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New optimality conditions for unconstrained vector equilibrium problem in terms of contingent derivatives in Banach spaces

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Abstract

This article presents necessary and sufficient optimality conditions for weakly efficient solution, Henig efficient solution, globally efficient solution and superefficient solution of vector equilibrium problem without constraints in terms of contingent derivatives in Banach spaces with stable functions. Using the steadiness and stability on a neighborhood of optimal point, necessary optimality conditions for efficient solutions are derived. Under suitable assumptions on generalized convexity, sufficient optimality conditions are established. Without assumptions on generalized convexity, a necessary and sufficient optimality condition for efficient solutions of unconstrained vector equilibrium problem is also given. Many examples to illustrate for the obtained results in the paper are derived as well.

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Acknowledgements

The author would like to express many thanks to the referees for their valuable comments and suggestions. This research was supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grand number 101.01-2017.301.

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Authors and Affiliations

  1. Department of Mathematics, Quangnam University, 102 Hung Vuong, Tamky, Vietnam

    Tran Van Su

  2. Graduate University of Science and Technology, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Cau Giay, Hanoi, Vietnam

    Tran Van Su

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  1. Tran Van Su
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Su, T.V. New optimality conditions for unconstrained vector equilibrium problem in terms of contingent derivatives in Banach spaces. 4OR-Q J Oper Res 16, 173–198 (2018). https://doi.org/10.1007/s10288-017-0360-4

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  • DOI: https://doi.org/10.1007/s10288-017-0360-4

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