Two New Modified Regularized Methods for Solving the Variational Inclusion and Null Point Problems

Abstract

In this article, based on the regularization techniques, we construct two new algorithms combining the forward-backward splitting algorithm and the proximal contraction algorithm, respectively. Iterative sequences of the new algorithms can converge strongly to a common solution of the variational inclusion and null point problems in real Hilbert spaces. Multi-inertial extrapolation steps are applied to expedite their convergence rate. We also give some numerical experiments to certify that our algorithms are viable and efficient.