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A Note on Nonconvex Minimax Theorem with Separable Homogeneous Polynomials

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  • G. Y. Li

    (University of New South Wales)

Abstract

The minimax theorem for a convex-concave bifunction is a fundamental theorem in optimization and convex analysis, and has a lot of applications in economics. In the last two decades, a nonconvex extension of this minimax theorem has been well studied under various generalized convexity assumptions. In this note, by exploiting the hidden convexity (joint range convexity) of separable homogeneous polynomials, we establish a nonconvex minimax theorem involving separable homogeneous polynomials. Our result complements the existing study of nonconvex minimax theorem by obtaining easily verifiable conditions for the nonconvex minimax theorem to hold.

Suggested Citation

  • G. Y. Li, 2011. "A Note on Nonconvex Minimax Theorem with Separable Homogeneous Polynomials," Journal of Optimization Theory and Applications, Springer, vol. 150(1), pages 194-203, July.
    • Handle: RePEc:spr:joptap:v:150:y:2011:i:1:d:10.1007_s10957-011-9827-1
    DOI: 10.1007/s10957-011-9827-1
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Y. Zhang & S. Li, 2013. "Minimax theorems for scalar set-valued mappings with nonconvex domains and applications," Journal of Global Optimization, Springer, vol. 57(4), pages 1359-1373, December.
    2. Chuanfeng Sun, 2018. "A Minimax Theorem for Lindelöf Sets," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 127-136, October.

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