一般线性空间中近似Benson真有效解的若干刻画  

Some characterizations for approximate Benson properly efficient solutions in general linear spaces

作　　者：陈楠 黄斌 徐义红[1] CHEN Nan;HUANG Bin;XU Yihong(Department of Mathematics,Nanchang University,Nanchang 330031,China)

机构地区：[1]南昌大学数学系,江西南昌330031

出　　处：《南昌大学学报（理科版）》2020年第3期205-209,共5页Journal of Nanchang University(Natural Science)

基　　金：国家自然科学基金资助项目(11961047);江西省自然科学基金资助项目(20192BAB2010100)。

摘　　要：在没有拓扑结构的一般线性空间中,引进了集值均衡问题的Benson真有效解和近似Benson真有效解,讨论了它们之间的关系。在广义锥-次类凸性假设下,利用凸集分离定理建立了带约束集值均衡近似Benson真有效解的最优性条件。利用集合严格正对偶的性质建立了充分条件。In a general linear space without topology,the concepts of Benson properly efficient solutions and approximate Benson properly efficient solutions are introduced respectively for the set-valued equilibrium problem.The relationship between Benson properly efficient solutions and approximate Benson properly efficient solutionsis discussed.Under the assumption of generalized cone-subconvexlikeness,the necessary optimality condition of approximate Benson properly efficient solutions of the set-valued equilibrium problem with constraints is established by using the separation theorem of convex sets.The sufficient optimality condition is established by applying the properties of the strict positivedual of a nonempty set.

关 键 词：集值映射 BENSON真有效解 最优性条件 

分 类 号：O221.6[理学—运筹学与控制论]