A Nonlinearly Preconditioned Forward-Backward Splitting Method and Applications. (30th March 2022)

• Record Type: Journal Article
• Authors: Vũ, Bă`ng Công; Papadimitriou, Dimitri
• Is Part Of: Numerical functional analysis and optimization. Volume 42:Number 16(2021)
• Page Start: 1880
• Page End: 1895
• Publication Date: 2022-03-30
• Subjects: Cocoercive -- composite operator -- forward-backward algorithm -- hypercocoercive -- hypermonotone -- monotone inclusion -- monotone operator -- operator splitting -- preconditioning; 47H05 -- 49M29 -- 49M27 -- 90C25; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.2001824
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this paper, we prove the weak convergence of the iterates generated by the nonlinearly preconditioned forward-backward splitting method for the sum of a maximally hypermonotone operator A and a hypercocoercive operator B under several suitable conditions. We provide several choices of the nonlinear preconditioners for solving nonlinearly composed inclusions. In particular, the backward-forward splitting method is recovered by the nonlinearly preconditioned forward-backward splitting method with a special choice of the nonlinear preconditioner.