A Nonlinearly Preconditioned Forward-Backward Splitting Method and Applications. (30th March 2022) - Vũ, Bă`ng Công; Papadimitriou, Dimitri
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.