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On linear programming duality and necessary and sufficient conditions in minimax theory

Author

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  • Frenk, J.B.G.
  • Kas, P.
  • Kassay, G.

Abstract

In this paper we discuss necessary and sufficient conditions for different minimax results to hold using only linear programming duality and the finite intersection property of compact sets. It turns out that these necessary and sufficient conditions have a clear interpretation within zero-sum game theory. In the last section we apply these results to derive necessary and sufficient conditions for strong Lagrangean duality for a large class of optimization problems.

Suggested Citation

  • Frenk, J.B.G. & Kas, P. & Kassay, G., 2004. "On linear programming duality and necessary and sufficient conditions in minimax theory," Econometric Institute Research Papers EI 2004-14, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:1219
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    File URL: https://repub.eur.nl/pub/1219/ei200414.pdf
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    References listed on IDEAS

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    1. Frenk, J.B.G. & Kassay, G. & Protassov, V., 2002. "On Borel Probability Measures and Noncooperative Game Theory," ERIM Report Series Research in Management ERS-2002-85-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    2. Frenk, J.B.G. & Kassay, G. & Kolumban, J., 2002. "Equivalent Results in Minimax Theory," ERIM Report Series Research in Management ERS-2002-08-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    3. Frenk, J.B.G. & Kassay, G. & Protassov, V., 2002. "On Borel Probability Measures and Noncooperative Game Theory," Econometric Institute Research Papers ERS-2002-85-LIS, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    4. J.B.G. Frenk & G. Kassay & V. Protassov, 2002. "On Borel Probability Measures and Noncooperative Game Theory," Tinbergen Institute Discussion Papers 02-093/4, Tinbergen Institute.
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    Cited by:

    1. J. B. G. Frenk & P. Kas & G. Kassay, 2007. "On Linear Programming Duality and Necessary and Sufficient Conditions in Minimax Theory," Journal of Optimization Theory and Applications, Springer, vol. 132(3), pages 423-439, March.

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