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Dual Programming Problems as Hemi-Games

Author

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  • Enrique Cansado

    (Director Inter American Statistical Training Center, Santiago, Chile)

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.

Suggested Citation

  • Enrique Cansado, 1969. "Dual Programming Problems as Hemi-Games," Management Science, INFORMS, vol. 15(9), pages 539-549, May.
    • Handle: RePEc:inm:ormnsc:v:15:y:1969:i:9:p:539-549
    DOI: 10.1287/mnsc.15.9.539
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