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Necessary Optimality Conditions for Second-Order Local Strict Efficiency for Constrained Nonsmooth Vector Equilibrium Problems

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Abstract

This paper is concerned with primal and dual second-order optimality conditions for the second-order strict efficiency of nonsmooth vector equilibrium problem with set, cone and equality conditions. First, we propose some second-order constraint qualifications via the second-order tangent sets. Second, we establish necessary optimality conditions of order two in terms of second-order contingent derivatives and second-order Shi sets for a second-order strict local Pareto minima to such problem under suitable assumptions on the second-order constraint qualifications. An application of the result for the twice Fréchet differentiable functions for the second-order local strict efficiency of that problem is also presented. Some illustrative examples are also provided for our findings.

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Acknowledgements

The authors would like to express their sincere gratitude to the editor and anonymous reviewers for their through and helpful reviews which significantly improved the quality of the paper.

Funding

This research is funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 101.01-2021.06.

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Authors and Affiliations

  1. Department of Mathematics, The University of Danang-University of Science and Education, 459 Ton Duc Thang, Lien Chieu, Da Nang, 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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Van Su, T., Hang, D.D. Necessary Optimality Conditions for Second-Order Local Strict Efficiency for Constrained Nonsmooth Vector Equilibrium Problems. Acta Math Vietnam 48, 321–341 (2023). https://doi.org/10.1007/s40306-022-00491-0

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  • DOI: https://doi.org/10.1007/s40306-022-00491-0

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