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.
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