集值映射超有效解的次微分和最优性条件

Super Efficient Sub-differential for Set-Valued Mapping and Optimality Conditions

在局部凸拓扑线性空间中引进集值映射超有效次微分的概念,在一定条件下通过凸集分离定理得到了该次微分的存在性定理.作为应用,建立了约束集值优化问题超有效解在Lagrange乘子形式下的最优性必要条件.

In locally convex topological linear spaces,the concept of super efficient subdifferential for a set-valued mapping is introduced.Under certain conditions,by using the convex set separation theorem,the existence theorem for the super efficient subdifferential is proposed.As an application,the necessary optimality condition of the constraint set-valued optimization problem for super efficient solutions is established in terms of Lagrange multiplier by using the concept of super efficient subdifferential for set-valued mapping.