Error bounds for convex differentiable inequality systems in Banach spaces

• 成果类型: Article
• 署名作者: van Ngai, H; Théra, M
• 署名单位: Universite de Limoges; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-005-0624-1
• 发表日期: 2005
• 页码: 465-482
• 关键词: lower semicontinuous functions; subdifferential calculus; metric regularity; points

摘要

The paper is devoted to studying the Hoffman global error bound for convex quadratic/affine inequality/equality systems in the context of Banach spaces. We prove that the global error bound holds if the Hoffman local error bound is satisfied for each subsystem at some point of the solution set of the system under consideration. This result is applied to establishing the equivalence between the Hoffman error bound and the Abadie qualification condition, as well as a general version of Wang & Pang's result [30], on error bound of Holderian type. The results in the present paper generalize and unify recent works by Luo & Luo in [17], Li in [16] and Wang & Pang in [30].