Resolvent-Free Method for Solving Monotone Inclusions

Abstract

In this work, we consider the monotone inclusion problem in real Hilbert spaces and propose a simple inertial method that does not include any evaluations of the associated resolvent and projection. Under suitable assumptions, we establish the strong convergence of the method to a minimal norm solution. Saddle points of minimax problems and critical points problems are considered as the applications. Numerical examples in finite- and infinite-dimensional spaces illustrate the performances of our scheme.