集值优化问题的广义梯度与强有效解的最优性条件

Generalized Gradient of Set-valued Optimization Problems and Optimality Conditions of Strong-efficient Solutions

在锥序Banach空间中引入了集值映射强有效意义下的广义梯度,在连通性条件下,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强有效解的充分和必要条件.

A kind of generalized gradient for set-valued map is introduced in ordered Banach spaces.Under the connected condition,its existence is proved by the separation theorem for convex sets.As an application,the optimality necessary and sufficient conditions of strongefficient solution for set-valued optimization problem are established in terms of the generalized gradient.