Journal of Convex Analysis 28 (2021), No. 3, 903--926
Copyright Heldermann Verlag 2021
Second-Order Efficiency Conditions for Vector Equilibrium Problems with Constraints via Contingent Epiderivatives
Do Van Luu
Thang Long University, and: Institute of Mathematics, Vietnam Academy of Science and Technology, Ha Noi, Vietnam
dvluu@math.ac.vn
Tran Van Su
Department of Mathematics, Quang Nam University, Tamky, Vietnam
vansudhdntt@gmail.com
Nguyen Cong Dieu
Thang Long University, and: Institute of Information Technology, Vietnam Academy of Science and Technology, Ha Noi, Vietnam
ncdieu@ioit.ac.vn
We establish second-order necessary and sufficient conditions for weakly efficient, Henig efficient, globally efficient and superefficient solutions of vector equilibrium problems with constraints in terms of contingent epiderivatives in Banach spaces. Firstly, some results on the existence and the uniqueness of second-order contingent epiderivatives with the functions defined on infinite-dimensional spaces are established. Secondly, under suitable assumptions, second-order necessary and sufficient conditions for weakly efficient solutions of such problems are derived. As applications, we provide the second-order necessary and sufficient efficiency conditions for Henig efficient, globally efficient and superefficient solutions of constrained vector equilibrium problems via contingent epiderivatives. Some illustrative examples are given as well.
Keywords: Vector equilibrium problem, second-order efficiency conditions, second-order contingent epiderivative, efficient solutions.
MSC: 90C46, 90C29, 90C48, 49J52.
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