Convex Optimization: Stephen Boyd and Lieven Vandenberghe
Convex Optimization
Convex Optimization
Stephen Boyd
Department of Electrical Engineering
Stanford University
Lieven Vandenberghe
Electrical Engineering Department
University of California, Los Angeles
cambridge university press
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, S˜o Paolo, Delhi a Cambridge University Press
The Edinburgh Building, Cambridge, CB2 8RU, UK
Published in the United States of America by Cambridge University Press, New York http://www.cambridge.org Information on this title: www.cambridge.org/9780521833783 c Cambridge University Press 2004
This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press.
First published 2004
Seventh printing with corrections 2009
Printed in the United Kingdom at the University Press, Cambridge
A catalogue record for this publication is available from the British Library
Library of Congress Cataloguing-in-Publication data
Boyd, Stephen P.
Convex Optimization / Stephen Boyd & Lieven Vandenberghe
p. cm.
Includes bibliographical references and index.
ISBN 0 521 83378 7
1. Mathematical optimization. 2. Convex functions. I. Vandenberghe, Lieven. II. Title.
QA402.5.B69 2004
519.6–dc22
2003063284
ISBN 978-0-521-83378-3 hardback
Cambridge University Press has no responsiblity for the persistency or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.
For
Anna, Nicholas, and Nora
Dani¨l and Margriet e Contents
Preface
1 Introduction
1.1 Mathematical optimization . . . . . .
1.2 Least-squares and linear programming
1.3 Convex optimization . . . . . . . . . .
1.4 Nonlinear optimization . . . . . . . .
1.5 Outline . . . . . . . .
Convex Optimization
Stephen Boyd
Department of Electrical Engineering
Stanford University
Lieven Vandenberghe
Electrical Engineering Department
University of California, Los Angeles
cambridge university press
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, S˜o Paolo, Delhi a Cambridge University Press
The Edinburgh Building, Cambridge, CB2 8RU, UK
Published in the United States of America by Cambridge University Press, New York http://www.cambridge.org Information on this title: www.cambridge.org/9780521833783 c Cambridge University Press 2004
This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press.
First published 2004
Seventh printing with corrections 2009
Printed in the United Kingdom at the University Press, Cambridge
A catalogue record for this publication is available from the British Library
Library of Congress Cataloguing-in-Publication data
Boyd, Stephen P.
Convex Optimization / Stephen Boyd & Lieven Vandenberghe
p. cm.
Includes bibliographical references and index.
ISBN 0 521 83378 7
1. Mathematical optimization. 2. Convex functions. I. Vandenberghe, Lieven. II. Title.
QA402.5.B69 2004
519.6–dc22
2003063284
ISBN 978-0-521-83378-3 hardback
Cambridge University Press has no responsiblity for the persistency or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.
For
Anna, Nicholas, and Nora
Dani¨l and Margriet e Contents
Preface
1 Introduction
1.1 Mathematical optimization . . . . . .
1.2 Least-squares and linear programming
1.3 Convex optimization . . . . . . . . . .
1.4 Nonlinear optimization . . . . . . . .
1.5 Outline . . . . . . . .
References: Design. McGraw-Hill, 1984. edition, 2000. Press, 1991. pages 49–95, 1995. John von Neumann. Collected Works, volume VI, pages 89–95. Pergamon Press, 1963 R. Webster. Convexity. Oxford University Press, 1994. Algebra and Its Applications, 40:101–118, 1981. Applied Mathematics, 1997. Research, 62:151–172, 1996. constraints. Mathematical Programming, 84:219–226, 1999.