Perturbation of error bounds

• 成果类型: Article
• 署名作者: Kruger, A. Y.; Lopez, M. A.; Thera, M. A.
• 署名单位: Federation University Australia; Universitat d'Alacant; Centre National de la Recherche Scientifique (CNRS); Universite de Limoges
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-017-1129-4
• 发表日期: 2018
• 页码: 533-554
• 关键词: lower semicontinuous functions; metric subregularity; projection algorithms; generalized equations; convergence rate; calmness moduli; REGULARITY; subdifferentials; STABILITY; systems

摘要

Our aim in the current article is to extend the developments in Kruger et al. (SIAM J Optim 20(6):3280-3296, 2010. doi:10.1137/100782206) and, more precisely, to characterize, in the Banach space setting, the stability of the local and global error bound property of inequalities determined by lower semicontinuous functions under data perturbations. We propose new concepts of (arbitrary, convex and linear) perturbations of the given function defining the system under consideration, which turn out to be a useful tool in our analysis. The characterizations of error bounds for families of perturbations can be interpreted as estimates of the 'radius of error bounds'. The definitions and characterizations are illustrated by examples.