Regularity Concepts in Nonsmooth Analysis Theory and Applications
Regularity concepts have played an increasingly important role in the applications of nonsmooth analysis, including differential inclusions, optimization, and variational inequalities. This heightened role has made it beneficial to introduce graduate stud
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Aims and Scope Optimization has been expanding in all directions at an astonishing rate during the last few decades. New algorithmic and theoretical techniques have been developed, the diffusion into other disciplines has proceeded at a rapid pace, and our knowledge of all aspects of the field has grown even more profound. At the same time, one of the most striking trends in optimization is the constantly increasing emphasis on the interdisciplinary nature of the field. Optimization has been a basic tool in all areas of applied mathematics, engineering, medicine, economics, and other sciences. The series Springer Optimization and Its Applications publishes undergraduate and graduate textbooks, monographs and state-of-the-art expository work that focus on algorithms for solving optimization problems and also study applications involving such problems. Some of the topics covered include nonlinear optimization (convex and nonconvex), network flow problems, stochastic optimization, optimal control, discrete optimization, multi-objective programming, description of software packages, approximation techniques and heuristic approaches.
For further volumes: http://www.springer.com/series/7393
Messaoud Bounkhel
Regularity Concepts in Nonsmooth Analysis Theory and Applications
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Messaoud Bounkhel Department of Mathematics College of Science King Saud University 11451 Riyadh Saudi Arabia [email protected]
ISSN 1931-6828 ISBN 978-1-4614-1018-8 e-ISBN 978-1-4614-1019-5 DOI 10.1007/978-1-4614-1019-5 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2011938686 © 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)
To the soul of my dear father, Ahmed, who died in 1994 and who always believed in me and encouraged me to study mathematics. To my dear mother Fatma, who has always stood behind all my successes. To my wife Leila, my children Saged, Kawtar, and Yakine, and to my brothers and sisters and all the members of my family.
Preface
The term nonsmooth analysis theory had been used in the 1970s by F. Clarke when he studied and applied the differential properties of functions and sets that are not differentiable in the usual sense. Since Clarke’s work, the field of nonsmooth analysis
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