Characterization of regularity via variational stability of alternating projection sequences

• 成果类型: Article; Early Access
• 署名作者: Battistoni, F.; Daniilidis, A.; De Bernardi, C. A.; Miglierina, E.
• 署名单位: Catholic University of the Sacred Heart; Technische Universitat Wien
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610; 1436-4646
• DOI: 10.1007/s10107-026-02374-w
• 发表日期: 2026-06-05
• 关键词: Alternating projection method; convex feasibility problem; d-stability; REGULARITY; Attouch-Wets convergence

摘要

The notion of regular pair (A, B) for two nonempty closed convex subsets A and B of a Hilbert space H\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {H}$$\end{document} was introduced by Borwein and Bauschke in 1993 to ensure convergence (in norm) of the alternating projection method to some point of the best approximation set. In 2022, De Bernardi and Miglierina showed that regularity of the pair (A, B) guarantees, additionally, the convergence for any variational perturbation of the alternating projection method, provided the corresponding best approximation sets are bounded. In this work, we show that the converse assertion is also true. Moreover, this converse assertion holds without requiring the best approximation sets to be bounded.