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Necessary and sufficient optimality conditions for constrained vector equilibrium problems using contingent hypoderivatives

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Abstract

In this paper, we study the Fritz John necessary and sufficient optimality conditions for weak efficient solutions of vector equilibrium problem with constraints via contingent hypoderivatives in finite-dimensional spaces. Using the stability of objective functions at a given optimal point and assumming, in addition, that the regularity condition (RC) holds, some primal and dual necessary optimality conditions for weak efficient solutions are derived. Furthermore, a dual necessary optimality condition is also established for the case of Fréchet differentiable functions. Making use of the concept of a support function on the feasible set of vector equilibrium problems with constraints, some primal and dual sufficient optimality conditions are given for the class of stable functions and Fréchet differentiable functions at a given feasible point. As an application, several necessary and sufficient optimality conditions for weak efficient solution are also obtained with the class of Hadamard differentiable functions. Examples to illustrate our results are provided as well.

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Acknowledgements

The author would like to express their sincere gratitude to the two anonymous reviewers for their through and helpful reviews which significantly improved the quality of the paper. Further the author acknowledges the editors for sending our manuscript to reviewers. The first author recognizes partial support from the National Foundation for Science and Technology Development of Vietnam (NAFOSTED) through Grant Number 101.01-2017.301.

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Authors and Affiliations

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

    Tran Van Su

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

    Tran Van Su

  3. Office of Scientific Research and Technology, Duy Tan University, Da Nang, Vietnam

    Nguyen Duc Hien

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  1. Tran Van Su
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  2. Nguyen Duc Hien
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Correspondence to Tran Van Su.

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Su, T.V., Hien, N.D. Necessary and sufficient optimality conditions for constrained vector equilibrium problems using contingent hypoderivatives. Optim Eng 21, 585–609 (2020). https://doi.org/10.1007/s11081-019-09464-z

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  • DOI: https://doi.org/10.1007/s11081-019-09464-z

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