The Linearization Method for Constrained Optimization
Techniques of optimization are applied in many problems in economics, automatic control, engineering, etc. and a wealth of literature is devoted to this subject. The first computer applications involved linear programming problems with simp- le structure
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Editorial Board R. L. Graham, Murray Hill (NJ) J. Stoer, WOrzburg R. Varga, Kent (Ohio)
B. N. Pshenichnyj
The Linearization Method for Constrained Optimization Translated from the Russian by Stephen S. Wilson With 6 tab les
Springer-Verlag Berlin Heidelberg GmbH
Boris N. Pshenichnyj Institute of Cybernetics of the Academy of the Ukrainian SSR 142/144-4 Oletiya Oktyabrya ul. 25227 Kiev - 207 Ukraina, CIS Translator Stephen S. Wilson Fourwinds 79 New Barn Lane Prestbury Cheltenham Gloucestershire GL 52 3LE United Kingdom
Mathematics Subject Classification (1991 ):49Kxx, 49M35, 49M40, 49M45,65K05,65K10,90C05,90C20,90C25 Nauka, Moscow 1983: B. N. Pshenichnyj, Metod Linearizatsii ISBN 978-3-642-63401-7
Library 01 Congress Cataloging-in-Publication Data PshenichnYI, B. N. (Boris Nikolaevich) [Metod linearizatsii. Englishj The linearization method lor constrained optimization/B. N. Pshenichnyj; translated Irom the Russian by Stephen S. Wilson. p. cm. - (Springer series in computational mathematics; 22) Includes bibliographical relerences and index. ISBN 978-3-642-63401-7 ISBN 978-3-642-57918-9 (eBook) DOI 10.1007/978-3-642-57918-9 1. Nonlinear programming. 1. Title. II. Series. T57.8.P7913 1994 519.7'6-dc20 94-1938 CIP This work is subject to copyright. AII rights are reserved, whether the whole ar part 01 the material is concerned, specilically the rights 01 translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication 01 this publication ar parts thereof is permitted only under the provisions 01 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. © Springer-Verlag Berlin Heidelberg 1994
Originally published by Springer-Verlag Berlin Heidelberg New York in 1994 Softcover reprint of the hardcover IsI edilion 1994 41/3140 - 5 4 3 2 1 O - Printed on acid-free paper
Foreword
It is customary in a foreword to write about the practical importance of the problem and to describe the contents of the book. However, the practical importance of solving optimization problems has been unquestioned for some time. A wealth of scientific and popular scientific literature is devoted to this subject, so that it is almost unnecessary to repeat yet again that the theory and techniques of optimization are applied in many problems in economics, automatic control, engineering etc. On the other hand, a comprehensive summary of the contents of the book is given in the first introductory section. Therefore, I shall not dwell on this here. Instead, I shall allow myself a number of general remarks on the theory and the numerical techniques of optimization and the interlinking of these in the solution of a complicated real problem. Electronic computers were first applied to solve optimization problems in their earliest days. The first such applications involved linear programming pro
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