含参集值向量均衡问题有效解下半连续的最优条件  

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

作　　者：张传美[1] 孟旭东[1] ZHANG Chuanmei;MENG Xudong(Department of Arts and Sciences,Science and Technology College of NCHU,Nanchang 330034,China)

机构地区：[1]南昌航空大学科技学院文理学部,南昌330034

出　　处：《吉林大学学报（理学版）》2020年第5期1142-1148,共7页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11201216);江西省教育厅科学技术重点研究项目(批准号:GJJ181565,GJJ191614);江西省教育厅科学技术研究项目(批准号:GJJ161597).

摘　　要：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.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.

关 键 词：有效解 下半连续 最优性 近似锥-次类凸集值映射 含参集值向量 均衡问题 

分 类 号：O221.3[理学—运筹学与控制论]