集值映射Henig有效解的最优性条件

Optimality Conditions of Henig Efficient Solutions for Set-valued Mapping

在锥偏序Banach空间中利用集值映射的上图导数引进了Henig有效意义下的广义梯度,在一定条件下,利用凸集分离定理证明了该广义梯度的存在性。作为应用,给出了用广义梯度刻画集值优化问题Henig有效解的充分条件。

The concept of the generalized gradient in sense of Henig efficiency is introduced by epiderivative for a set-valued map in ordered Banach spaces.Under some conditions,its existence is proved by the separation theorem for convex sets.As an application,the optimality sufficient condition of Henig-efficient solution for set-valued optimization problem is established in terms of the generalized gradient.