 Dual Programming Problems as Hemi-GamesEnrique Cansado
Management Science, 1969, vol. 15, issue 9, 539-549 Abstract: It is proposed here a new and unifying formal framework for duality in optimization problems, relating more closely programs to games, by means of the concepts of "hemi-games" and "quasi-duality". A new generalization of the idea of La-grange multipliers is also presented. Associated with each programming problem, we consider (through a generalization of the Lagrange's function) one particular game (from the many possible ones) such that our programming problem is one of the two hemi-games of such a game. Each hemi-game can be considered as a programming problem. Then, for each game we have a pair of programming problems: the two hemi-games of the game considered. If the game has a solution, then so does each of the two associated programming problems; and the solution of each one is an optimal strategy for the respective player. This couple of programming problems constitute a pair of dual problems. And each pair of dual problems can be thought out as such a couple of programming problems associated with the two players of a solvable game. Various and seemingly disparate dualities, already considered in the literature, are then exhibited in order to show how they can be obtained from the hemi-game notion proposed. This conceptual framework of duality is not used here for obtaining "new" results, but seems sufficiently interesting in itself. Date: 1969 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:15:y:1969:i:9:p:539-549 Access Statistics for this article More articles in Management Science from INFORMS Contact information at EDIRC. |
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