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Minimax Results and Finite-Dimensional Separation

Author

Listed:
  • J.F.B. Frenk

    (Erasmus University Rotterdam)

  • G. Kassay

    (Babes–Bolyai University)

Abstract

In this paper, we review and unify some classes of generalized convex functions introduced by different authors to prove minimax results in infinite-dimensional spaces and show the relations between these classes. We list also for the most general class already introduced by Jeyakumar (Ref. 1) an elementary proof of a minimax result. The proof of this result uses only a finite-dimensional separa- tion theorem; although this minimax result was already presented by Neumann (Ref. 2) and independently by Jeyakumar (Ref. 1), we believe that the present proof is shorter and more transparent.

Suggested Citation

  • J.F.B. Frenk & G. Kassay, 2002. "Minimax Results and Finite-Dimensional Separation," Journal of Optimization Theory and Applications, Springer, vol. 113(2), pages 409-421, May.
    • Handle: RePEc:spr:joptap:v:113:y:2002:i:2:d:10.1023_a:1014843327958
    DOI: 10.1023/A:1014843327958
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    Citations

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    Cited by:

    1. Fernando Luque-Vásquez & J. Adolfo Minjárez-Sosa & Max E. Mitre-Báez, 2016. "A Note on König and Close Convexity in Minimax Theorems," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 65-71, July.
    2. J. B. G. Frenk & G. Kassay, 2007. "Lagrangian Duality and Cone Convexlike Functions," Journal of Optimization Theory and Applications, Springer, vol. 134(2), pages 207-222, August.
    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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