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Optimization and Operations Research

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

  • Conference proceedings
  • © 1976

Overview

Editors:
  1. Werner Oettli

    1. Fakultät für Mathematik und Informatik, Universität Mannheim, Mannheim 1, Deutschland

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  2. Klaus Ritter

    1. Mathematisches Institut A, Universität Stuttgart, Stuttgart 80, Deutschland

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    You can also search for this editor in PubMed   Google Scholar

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

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Table of contents (27 papers)

  1. Front Matter

    Pages N2-IV
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  2. Reduction and Dekomposition of Modulo Optimization Problems

    • A. Bachem
    Pages 1-8

  3. Optimization of Elastic Structures by Mathematical Programming Techniques

    • H. Baier
    Pages 9-22

  4. On Closed Sets Having A Least Element

    • Peter Bod
    Pages 23-34

  5. On the Convergence of the Variable Metric Method with Numerical Derivatives and the Effect of Noise in the Function Evaluation

    • L. C. W. Dixon
    Pages 35-53

  6. Parallel Path Strategy Theory and Numerical Illustrations

    • Hilmar Drygas
    Pages 55-75

  7. On minimization under linear equality constraints

    • Jürgen Fischer
    Pages 77-81

  8. On Constrained Shortest-Route Problems

    • Wolfgang Gaul
    Pages 83-91

  9. Bang-Bang Solution of a Control Problem for the Heat Equation

    • Klaus Glashoff
    Pages 93-98

  10. Generalized Stirling-Newton Methods

    • J. Gwinner
    Pages 99-113

  11. On a Method for Computing Pseudoinverses

    • Joachim Hartung
    Pages 115-125

  12. Charakterisierung Lokaler Pareto-Optima

    • R. Hettich, T. H. Twente
    Pages 127-141

  13. On the Exact Evaluation of Finite Activity Networks with Stochastic Durations of Activities

    • E. Höpfinger, U. Steinhardt
    Pages 143-145

  14. Approximation of a Parabolic Boundary Control Problem by the Line Method

    • M. Köhler
    Pages 147-159

  15. Regularisation of Optimization Problems and Operator Equations

    • Peter Kosmol
    Pages 161-170

  16. Some extensions of linearly constrained nonlinear programming

    • Vera Kovacevic
    Pages 171-182

  17. Boundary Control of the Higher-Dimensional Wave Equation

    • W. Krabs
    Pages 183-189

  18. Nondifferentiable Optimisation Subgradient and ε — Subgradient Methods

    • Claude Lemarechal
    Pages 191-199

  19. Approximations to Stochastic Optimization Problems

    • Kurt Marti
    Pages 201-213

  20. Models in Resource Allocation — Trees of Queues

    • Bernd Meister
    Pages 215-223
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Keywords

About this book

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.

Editors and Affiliations

  • Fakultät für Mathematik und Informatik, Universität Mannheim, Mannheim 1, Deutschland

    Werner Oettli

  • Mathematisches Institut A, Universität Stuttgart, Stuttgart 80, Deutschland

    Klaus Ritter

Bibliographic Information

  • Book Title: Optimization and Operations Research

  • Book Subtitle: Proceedings of a Conference Held at Oberwolfach, July 27–August 2, 1975

  • Editors: Werner Oettli, Klaus Ritter

  • Series Title: Lecture Notes in Economics and Mathematical Systems

  • DOI: https://doi.org/10.1007/978-3-642-46329-7

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin · Heidelberg 1976

  • Softcover ISBN: 978-3-540-07616-2Published: 01 February 1976

  • eBook ISBN: 978-3-642-46329-7Published: 06 December 2012

  • Series ISSN: 0075-8442

  • Series E-ISSN: 2196-9957

  • Edition Number: 1

  • Number of Pages: IV, 318

  • Number of Illustrations: 8 b/w illustrations

  • Topics: Operations Research/Decision Theory

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