Handbook of Semidefinite Programming

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

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.

• Analysis
• Optimality Conditions
• Optimization Theory
• Optimization and Control Theory
• algorithms
• combinatorial optimization
• linear algebra
• linear optimization
• nonlinear optimization
• optimization

• 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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