Weak Subdifferentials for Set-Valued Mappings
The purpose of this paper is to study the weak subdifferential for set-valued mappings, which was introduced by Chen and Jahn (Math. Methods Oper. Res., 48:187200, 1998). Two existence theorems of weak subgradients for set-valued mappings are obtained. Moreover, some properties of the weak subdifferential for set-valued mappings are derived. Our results improve the corresponding ones in the literature. Some examples are given to illustrate our results.
set-valued mapping existence weak subgradient contingent derivative