# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2020164

## Second-Order characterizations for set-valued equilibrium problems with variable ordering structures

 Department of Mathematics, Nanchang University, Nanchang, 330031, China

* Corresponding author: Yihong Xu

Received  September 2019 Revised  July 2020 Published  November 2020

Fund Project: This research was supported by the National Natural Science Foundation of China Grant (11961047) and the Natural Science Foundation of Jiangxi Province (20192BAB201010)

The concepts of weakly efficient solutions and globally efficient solutions are introduced for constrained set-valued equilibrium problems with variable ordering structures. By applying the second-order tangent epiderivative and a nonlinear functional, necessary optimality conditions for weakly efficient solutions and globally efficient solutions are established without any convexity assumption. Under the cone-convexity of the objective and constraint functions, sufficient optimality conditions are given. In addition, the tangent derivatives of objective and constraint functions are separated. Simultaneously, a unified necessary and sufficient optimality conditions for weakly efficient solutions is derived, and the same goes for globally efficient solutions. In particular, we give specific examples to illustrate the optimality conditions, respectively.

Citation: Shasha Hu, Yihong Xu, Yuhan Zhang. Second-Order characterizations for set-valued equilibrium problems with variable ordering structures. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2020164
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