Handbook on Semidefinite, Conic and Polynomial Optimization

  • Miguel F. Anjos
  • Jean B. Lasserre
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 166)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Miguel F. Anjos, Jean B. Lasserre
    Pages 1-22
  3. Theory

    1. Front Matter
      Pages 23-23
    2. Monique Laurent, Philipp Rostalski
      Pages 25-60
    3. J. William Helton, Jiawang Nie
      Pages 77-112
    4. João Gouveia, Rekha Thomas
      Pages 113-138
    5. Eden Chlamtac, Madhur Tulsiani
      Pages 139-169
    6. Etienne de Klerk, Fernando M. de Oliveira Filho, Dmitrii V. Pasechnik
      Pages 171-199
    7. Samuel Burer
      Pages 201-218
    8. Christine Bachoc, Dion C. Gijswijt, Alexander Schrijver, Frank Vallentin
      Pages 219-269
    9. Jean B. Lasserre
      Pages 271-295
    10. J. William Helton, Igor Klep, Scott McCullough
      Pages 377-405
    11. Jean B. Lasserre, Mihai Putinar
      Pages 407-434
  4. Algorithms

About this book

Introduction

Semidefinite and conic optimization is a major and thriving research area within the optimization community. Although semidefinite optimization has been studied (under different names) since at least the 1940s, its importance grew immensely during the 1990s after polynomial-time interior-point methods for linear optimization were extended to solve semidefinite optimization problems.

Since the beginning of the 21st century, not only has research into semidefinite and conic optimization continued unabated, but also a fruitful interaction has developed with algebraic geometry through the close connections between semidefinite matrices and polynomial optimization. This has brought about important new results and led to an even higher level of research activity.

This Handbook on Semidefinite, Conic and Polynomial Optimization provides the reader with a snapshot of the state-of-the-art in the growing and mutually enriching areas of semidefinite optimization, conic optimization, and polynomial optimization. It contains a compendium of the recent research activity that has taken place in these thrilling areas, and will appeal to doctoral students, young graduates, and experienced researchers alike.

The Handbook’s thirty-one chapters are organized into four parts:

  • Theory, covering significant theoretical developments as well as the interactions between conic optimization and polynomial optimization;
  • Algorithms, documenting the directions of current algorithmic development;
  • Software, providing an overview of the state-of-the-art;
  • Applications, dealing with the application areas where semidefinite and conic optimization has made a significant impact in recent years.

Keywords

Combinatorial Optimization Conic Optimization Convex Relaxation Mathematical Programming Operations Research Optimization Models Polynomial Optimization Semidefinite Optimization

Editors and affiliations

  • Miguel F. Anjos
    • 1
  • Jean B. Lasserre
    • 2
  1. 1., Department of Mathematics and IndustrialEcole Polytechnique MontrealMontrealCanada
  2. 2.LAAS-CNRSToulouse Cedex 4France

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-0769-0
  • Copyright Information Springer Science+Business Media, LLC 2012
  • Publisher Name Springer, Boston, MA
  • eBook Packages Business and Economics
  • Print ISBN 978-1-4614-0768-3
  • Online ISBN 978-1-4614-0769-0
  • Series Print ISSN 0884-8289
  • About this book