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Selected Topics in Operations Research and Mathematical Economics

Proceedings of the 8th Symposium on Operations Research, Held at the University of Karlsruhe, West Germany August 22–25, 1983

  • Conference proceedings
  • © 1984

Overview

Editors:
  1. Gerald Hammer

    1. Lehrstuhl für Anwendungen des Operations Research, Universität Karlsruhe, Karlsruhe 1, Germany

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  2. Diethard Pallaschke

    1. Institut für Statistik und Mathematische Wirtschaftstheorie, Universität Karlsruhe, Karlsruhe 1, Germany

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Part of the book series: Lecture Notes in Economics and Mathematical Systems (LNE, volume 226)

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Table of contents (37 papers)

  1. Front Matter

    Pages I-IX
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  3. Control Theory

    1. Front Matter

      Pages 129-129
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    2. On the Principle of “Internal Modelling” in Linear Control Theory

      • H. W. Knobloch
      Pages 131-151

    3. On Optimal Observability of Lipschitz Systems

      • S. Rolewicz
      Pages 152-158

  4. Mathematical Economics

    1. Front Matter

      Pages 159-159
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    2. Convergence of σ-Fields and Applications to Mathematical Economics

      • Beth Allen
      Pages 161-174

    3. Optimal Growth Policies for Resource-Dependent Open Economies

      • Wolfgang Eichhorn, Hans Ulrich Buhl
      Pages 175-187

    4. A Characterization of the Proportional Income Tax

      • Wolfgang Eichhorn, Helmut Funke
      Pages 188-192

    5. Duality in the Theory of Social Choice

      • Susanne Fuchs-Seliger
      Pages 193-204

    6. Nonlinear Models of Business Cycle Theory

      • Guenter Gabisch
      Pages 205-222

    7. Existence of Economic Equilibrium: New Results and Open Problems

      • Hans Keiding
      Pages 223-242
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Keywords

About this book

Let eRN be the usual vector-space of real N-uples with the usual inner product denoted by (. ,. ). In this paper P is a nonempty compact polyhedral set of mN, f is a real-valued function defined on (RN continuously differentiable and fP is the line- ly constrained minimization problem stated as : min (f(x) I x € P) • For computing stationary points of problemtj) we propose a method which attempts to operate within the linear-simplex method structure. This method then appears as a same type of method as the convex-simplex method of Zangwill [6]. It is however, different and has the advantage of being less technical with regards to the Zangwill method. It has also a simple geometrical interpretation which makes it more under­ standable and more open to other improvements. Also in the case where f is convex an implementable line-search is proposed which is not the case in the Zangwill method. Moreover, if f(x) = (c,x) this method will coincide with the simplex method (this is also true in the case of the convex simplex method) i if f(x) = I Ixl 12 it will be almost the same as the algorithm given by Bazaraa, Goode, Rardin [2].

Editors and Affiliations

  • Lehrstuhl für Anwendungen des Operations Research, Universität Karlsruhe, Karlsruhe 1, Germany

    Gerald Hammer

  • Institut für Statistik und Mathematische Wirtschaftstheorie, Universität Karlsruhe, Karlsruhe 1, Germany

    Diethard Pallaschke

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