含参集值向量均衡问题有效解下半连续的最优条件

在实Hausdorff拓扑向量空间中, 讨论含参集值向量均衡问题有效解下半连续的最优条件. 首先, 给出含参集值向量均衡问题的弱有效解、 Henig有效解、Global有效解、 超有效解和f-有效解的概念. 其次, 在近似锥-次类凸的基础上, 借助f-有效解的形式, 用凸集分离定理给出弱有效解、 Henig有效解、 Global有效解和超有效解的标量化结果. 最后, 在集值映射弱f-性的条件下, 建立含参集值向量均衡问题有效解下半连续的最优性定理.

Optimal Conditions for Lower Semicontionuity of Efficient Solutions to Parametric Set-Valued Vector Equilibrium Problem

We discussed the optimal conditions for lower semicontionuity of efficient solutions to parametric set-valued vector equilibrium problem in real Hausdorff topological vector space. Firstly, we gave the concepts of weak efficient solution,Henig efficient solution,Global efficient solution, super efficient solution and f-efficient solution for the parametric set-valued vector equilibrium problem. Secondly, on the basis of nearly cone-subconvexlike, we gave the characterization results of weak efficient solution, Henig efficient solution, Global efficient solution and super efficient solution by using the form of f-efficient solution and the separation theorem of convex sets. Finally, we established the optimality theorems of lower semicontinuity for the efficient solutions to parametric set valued vector equilibrium problem under the weak-f-property of set-valued mapping.