Journal article
Polyextremal principles and separably-infinite programs
Zeitschrift für Operations Research, Vol.24(7), pp.211-234
12/1980
DOI: 10.1007/BF01919901
Abstract
As a direct extension of Charnes' characterization of two-person zero-sum constrained games by linear programming, we show 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 an 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 a 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.
Details
- Title: Subtitle
- Polyextremal principles and separably-infinite programs
- Creators
- A. Charnes - The University of Texas at AustinP. R. Gribik - Pacific EnvironmentK. O. Kortanek - Carnegie Mellon University
- Resource Type
- Journal article
- Publication Details
- Zeitschrift für Operations Research, Vol.24(7), pp.211-234
- DOI
- 10.1007/BF01919901
- ISSN
- 0340-9422
- eISSN
- 1432-5217
- Number of pages
- 24
- Language
- English
- Date published
- 12/1980
- Academic Unit
- Business Analytics
- Record Identifier
- 9984963118402771
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