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

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.