Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Do Van Luu

Thang Long University, and: Institute of Mathematics, Vietnam Academy of Science and Technology, Ha Noi, Vietnam

dvluu@math.ac.vn

Nguyen Cong Dieu

Thang Long University, and: Institute of Information Technology, Vietnam Academy of Science and Technology, Ha Noi, Vietnam

ncdieu@ioit.ac.vn

Keywords

  • Vector equilibrium problem
  • second-order efficiency conditions
  • second-order contingent epiderivative
  • efficient solutions

Mathematics Subject Classification

90C46, 90C29, 90C48, 49J52

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Suggested citation

D. V. Luu, T. V. Su, N. C. Dieu. “Second-Order Efficiency Conditions for Vector Equilibrium Problems with Constraints via Contingent Epiderivatives.” Journal of Convex Analysis 28 (2021), No. 3, 903–926. https://doi.org/10.68381/jca28052

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Published by Heldermann Verlag, 2021. Rights now held by Banach Press LLC.