Shrinking projection methods involving inertial forward–backward splitting methods for inclusion problems

Abstract

© 2018, Springer-Verlag Italia S.r.l., part of Springer Nature. In this paper, we propose a modified forward–backward splitting method using the shrinking projection and the inertial technique for solving the inclusion problem of the sum of two monotone operators. We prove its strong convergence under some suitable conditions in Hilbert spaces. We provide some numerical experiments including a comparison to show the implementation and the efficiency of our method.