MODIFIED FORWARD-BACKWARD SPLITTING METHODS IN HILBERT SPACES

Abstract

In this paper, for finding a zero of a monotone variational inclusion in Hilbert spaces, we introduce new modifications of the Halpern forwardbackward splitting methods, strong convergence of which is proved under new condition on the resolvent parameter. We show that these methods are particular cases of two new methods, introduced for solving a monotone variational inequality problem over the set of zeros of the inclusion. Numerical experiments are given for illustration and comparison.