Inertial Projection Method for Solving Monotone Operator Equations

Abstract

In this article, inspired by the overwhelming suc-cesses recorded by the inertial effect on existing iterative methods, we propose an inertial projection conjugate gradient (CG) method for solving nonlinear monotone operator equations with convex constraints. As a starting point, the inertial step is added to an existing CG method called PCG with the aim of speeding up its convergence. Under appropriate assumptions, the global convergence of the method is established. Numerical results are reported and in comparison with the PCG method, the effect of the inertial term is clearly seen as the propose approach outperforms the PCG method based on all metrics considered. This is evident that the inertial term has really performed its duty as expected.