Lipschitz functions with maximal Clarke subdifferentials are generic

被引：15

作者：

Borwein, JM ^{[1
]}

Wang, XF ^{[1
]}

机构：

[1] Simon Fraser Univ, Dept Math & Stat, Ctr Expt & Construct Math, Burnaby, BC V5A 1S6, Canada

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2000年 / 128卷 / 11期

关键词：

Lipschitz function; Clarke subdifferential; separable Banach spaces; Baire category; partial ordering; Banach lattice; approximate subdifferential;

D O I：

10.1090/S0002-9939-00-05914-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that on a separable Banach space most Lipschitz functions have maximal Clarke subdifferential mappings. In particular, the generic nonexpansive function has the dual unit ball as its Clarke subdifferential at every point. Diverse corollaries are given.

引用

页码：3221 / 3229

页数：9