicz. 19. Eigenvalue Problems and Nonconvex Minimization; F. Jarre. 20. General Nonlinear Programming; S. Kruk, H. Wolkowicz. References. Appendix A-.1. Conclusion and Further Historical Notes. A-.2.Index.