On error bound moduli for locally Lipschitz and regular functions

• 成果类型: Article
• 署名作者: Li, M. H.; Meng, K. W.; Yang, X. Q.
• 署名单位: Chongqing University of Arts & Sciences; Hong Kong Polytechnic University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-017-1200-1
• 发表日期: 2018
• 页码: 463-487
• 关键词: weak sharp minima; lower semicontinuous functions; linear inequality systems; constraint qualifications; convex inequalities; banach-spaces; metric regularity; Sufficient conditions; calmness; STABILITY

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.