Mathematical Programming

, Volume 34, Issue 2, pp 232–234 | Cite as

On Fan's minimax theorem

  • J. M. Borwein
  • D. Zhuang


A new brief proof of Fan's minimax theorem for convex-concave like functions is established using separation arguments.

Key words

Convex-Concave Like Functions Fan's Minimax Theorem Separation Theorem 


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    C.E. Blair, R.J. Duffin and R.G. Jeroslow, “A limiting infisup theorem“,Journal of Optimization Theory and Applications 37 (1982) 163–175.Google Scholar
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    K. Fan, “Minimax theorems“,National Academy of Sciences, Washington, DC, Proceedings USA 39 (1953) 42–47.Google Scholar
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    R.T. Rockafellar,Convex Analysis (Princeton University Press, Princeton, NJ, 1969).Google Scholar
  4. [4]
    J. Stoer and C. Witzgall,Convexity and optimization in finite dimensions: I (Springer-Verlag, New York, 1970).Google Scholar

Copyright information

© The Mathematical Programming Society, Inc. 1986

Authors and Affiliations

  • J. M. Borwein
    • 1
  • D. Zhuang
    • 1
  1. 1.Department of Mathematics, Statistics and Computing ScienceDalhousie UniversityHalifaxCanada

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