Polyextremal Principles and Separably-Infinite Programs.

Abstract

As a direct extension of Charnes' characterization of two-person zero-sum constrained games by linear programming, it is shown how a general class of saddle value problems can be reduced to a pair of uniextremal dual separably-infinite programs. These programs have an infinite number of variables and an infinite number of constraints, but only a finite number of variables appear in a infinite number of constraints and only a finite number of constraints have an infinite number of variables. The conditions under which the characterization holds are among the more general ones appearing in the literature sufficient to guarantee the existence of a saddle point of concave-convex function. The key construction involves augmenting a given player's original set of variables by generalized finite sequences determined by the other player's constraint set and objective function. A duality theory is developed which includes complementarity conditions, thereby making contact with the numerical treatment of semi-infinite programming.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1980
Accession Number
ADA081943

Entities

People

  • A. Levine
  • Abraham Charnes
  • K. Kortanke
  • P. Gribik

Organizations

  • University of Texas at Austin

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Communities of Interest

  • Human Systems

DTIC Thesaurus Topics

  • Abstracts
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  • Computer Programming
  • Construction
  • Convex Programming
  • Convex Sets
  • Economics
  • Guarantees
  • Linear Programming
  • Literature
  • Mathematical Programming
  • New York
  • Operations Research
  • Optimization
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Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Operations Research