An inertial viscosity algorithm for solving monotone variational inclusion and common fixed point problems of strict pseudocontractions

Abstract

In this paper, we study the problem of finding the solution of monotone variational inclusion problem (MVIP) with constraint of common fixed point problem (CFPP) of strict pseudocontractions. We propose a new viscosity method, which combines the inertial technique with self-adaptive step size strategy for approximating the solution of the problem in the framework of Hilbert spaces. Unlike several of the existing results in the literature, our proposed method does not require the co-coerciveness and Lipschitz continuity assumptions of the associated single-valued operator. Also, our method does not involve any linesearch technique which could be time-consuming, rather we employ a self-adaptive step size technique that generates a nonmonotonic sequence of step sizes. Moreover, we prove strong convergence result for our algorithm under some mild conditions and apply our result to study other optimization problems. We present several numerical experiments to demonstrate the computational advantage of our proposed method over the existing methods in the literature. Our result complements several of the existing results in the current literature in this direction.

On Bilevel Monotone Inclusion and Variational Inequality Problems

“…Moreover, we compare the image recovery efficiency of method Algorithms 5 (in short, OAURN3) and 6 (in short, OAURN4) with Algorithm 3.3 by Adamu et al [36] (in short, ADIA Alg. 3.3) and Algorithm 3.1 by Alakoya et al [15] (in short, AOM Alg. 3.1).…”

“…Moreover, we compare them with Algorithm 3.3 by Adamu et al [36] (in short, ADIA Alg. 3.3) and Algorithm 3.1 by Alakoya et al [15] (in short, AOM Alg. 3.1).…”

“…Therefore, it is necessary to modify (3), such that it can achieve strong convergence in real Hilbert spaces. In the last two decades, so many modifications of the forward-backward method have been constructed to obtain strong convergence results in real Hilbert spaces; see [11,12,15,16] and the references in them.…”