Quadratic rates of asymptotic regularity for the Tikhonov–Mann iteration. (2nd November 2022)

• Record Type: Journal Article
• Authors: Cheval, Horaţiu; Leuştean, Laurenţiu
• Is Part Of: Optimization methods and software. Volume 37:Number 6(2022)
• Page Start: 2225
• Page End: 2240
• Publication Date: 2022-11-02
• Subjects: Mann iteration -- Tikhonov regularization -- rates of asymptotic regularity -- Douglas–Rachford algorithm -- forward-backward algorithm -- proof mining; 47J25 -- 47H09 -- 03F10; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2022.2060974
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : In this paper, we compute quadratic rates of asymptotic regularity for the Tikhonov–Mann iteration in W -hyperbolic spaces. This iteration is an extension to a nonlinear setting of the modified Mann iteration defined recently by Boţ, Csetnek and Meier in Hilbert spaces. Furthermore, we show that the Douglas–Rachford and forward-backward algorithms with Tikhonov regularization terms are special cases, in Hilbert spaces, of our Tikhonov–Mann iteration.