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

    1. Front Matter
      Pages 435-435
    2. Maziar Salahi, Tamás Terlaky
      Pages 437-454
    3. Zaiwen Wen, Donald Goldfarb, Katya Scheinberg
      Pages 533-564
    4. Didier Henrion, Jérôme Malick
      Pages 565-600
    5. Miguel Navascués, Stefano Pironio, Antonio Acín
      Pages 601-634
    6. Willem-Jan van Hoeve
      Pages 635-668
  5. Software

    1. Front Matter
      Pages 669-669
    2. Hans D. Mittelmann
      Pages 671-686
    3. Makoto Yamashita, Katsuki Fujisawa, Mituhiro Fukuda, Kazuhiro Kobayashi, Kazuhide Nakata, Maho Nakata
      Pages 687-713
    4. Michal Kocvara, Michael Stingl
      Pages 755-791
  6. Applications

    1. Front Matter
      Pages 793-793
    2. Laura Palagi, Veronica Piccialli, Franz Rendl, Giovanni Rinaldi, Angelika Wiegele
      Pages 821-847
    3. Miguel F. Anjos, Frauke Liers
      Pages 849-877
    4. Nathan Krislock, Henry Wolkowicz
      Pages 879-914
    5. Youwei Zhang, Alexandre d’Aspremont, Laurent El Ghaoui
      Pages 915-940
  7. Back Matter
    Pages 941-957

About this book


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.


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

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