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Minimization Methods for Non-Differentiable Functions

  • Naum Zuselevich Shor

Part of the Springer Series in Computational Mathematics book series (SSCM, volume 3)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Naun Zuselevich Shor
    Pages 1-5
  3. Naun Zuselevich Shor
    Pages 22-47
  4. Naun Zuselevich Shor
    Pages 48-92
  5. Back Matter
    Pages 150-164

About this book

Introduction

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 significance of optimization algorithms in math­ ematical software packages for al,ltomatic systems of various levels and pur­ poses. 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 con­ struction 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 of V.S. Mikhalevich, a member of the Ukrainian Academy of Sciences, in connection with the need for solutions to important, practical problems of optimal planning and design. In Chap. I we describe basic classes of nonsmooth functions that are dif­ ferentiable almost everywhere, and analyze various ways of defining generalized gradient sets. In Chap. 2 we study in detail various versions of the su bgradient method, show their relation to the methods of Fejer-type approximations and briefly present the fundamentals of e-subgradient methods.

Keywords

Applications Approximation Functions algorithms optimization

Authors and affiliations

  • Naum Zuselevich Shor
    • 1
  1. 1.Institute of Cybernetics of the Academy of Sciences of the Ukrainian SSRKiev-207USSR

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-82118-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 1985
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-82120-2
  • Online ISBN 978-3-642-82118-9
  • Series Print ISSN 0179-3632
  • Buy this book on publisher's site