Optimization and
Nonsmooth Analysis/
SIAM's Classics in Applied Mathematics series consists of books that were previously
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Classics in Applied Mathematics
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Johan G. F. Belinfante and Bernard Kolman, A Survey of Lie Groups and Lie Algebras
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James M. Ortega, Numerical Analysis: A Second Course
Anthony V. Fiacco and Garth P. McCormick, Nonlinear Programming: Sequential
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F. H. Clarke, Optimization and Nonsmooth Analysis
George F. Carrier and Carl E. Pearson, Ordinary Differential Equations
Leo Breiman, Probability
R. Bellman and G. M. Wing, An Introduction to Invariant Imbedding
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Richard E. Barlow and Frank Proschan, Mathematical Theory of Reliability
Cornelius Lanczos, Linear Differential Operators
Richard Bellman, Introduction to Matrix Analysis, Second Edition
Beresford N. Parlett, The Symmetric Eigenvalue Problem
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ii
Classics in Applied Mathematics (continued)
Richard Haberman, Mathematical Models: Mechanical Vibrations, Population
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Peter W. M. John, Statistical Design and Analysis of Experiments
Tamer Ba§ar and Geert Jan Olsder, Dynamic Noncooperative Game Theory, Second
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Philip Hartman, Ordinary Differential Equations, Second Edition
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Eugene L. Allgower and Kurt Georg, Introduction to Numerical Continuation Methods
Heinz-Otto Kreiss and Jens Lorenz, Initial-Boundary Value Problems and the Navier-
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J. L. Hodges, Jr. and E. L. Lehmann, Basic Concepts of Probability and Statistics,
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iii
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Optimization and
Nonsmooth Analysis/
Frank H. Clarke
University of Montreal
BIHJTL
Society for Industrial and Applied Mathematics
Philadelphia
Library of Congress Cataloging-in-Publication Data
Clarke, Frank H.
Optimization and nonsmooth analysis / F. H. Clarke.
p. cm. - (Classics in applied mathematics ; 5)
Reprint. Originally published: New York : Wiley, 1983.
Includes bibliographical references.
ISBN 0-89871-256-4
1. Mathematical optimization. 2. Mathematical analysis.
I. Title. II. Title: Nonsmooth analysis. III. Series: Classics in
applied mathematics ; vol. 5.
QA402.5.C53 1990
519.3-dc20
90-35113
CIP
1 0 9 8 7 6 5 4
Copyright © 1990 by the Society for Industrial and Applied Mathematics
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This SI AM edition is an unabridged, corrected republication of the work first published
by John Wiley & Sons, Inc., New York, 1983.
51HJTI is a registered trademark.
This book is dedicated to my mother