次微分意义下集值映射优化问题的最优性条件

Optimal conditions of set-valued maps optimization with subdifferential

在实赋范空间中,研究集值向量优化问题解的最优性条件。给出了锥凸集值映射次梯度和次微分的概念,通过锥凸集值映射的上图象的条件锥定义了锥凸集值映射的条件上导数,研究了次微分的性质。在次微分意义下,获得了集值映射优化的弱极小元的最优性条件。

The vector optimization of setvalued maps was considered in real normal spaces. The concept of subgradient and subdifferential of cone convex setvalued maps was given. The contingent epiderivative of cone convex setvalued maps was defined by using the concept of epigraph. Two properties of subdifferential were presented. Optimal condition for weak minimizer was obtained based on the subdifferential.