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Second-Order Necessary and Sufficient Optimality Conditions for Constrained Vector Equilibrium Problem with Applications

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Abstract

In this paper, we study a generalized convex vector equilibrium problem with cone and set constraints in real Banach spaces. We provide some basic characterizations on generalized convexity for the first- and second-order directional derivatives. We obtain Kuhn–Tucker second-order necessary and sufficient optimality conditions for efficiency to such problem under suitable assumptions on the generalized convexity of objective and constraint functions. As an application, we present Kuhn–Tucker second-order necessary and sufficient optimality conditions to a generalized convex vector variational inequality problem and a generalized convex vector optimization problem with constraints. Some examples are also given to demonstrate the main results of the paper.

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Acknowledgements

The authors would like to express their sincere gratitude to the anonymous reviewers for their thorough and helpful reviews which significantly improved the quality of the paper. Further, the authors acknowledge the editors for sending our manuscript to the reviewers.

Funding

The first author was funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 101.01-2017.301.

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Authors and Affiliations

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

    Tran Van Su

  2. Department of Basic Sciences, Thai Nguyen University of Information and Communication Technology, Thai Nguyen, Vietnam

    Dinh Dieu Hang

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  1. Tran Van Su
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  2. Dinh Dieu Hang
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Correspondence to Tran Van Su.

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Communicated by Majid Soleimani-damaneh.

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Su, T.V., Hang, D.D. Second-Order Necessary and Sufficient Optimality Conditions for Constrained Vector Equilibrium Problem with Applications. Bull. Iran. Math. Soc. 47, 1337–1362 (2021). https://doi.org/10.1007/s41980-020-00445-y

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