On error bound moduli for locally Lipschitz and regular functions

被引：13

作者：

Li, M. H. ^{[1
]}

Meng, K. W. ^{[2
]}

Yang, X. Q. ^{[3
]}

机构：

[1] Chongqing Univ Arts & Sci, Sch Math & Finance, Chongqing 402160, Peoples R China

[2] Southwestern Univ Finance & Econ, Sch Econ & Math, Chengdu 61130, Sichuan, Peoples R China

[3] Hong Kong Polytech Univ, Dept Appl Math, Hong Kong, Hong Kong, Peoples R China

来源：

MATHEMATICAL PROGRAMMING | 2018年 / 171卷 / 1-2期

基金：

中国国家自然科学基金;

关键词：

Error bound modulus; Locally Lipschitz; Outer limiting subdifferential; Support function; End set; Lower C-1 function; WEAK SHARP MINIMA; LOWER SEMICONTINUOUS FUNCTIONS; LINEAR INEQUALITY SYSTEMS; CONSTRAINT QUALIFICATIONS; CONVEX INEQUALITIES; BANACH-SPACES; METRIC REGULARITY; SUFFICIENT CONDITIONS; CALMNESS; STABILITY;

D O I：

10.1007/s10107-017-1200-1

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

In this paper we study local error bound moduli for a locally Lipschitz and regular function via outer limiting subdifferential sets. We show that the distance from 0 to the outer limiting subdifferential of the support function of the subdifferential set, which is essentially the distance from 0 to the end set of the subdifferential set, is an upper estimate of the local error bound modulus. This upper estimate becomes tight for a convex function under some regularity conditions. We show that the distance from 0 to the outer limiting subdifferential set of a lower C-1 function is equal to the local error bound modulus.

引用

页码：463 / 487

页数：25

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