Another characterization of convexity for set-valued maps

被引：0

作者：

Sach, PH ^{[1
]}

机构：

[1] Hanoi Inst Math, Hanoi, Vietnam

来源：

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 1999年 / 20卷 / 3-4期

关键词：

set-valued map; convexity; coderivative;

D O I：

10.1080/01630569908816896

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give a new necessary and sufficient condition for convexity of a set-valued map F between Banach spaces. It is established for a closed map F having nonconvex values. The main tool in this paper is the coderivative of F which is constructed with the help of an abstract subdifferential notion of Penot [16]. A detailed discussion is devoted to special cases when the contingent, the Frechet and the Clarke-Rockafellar subdifferentials are used as this abstract subdifferential.

引用

页码：341 / 351

页数：11

共 22 条

[1] MEAN-VALUE PROPERTY AND SUBDIFFERENTIAL CRITERIA FOR LOWER SEMICONTINUOUS FUNCTIONS [J].