Set regularities and feasibility problems

• 成果类型: Article
• 署名作者: Kruger, Alexander Y.; Luke, D. Russell; Thao, Nguyen H.
• 署名单位: Federation University Australia; University of Gottingen; Can Tho University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-016-1039-x
• 发表日期: 2018
• 页码: 279-311
• 关键词: weak sharp minima; linear regularity; error-bounds; metric subregularity; alternating projections; generalized equations; strong chip; CONVERGENCE; qualification; collections

摘要

We synthesize and unify notions of regularity, both of individual sets and of collections of sets, as they appear in the convergence theory of projection methods for consistent feasibility problems. Several new characterizations of regularities are presented which shed light on the relations between seemingly different ideas and point to possible necessary conditions for local linear convergence of fundamental algorithms.