Handbook on Semidefinite, Conic and Polynomial Optimization
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 199
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Series Editor Frederick S. Hillier Stanford University, CA, USA Special Editorial Consultant Camille C. Price Stephen F. Austin State University, TX, USA
For further volumes: http://www.springer.com/series/6161
Miguel F. Anjos • Jean B. Lasserre Editors
Handbook on Semidefinite, Conic and Polynomial Optimization
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Editors Miguel F. Anjos Department of Mathematics and Industrial Engineering & GERAD ´ Ecole Polytechnique de Montr´eal Montr´eal, QC, Canada H3C 3A7 [email protected]
Jean B. Lasserre LAAS-CNRS and Institute of Mathematics 7 Avenue du Colonel Roche 31077 Toulouse Cedex 4 France [email protected]
ISSN 0884-8289 ISBN 978-1-4614-0768-3 e-ISBN 978-1-4614-0769-0 DOI 10.1007/978-1-4614-0769-0 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2011938887 © Springer Science+Business Media, LLC 2012 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
Conic optimization is a significant and thriving research area within the optimization community. Conic optimization is the general class of problems concerned with optimizing a linear function over the intersection of an affine space and a closed convex cone. One special case of great interest is the choice of the cone of positive semidefinite matrices for which the resulting optimization problem is called a semidefinite optimization problem. Semidefinite optimization, or semidefinite programming (SDP), 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 SDP problems (and more generally, to solve convex optimization problems with efficiently computable self-concordant barrier functions). Some of the earliest applications of SDP that followed this development were the solution of linear matrix inequalities in control theory, and the design of polynomial-time approximation schemes for hard combinatorial problems such as the maximum-cut problem. This burst of activity in the 1990s led to the publication of the Handbook of Semidefinite Programming in the year 2000. That Handbook, edited by Wolkowicz, Saigal, and Vandenberghe, provided an overview of much of the activity in the area. Research into semidefin
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