集值映射的弱有效广义梯度

The Weak Efficient Generalized Gradient of Set-Valued Maps

在锥序Banach空间中,对于集值优化问题(SOP),利用contingent上图切导数,引进了集值映射弱有效意义下的广义梯度;在集值映射具有连通性条件下,利用凸集分离定理证明了集值映射弱有效广义梯度的存在性,由此建立了集值映射优化问题弱有效解在广义梯度下的最优性条件.

For the set-valued vector optimization problem（SOP）,the concept of the generalized gradient in sense of set-valued map weak efficiency is introduced by means of contingent epiderivative in order Banach space.Under the condition of connectedness,its existence is proved by the separation theorem of convex sets.Thus the optimality condition of weak efficient solution of set-valued optimization problems is established in the sense of generalized gradient.