Global Optimization Deterministic Approaches
The enormous practical need for solving global optimization problems coupled with a rapidly advancing computer technology has allowed one to consider problems which a few years ago would have been considered computationally intractable. As a consequence,
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Global Optimization Deterministic Approaches
With 55 Figures
Springer-Verlag Berlin Heidelberg GmbH
Professor Or. Reiner Horst University of Trier Oepartment of Mathematics P.O.Box 3825 0-5500 Trier, FRG Professor Or. Hoang Tuy Vien Toan Hoc Institute of Mathematics P.O.Box 631, BO-HO 10000 Hanoi, Vietnam
ISBN 978-3-662-02600-7 ISBN 978-3-662-02598-7 (eBook) DOI 10.1007/978-3-662-02598-7 This work is subject to copyright. Ali rights are reserved, whether the whole or part ofthe material is concemed, specifically the rights oftranslation, reprinting, reuse ofillustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication ofthis publication or parts thereof is ooly permitted under the provisions ofthe German Copyright Law ofSeptember 9,1965, in its version ofJune 24, 1985, and a copyright fee must always be paid. Violations fali under the prosecution act ofthe German Copyright Law. © Springer-Verlag Berlin Heidelberg 1990 OriginaIly published by Springer-Verlag Berlin Heidelberg New York Tokyo in 1990 Softcover reprint of the hardcover 1st edition 1990 The use ofregistered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. 2142/7130-543210
PREFACE
The enormous practical need for solving global optimization problems coupled with a rapidly advancing computer technology has allowed one to consider problems which a few years ago would have been considered computationally intractable. As a consequence, we are seeing the creation of a large and increasing number of diverse algorithms for solving a wide variety of multiextremal global optimization problems. The goal of this book is to systematically clarify and unify these diverse approaches in order to provide insight into the underlying concepts and their properties. Aside from a coherent view of the field much new material is presented. By definition, a multiextremal global optimization problem seeks at least one global minimizer of a real-valued objective function that possesses different local minimizers. The feasible set of points in IRn is usually determined by a system of inequalities. It is well known that in practically all disciplines where mathematical models are used there are many real-world problems which can be formulated as multi extremal global optimization problems. Standard nonlinear programming techniques have not been successful for solving these problems. Their deficiency is due to the intrinsic multiextremality of the formulation and not to the lack of smoothness or continuity, for often the latter properties are present. One can observe that local· tools such as gradients, subgradients, and second order constructions such as Hessians, cannot be expected to yield more than local solutions. One finds, for example, that a stationary point is often detected for which there is even no guarantee of local minimality. Moreover
