广义梯度和ε-严有效解的最优性条件

Generalized Gradient and Optimality Conditions of ε-Strictly Efficient Solutions

在锥序Banach空间中引入了集值映射ε-严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ε-严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 ofε-strictly efficient solution for set-valued optimization problem are established in terms of the generalized gradient.