Revisiting jointly firmly nonexpansive families of mappings. (9th December 2022)

• Record Type: Journal Article
• Authors: Sipoş, Andrei
• Is Part Of: Optimization. Volume 71:Number 13(2022)
• Page Start: 3819
• Page End: 3834
• Publication Date: 2022-12-09
• Subjects: Convergence of resolvents -- proximal point algorithm -- CAT(0) spaces -- jointly firmly nonexpansive families -- proof mining; 90C25 -- 46N10 -- 47J25 -- 47H09 -- 03F10; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1915312
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : Recently, the author, together with L. Leuştean and A. Nicolae, introduced the notion of jointly firmly nonexpansive families of mappings in order to investigate in an abstract manner the convergence of proximal methods. Here, we further the study of this concept, by giving a characterization in terms of the classical resolvent identity, by improving on the rate of convergence previously obtained for the uniform case, and by giving a treatment of the asymptotic behaviour at infinity of such families.