Minimization Methods for Non-Differentiable Functions
In recent years much attention has been given to the development of auto matic systems of planning, design and control in various branches of the national economy. Quality of decisions is an issue which has come to the forefront, increasing the significa
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Editorial Board R. L. Graham, Murray Hill J. Stoer, WOrzburg R. Varga,.Cleveland
N.Z.Shor
Minimization Methods for Non-Differentiable Functions Translated from the Russian by K. C. Kiwiel and A. Ruszczynski
Springer-Verlag Berlin Heidelberg New York Tokyo
Naum Zuselevich Shor Institute of Cybernetics of the Academy of Sciences of the Ukrainian SSR, 142/144 4D-letiya Oktyabrya Avenue 25227, Kiev-207, USSR Krzysztof C. Kiwiel Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6,01-447 Warsaw, Poland Andrzej Ruszczynski Institute of Automatic Control, Technical University of Warsaw, ul. Nowowiejska 15/19, 00-665 Warsaw, Poland
Title of the Russian original edition: Metody minimizatsii nedifferentsiruemykh funktsij i ikh prilozheniya Published by Naukova Dumka, Kiev 1979
AMS Subject Classifications: 26B25, 49007, 49027, 49037, 52A40, 65H10, 65 K05, 9OC06, 90C30 ISBN-13: 978-3-642-82120-2
e-ISBN-13: 978-3-642-82118-9
001: 10.1007/978-3-642-82118-9 Library of Congress Cataloging in Publication Data. Shor, Naum Zuselevich. Minimization methods for non-differentiable functions. (Springer series in computational mathematics; 3) Translation of: Metody minimizafuii nedifferentsiruemykh funktsiT i ikh prilozheniia. Bibliography: p. Includes index. 1. Mathematical optimization. 2. Nondifferentiable functions. I. Title. II. Series. 519 84-23594 QA402.5.S5413 1985 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to "Verwertungsgesellschaft Wort", Munich.
© by Springer-Verlag Berlin, Heidelberg 1985 Softcover reprint of the hardcover 1st edition 1985 Typesetting: Graphischer Betrieb Konrad Triltsch, WUrzburg Bookbinding: B. Helm, Berlin 2141/~543210
Preface
In recent years much attention has been given to the development of automatic systems of planning, design and control in various branches of the national economy. Quality of decisions is an issue which has come to the forefront, increasing the significance of optimization algorithms in mathematical software packages for al,ltomatic systems of various levels and purposes. Methods for minimizing functions with discontinuous gradients are gaining in importance and the ~xperts in the computational methods of mathematical programming tend to agree that progress in the development of algorithms for minimizing nonsmooth functions is the key to the construction of efficient techniques for solving large scale problems. This monograph summarizes to a certain extent fifteen years of the author's work on developing generalized gradient methods for nonsmooth minimization. This work started in the department of economic cybernetics of the Institute of Cybernetics of the Ukrainian Academy of Sciences under the supervision o
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