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Optimization and Operations Research

Proceedings of a Conference Held at Oberwolfach, July 27–August 2, 1975

  • Werner Oettli
  • Klaus Ritter
Conference proceedings

Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 117)

Table of contents

  1. Front Matter
    Pages N2-IV
  2. Wolfgang Gaul
    Pages 83-91
  3. J. Gwinner
    Pages 99-113
  4. Joachim Hartung
    Pages 115-125
  5. R. Hettich, T. H. Twente
    Pages 127-141
  6. C. P. Ortlieb
    Pages 225-236
  7. Back Matter
    Pages 317-319

About these proceedings

Introduction

The variable metric algorithm is widely recognised as one of the most efficient ways of solving the following problem:- Locate x* a local minimum point n ( 1) of f(x) x E R Considerable attention has been given to the study of the convergence prop- ties of this algorithm especially for the case where analytic expressions are avai- ble for the derivatives g. = af/ax. i 1 ••• n • (2) ~ ~ In particular we shall mention the results of Wolfe (1969) and Powell (1972), (1975). Wolfe established general conditions under which a descent algorithm will converge to a stationary point and Powell showed that two particular very efficient algorithms that cannot be shown to satisfy \,olfe's conditions do in fact converge to the minimum of convex functions under certain conditions. These results will be st- ed more completely in Section 2. In most practical problems analytic expressions for the gradient vector g (Equ. 2) are not available and numerical derivatives are subject to truncation error. In Section 3 we shall consider the effects of these errors on Wolfe's convergent prop- ties and will discuss possible modifications of the algorithms to make them reliable in these circumstances. The effects of rounding error are considered in Section 4, whilst in Section 5 these thoughts are extended to include the case of on-line fu- tion minimisation where each function evaluation is subject to random noise.

Keywords

Oberwolfach algorithms evaluation operations research optimization

Editors and affiliations

  • Werner Oettli
    • 1
  • Klaus Ritter
    • 2
  1. 1.Fakultät für Mathematik und InformatikUniversität MannheimMannheim 1Deutschland
  2. 2.Mathematisches Institut AUniversität StuttgartStuttgart 80Deutschland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-46329-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 1976
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-07616-2
  • Online ISBN 978-3-642-46329-7
  • Series Print ISSN 0075-8442
  • Buy this book on publisher's site