Optimization and Control with Applications
This book contains refereed papers which were presented at the 34th Workshop of the International School of Mathematics "G. Stampacchia,” the International Workshop on Optimization and Control with Applications. The book contains 28 papers that are groupe
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Liqun Qi Koklay Teo Xiaoqi Yang (Eds.)
OPTIMIZATION AND CONTROL WITH APPLICATIONS
OPTIMIZATION AND CONTROL WITH APPLICATIONS
Applied Optimization VOLUME 96 Series Editors:
Panos M. Pardalos University of Florida, U.S.A. Donald W. H e m University of Florida, U.S.A.
OPTIMIZATION AND CONTROL WITH APPLICATIONS
Edited by LIQUN QI The Hong Kong Polytechnic University, Hong Kong KOKLAY TEO The Hong Kong Polytechnic University, Hong Kong XIAOQI YANG The Hong Kong Polytechnic University, Hong Kong
Q - Springer
Library of Congress Cataloging-in-Publication Data A C.I.P. record for this book is available from the Library of Congress.
ISBN 0-387-24254-6
e-ISBN 0-387-24255-4
Printed on acid-free paper.
O 2005 Springer Science+Business Media, Inc.
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, Inc., 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 know or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks and similar terms, even if the 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 in the United States of America. 9 8 7 6 5 4 3 2 1
SPIN 11367154
Contents
Preface Biographical Sketch of Elijah Polak Publications of Elijah Polak Part I DUALITY AND OPTlMALlTY CONDITIONS 1 ON MINIMIZATION OF MAX-MIN FUNCTIONS A.M. Baqimv and A.M. Ruhin,oo 1 lntroduction 2 Special Classes of Max-min Objective Functions 3 Discrete Max-min Functions 4 Optimization Problems with Max-min Constraints 5 Minimization of Continuous Maximum Functions 6 Concluding Remarks
References L
A COMPARISON OF TWO APPROACHES T O SECOND-ORDER SUBDIFFERENTlABlLlTY CONCEPTS WITH APPLICATION T O OPTIMALITY CONDITIONS A . Eherhard and C . E. M. Prairr 1 lntroduction 2 Preliminaries 3 Characterization of Supported Operators 4 Generalized Convexity and Proximal Subderivatives 5 Generalized Convexity and Subjets 6 Subjet, Contingent Cone Inclusions 7 Some Consequences for Optimality Conditions 8 Appendix References DUALITY AND EXACT PENALIZATION VIA A GENERALIZED AUGMENTED LAGRANGIAN FUNCTION X . X . Hwqg and X. Q. Yang 1 lntroduction
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xv xvii
vi
OPTIMIZATION AND CONTROL WITH APPLICATIONS 2 3 4 5
Generalized Augmented Lagrangian Strong Duality Exact Penalty Representation Conclusions
References 4 DUALITY FOR SEMI-DEFINITE AND SEMI-INFINITE PROGRAMMING WITH EQUALITY CONSTRAINTS S. J. Li, X. Q. Yang and K. L. Teo 1 lntroduction and Preliminaries 2 Uniform Duality for Homogeneous (SDSIP) Uniform Duality for Nonhomogeneous (SDSIP) 3
References 5
THE USE OF NONSMOOTH ANALYSIS AND OF DUALITY METHODS FOR THE STUDY OF HAMILTON-JACOB1 EQUATIONS Jean-Paul Penot
