Fundamentals of Convex Analysis
This book is an abridged version of our two-volume opus Convex Analysis and Minimization Algorithms [18], about which we have received very positive feedback from users, readers, lecturers ever since it was published - by Springer-Verlag in 1993. Its peda
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Editors
A. Chenciner S. S. Chern B.Eckmann P. de la Harpe F. Hirzebruch N. Hitchin 1. Horrn ander M.-A. Knus A. Kupiainen G. Lebeau M. Ratner D. Serre Ya. G. Sinai N. J. A. Sloane J. Tits B. Totaro A. Vershik M. Waldschmidt
Managing Editors
M. Berger
J. Coates S. R. S. Varadhan
Springer-Verlag Berlin Heidelberg GmbH
Jean -Baptiste Hiriart -Urruty Claude Lemarechal
Fundatnentals of Convex Analysis With 66 Figures
i
Springer
Jean-Baptiste Hiriart-Urruty Departement de Mathematiques Universite Paul Sabatier 118, route de Narbonne 31062 Toulouse France e-mail: [email protected]
Claude Lemarechal INRIA, Rhone Alpes ZIRST 655, avenue de l'Europe 38330 Montbonnot France e-mail: [email protected] Library ofCongress Cataloging-in-Publication Data Hiriart-Unuty, Jean-Baptiste, 1949Fundamentals of convex ana1ysis / Jean-Baptiste Hiriart-Unuty, Claude Lemarecbal. p. em. -- (Gnmdlehren text editions) Includes bibliographical references and index. ISBN 978-3-540-42205-1 ISBN 978-3-642-56468-0 (eBook) DOI 10.1007/978-3-642-56468-0 1. Convex timctions. 2. Convex sets. 3. Mathematical ana1ysis. 1. Lemarecbal, Claude, 1944- II. Title. III. Series.
QA331.5 .H58 2001 51S.8--de21
2001053271
Corrected Second Printing 2004 Mathematics Subject Classification (2000): 21-01, 26B05, 52A41, 26Axx, 49Kxx, 49Mxx, 49-01, 93B30, 90CxX ISSN 1618-2685 ISBN 978-3-540-42205-1 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, re citation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. springeronline.com © Springer-Verlag Berlin Heidelberg 2001 Originally published by Springer-Verlag Berlin Heidelberg New York in 2001
The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: Erich Kirchner, Heidelberg Typeset by the authors using a Springer TJlX macro package Printed on acid-free paper
41/3142/LK - 5 43 210
Preface
This book is an abridged version of our two-volume opus Convex Analysis and Minimization Algorithms [18], about which we have received very positive feedback from users, readers, lecturers ever since it was published - by Springer-Verlag in 1993. Its pedagogical qualities were particularly appreciated, in the combination with a rather advanced technical material. Now [18] hasa dual but clearly defined nature: - an introduction to the basic concepts in convex analysis, - a study of convex minimization problems (with an
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