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On Linear Programming Duality and Necessary and Sufficient Conditions in Minimax Theory

Author

Listed:
  • J. B. G. Frenk

    (Erasmus University)

  • P. Kas

    (Eastern Mediterranean University)

  • G. Kassay

    (Babes-Bolyai University)

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 for compact sets. It turns out that these necessary and sufficient conditions have a clear interpretation within zero-sum game theory. We apply these results to derive necessary and sufficient conditions for strong duality for a general class of optimization problems.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:132:y:2007:i:3:d:10.1007_s10957-007-9164-6
    DOI: 10.1007/s10957-007-9164-6
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    References listed on IDEAS

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    1. J. B. G. Frenk & G. Kassay, 1999. "On Classes of Generalized Convex Functions, Gordan–Farkas Type Theorems, and Lagrangian Duality," Journal of Optimization Theory and Applications, Springer, vol. 102(2), pages 315-343, August.
    2. 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.
    3. Frenk, J. B. G. & Kassay, G. & Kolumban, J., 2004. "On equivalent results in minimax theory," European Journal of Operational Research, Elsevier, vol. 157(1), pages 46-58, August.
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