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A Generalized Ky Fan Minimax Inequality on Finite-Dimensional Spaces

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  • Marco Castellani

    (Department of Information Engineering, Computer Science and Mathematics)

  • Massimiliano Giuli

    (Department of Information Engineering, Computer Science and Mathematics)

Abstract

An existence result for a generalized inequality over a possible unbounded domain in a finite-dimensional space is established. The proof technique allows to avoid any monotonicity assumption. We adapt a weak coercivity condition introduced in Castellani and Giuli (J Glob Optim 75:163–176, 2019) for a generalized game which extends an older one proposed by Konnov and Dyabilkin (J Glob Optim 49:575–577, 2011) for equilibrium problems. Our main result encompasses and generalizes several existence results for equilibrium, quasiequilibrium and fixed-point problems.

Suggested Citation

  • Marco Castellani & Massimiliano Giuli, 2021. "A Generalized Ky Fan Minimax Inequality on Finite-Dimensional Spaces," Journal of Optimization Theory and Applications, Springer, vol. 190(2), pages 343-357, August.
    • Handle: RePEc:spr:joptap:v:190:y:2021:i:2:d:10.1007_s10957-021-01903-1
    DOI: 10.1007/s10957-021-01903-1
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    References listed on IDEAS

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    1. M. Castellani & M. Giuli, 2019. "A coercivity condition for nonmonotone quasiequilibria on finite-dimensional spaces," Journal of Global Optimization, Springer, vol. 75(1), pages 163-176, September.
    2. Marco Castellani & Massimiliano Giuli & Massimo Pappalardo, 2018. "A Ky Fan Minimax Inequality for Quasiequilibria on Finite-Dimensional Spaces," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 53-64, October.
    3. I. Konnov & D. Dyabilkin, 2011. "Nonmonotone equilibrium problems: coercivity conditions and weak regularization," Journal of Global Optimization, Springer, vol. 49(4), pages 575-587, April.
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