Dynamic String-Averaging Proximal Point Algorithm

Abstract

In a Hilbert space, we study the convergence of a dynamic string-averaging proximal point method to a common zero of a finite family of maximal monotone operators under the presence of perturbations. Our main goal is to obtain an approximate solution of the problem using perturbed algorithms. We show that the inexact dynamic string-averaging proximal point algorithm generates an approximate solution if perturbations are summable. We also show that if the perturbations are sufficiently small, then the inexact produces approximate solutions.