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.
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