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Handbook of Semidefinite Programming

Theory, Algorithms, and Applications

  • Book
  • © 2000

Overview

Editors:
  1. Henry Wolkowicz

    1. Department of Combinatorics and Optimization Faculty of Mathematics, University of Waterloo, Waterloo, Canada

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  2. Romesh Saigal

    1. Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, USA

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    You can also search for this editor in PubMed   Google Scholar

  3. Lieven Vandenberghe

    1. Electrical Engineering Department, UCLA, Los Angeles, USA

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: International Series in Operations Research & Management Science (ISOR, volume 27)

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Table of contents (20 chapters)

  1. Front Matter

    Pages i-xxvii
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  2. Introduction

    1. Introduction

      • Henry Wolkowicz, Romesh Saigal, Lieven Vandenberghe
      Pages 1-8

  3. Theory

    1. Front Matter

      Pages 9-11
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    2. Convex Analysis on Symmetric Matrices

      • Florian Jarre
      Pages 13-27

    3. The Geometry of Semidefinite Programming

      • Gábor Pataki
      Pages 29-65

    4. Duality and Optimality Conditions

      • Alexander Shapiro, Katya Scheinberg
      Pages 67-110

    5. Self-Dual Embeddings

      • Etienne de Klerk, Tamás Terlaky, Kees Roos
      Pages 111-138

    6. Robustness

      • Aharon Ben-Tal, Laurent El Ghaoui, Arkadi Nemirovski
      Pages 139-162

    7. Error Analysis

      • Zhiquan Luo, Jos Sturm
      Pages 163-189

  4. Algorithms

    1. Front Matter

      Pages 191-193
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    2. Symmetric Cones, Potential Reduction Methods and Word-by-Word Extensions

      • Farid Alizadeh, Stefan Schmieta
      Pages 195-233

    3. Potential Reduction and Primal-Dual Methods

      • Levent Tuncel
      Pages 235-265

    4. Path-Following Methods

      • Renato Monteiro, Michael Todd
      Pages 267-306

    5. Bundle Methods to Minimize the Maximum Eigenvalue Function

      • Christoph Helmberg, Francois Oustry
      Pages 307-337

  5. Applications and Extensions

    1. Front Matter

      Pages 339-341
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    2. Combinatorial Optimization

      • Michel Goemans, Franz Rendl
      Pages 343-360

    3. Semidefinite Programming Relaxations of Nonconvex Quadratic Optimization

      • Yuri Nesterov, Henry Wolkowicz, Yinyu Ye
      Pages 361-419

    4. Semidefinite Programming in Systems and Control Theory

      • Venkataramanan Balakrishnan, Fan Wang
      Pages 421-441

    5. Structural Design

      • Aharon Ben-Tal, Arkadi Nemirovski
      Pages 443-467

    6. Moment Problems and Semidefinite Optimization

      • Dimitris Bertsimas, Jay Sethuraman
      Pages 469-509
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Keywords

About this book

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 Handbook of Semidefinite Programming 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.

Editors and Affiliations

  • Department of Combinatorics and Optimization Faculty of Mathematics, University of Waterloo, Waterloo, Canada

    Henry Wolkowicz

  • Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, USA

    Romesh Saigal

  • Electrical Engineering Department, UCLA, Los Angeles, USA

    Lieven Vandenberghe

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