Selected Topics in Operations Research and Mathematical Economics

1. Front Matter

   Pages I-IX

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2. Optimization Theory

   1. Front Matter

      Pages 1-1

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   2. A Method for Linearly Constrained Minimization Problems

      • Alfred Auslender

      Pages 3-12

   3. On a Class of Nonconvex Optimization Problems

      • R. Deumlich, K.-H. Elster

      Pages 13-29

   4. Lower Semicontinuity of Marginal Functions

      • Szymon Dolecki

      Pages 30-41

   5. A New Approach to Symmetric Quasiconvex Conjugacy

      • J. E. Martínez-Legaz

      Pages 42-48

   6. Generalized Convexity, Functional Hulls and Applications to Conjugate Duality in Optimization

      • Ivan Singer

      Pages 49-79

   7. Conjugation Operators

      • Ivan Singer

      Pages 80-97

   8. Global Minimization of a Difference of Two Convex Functions

      • Hoang Tuy

      Pages 98-118

   9. Closures and Neighbourhoods Induced by Tangential Approximations

      • Milan Vlach

      Pages 119-127

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

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].

• Economics
• Operations
• Operations Research
• algorithms
• game theory
• optimization
• Ökonometrie

• 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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