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Minimax theorems for scalar set-valued mappings with nonconvex domains and applications

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  • Y. Zhang
  • S. Li

Abstract

In this paper, by virtue of the separation theorem of convex sets, we prove a minimax theorem, a cone saddle point theorem and a Ky Fan minimax theorem for a scalar set-valued mapping under nonconvex assumptions of its domains, respectively. As applications, we obtain an existence result for the generalized vector equilibrium problem with a set-valued mapping. Simultaneously, we also obtain some generalized Ky Fan minimax theorems for set-valued mappings, in which the minimization and the maximization of set-valued mappings are taken in the sense of vector optimization. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:57:y:2013:i:4:p:1359-1373
    DOI: 10.1007/s10898-012-9992-2
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    References listed on IDEAS

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    1. 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.
    2. S. J. Li & G. Y. Chen & G. M. Lee, 2000. "Minimax Theorems for Set-Valued Mappings," Journal of Optimization Theory and Applications, Springer, vol. 106(1), pages 183-200, July.
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    Cited by:

    1. Nguyen Xuan Hai & Nguyen Hong Quan & Vo Viet Tri, 2023. "Some saddle-point theorems for vector-valued functions," Journal of Global Optimization, Springer, vol. 86(1), pages 141-161, May.

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