文档介绍：Convex Optimization
Convex Optimization
Stephen Boyd
Department of Electrical Engineering
Stanford University
Lieven Vandenberghe
Electrical Engineering Department
University of California, Los Angeles
published by the press syndicate of the university of cambridge
The Pitt Building, Trumpington Street, Cambridge, United Kingdom
cambridge university press
The Edinburgh Building, Cambridge, CB2 2RU, UK
40 West 20th Street, New York, NY 10011-4211, USA
477 Williamstown Road, Port Melbourne, VIC 3207, Australia
Ruiz de Alarc´on 13, 28014 Madrid, Spain
Dock House, The Waterfront, Cape Town 8001, South Africa
c Cambridge University Press 2004
°
This book 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
Printed in the United Kingdom at the University Press, Cambridge
Typeset puter Modern Roman using LATEX
A catalogue record for this book is available from the British Library
Library of Congress Cataloguing in Publication data not yet available
ISBN 0 521 83378 7 hardback
For
Anna, Nicholas, and Nora
Dani¨el and Margriet
Contents
Preface xi
1 Introduction 1
Mathematical optimization . . . . . . . . . . . . . . . . . . . . . . . . 1
Least-squares and linear programming . . . . . . . . . . . . . . . . . . 4
Convex optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Nonlinear optimization . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
I Theory 19
2 Convex sets 21
Affine and convex sets . . . . . . . . . . . . . . . . . . . . . . . . . . . 2