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Existence results for vector equilibrium problems given by a sum of two functions

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  • Gábor Kassay
  • Mihaela Miholca

Abstract

We obtain existence results for the weak vector equilibrium problem where the function involved is a sum of two functions, and the assumptions are required separately on each of these functions. We show that some earlier results of this type contain too demanding assumptions. We relax several of these assumption without loosing the results. The special case of reflexive Banach spaces is also studied, where we make use of the fact that closed balls are weakly compact. Copyright Springer Science+Business Media New York 2015

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  • Gábor Kassay & Mihaela Miholca, 2015. "Existence results for vector equilibrium problems given by a sum of two functions," Journal of Global Optimization, Springer, vol. 63(1), pages 195-211, September.
    • Handle: RePEc:spr:jglopt:v:63:y:2015:i:1:p:195-211
    DOI: 10.1007/s10898-014-0264-1
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    References listed on IDEAS

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    1. X. H. Gong, 2001. "Efficiency and Henig Efficiency for Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 108(1), pages 139-154, January.
    2. Giancarlo Bigi & Mauro Passacantando, 2012. "Gap functions and penalization for solving equilibrium problems with nonlinear constraints," Computational Optimization and Applications, Springer, vol. 53(2), pages 323-346, October.
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    6. M. Bianchi & R. Pini, 2005. "Coercivity Conditions for Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 124(1), pages 79-92, January.
    7. Bigi, Giancarlo & Castellani, Marco & Pappalardo, Massimo & Passacantando, Mauro, 2013. "Existence and solution methods for equilibria," European Journal of Operational Research, Elsevier, vol. 227(1), pages 1-11.
    8. M. Bianchi & N. Hadjisavvas & S. Schaible, 1997. "Vector Equilibrium Problems with Generalized Monotone Bifunctions," Journal of Optimization Theory and Applications, Springer, vol. 92(3), pages 527-542, March.
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    Cited by:

    1. Ouayl Chadli & Qamrul Hasan Ansari & Suliman Al-Homidan, 2017. "Existence of Solutions and Algorithms for Bilevel Vector Equilibrium Problems: An Auxiliary Principle Technique," Journal of Optimization Theory and Applications, Springer, vol. 172(3), pages 726-758, March.
    2. Wensheng Jia & Xiaoling Qiu & Dingtao Peng, 2020. "An Approximation Theorem for Vector Equilibrium Problems under Bounded Rationality," Mathematics, MDPI, vol. 8(1), pages 1-9, January.
    3. Lam Quoc Anh & Tran Quoc Duy & Le Dung Muu & Truong Van Tri, 2021. "The Tikhonov regularization for vector equilibrium problems," Computational Optimization and Applications, Springer, vol. 78(3), pages 769-792, April.
    4. Gábor Kassay & Mihaela Miholca & Nguyen The Vinh, 2016. "Vector Quasi-Equilibrium Problems for the Sum of Two Multivalued Mappings," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 424-442, May.

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