Overview

Semidefinite programming (SDP) is one of the 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 research activity has been prompted by the discovery of 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. This handbook offers an advanced and broad overview of the field. It contains 19 chapters organized in three parts: theory, algorithms, and applications and extensions.

Full Product Details

Author:   Henry Wolkowicz ,  Romesh Saigal ,  Lieven Vandenberghe
Publisher:   Springer
Imprint:   Springer
Edition:   2000 ed.
Volume:   27
Dimensions:   Width: 15.50cm , Height: 3.60cm , Length: 23.50cm
Weight:   2.500kg
ISBN:  

9780792377719

ISBN 10:   0792377710
Pages:   654
Publication Date:   31 March 2000
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1 Introduction.- I Theory.- 2 Convex Analysis on Symmetric Matrices.- 3 The Geometry of Semidefinite Programming.- 4 Duality and Optimality Conditions.- 5 Self-Dual Embeddings.- 6 Robustness 139.- 7 Error Analysis 163.- II Algorithms.- 8 Symmetric Cones, Potential Reduction Methods.- 9 Potential Reduction and Primal-Dual Methods.- 10 Path-Following Methods.- 11 Bundle Methods and Eigenvalue Functions.- III Applications and Extensions.- 12 Combinatorial Optimization.- 13 Nonconvex Quadratic Optimization.- 14 SDP in Systems and Control Theory.- 15 Structural Design.- 16 Moment Problems and Semidefinite Optimization.- 17 Design of Experiments in Statistics.- 18 Matrix Completion Problems.- 19 Eigenvalue Problems and Nonconvex Minimization.- 20 General Nonlinear Programming.- References.- A-.1 Conclusion and Further Historical Notes.- A-.1.1 Combinatorial Problems.- A-.l.2 Complementarity Problems.- A-.l.3 Complexity, Distance to III-Posedness, and Condition Numbers.- A-.1.4 Cone Programming.- A-.1.5 Eigenvalue Functions.- A-.1.6 Engineering Applications.- A-.1.7 Financial Applications.- A-.1.8 Generalized Convexity.- A-.1.9 Geometry.- A-.l.10 Implementation.- A-.1.11 Matrix Completion Problems.- A-.1.12 Nonlinear and Nonconvex SDPs.- A-.1.13 Nonlinear Programming.- A-.1.14 Quadratic Constrained Quadratic Programs.- A-.1.15 Sensitivity Analysis.- A-. 1.16 Statistics.- A-. 1.17 Books and Related Material.- A-.1.18 Review Articles.- A-.1.19 Computer Packages and Test Problems.- A-.2 Index.

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