区间值映射的次可微性及其应用

A Study on the Sub-differential of Interval-valued Mapping and Its Application Problem

本文讨论了区间值映射的次可微性问题,给出了次可微的概念及其基本性质,证明了区间值映射的次微分是空集或闭凸集;作为次微分的一种应用,讨论了区间值映射的次可微与其凸化区间值映射的次可微之间的关系,给出了一类区间值映射存在凸扩张区间值映射的充分条件。

In this paper,we study the sub-differentiability of interval-valued mappings,give the concept of sub-differential and its basic properties, and it is proved that the sub-differentiation of interval-valued mappings is an empty set or a closed convex set. As an application of sub-differentiation, the relationship between the sub-differentiability of interval-valued mappings and the sub-differentiability of convexification interval-valued mappings is discussed, and a sufficient condition for a class of interval-valued mappings to exist convex extended interval-valued mappings is given.