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

  • * Corresponding author: Yihong Xu

    * Corresponding author: Yihong Xu 

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

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  • 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.

    Mathematics Subject Classification: Primary: 90C33, 90C46; Secondary: 90C59.


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