THE HALPERN APPROXIMATION OF THREE OPERATORS SPLITTING METHOD FOR CONVEX MINIMIZATION PROBLEMS WITH AN APPLICATION TO IMAGE INPAINTING

Abstract

The three-operator splitting algorithm is a state-of-art algorithm for finding monotone inclusion problems of the sum of maximally monotone operators, where one of the operators is a cocoercive operator. Since the resolvent operator in the original three-operator splitting algorithm is not available in a closed form, we propose an inexact three-operator splitting algorithm that combines inertial forward backward splitting algorithm with the Halpern approximation method to solve monotone inclusion problem. Under mild assumptions, the theoretical convergence properties of the presented iterative technique are studied on the iterative parameters in general Hilbert spaces. Furthermore, we extend this algorithm to solve image inpainting problem. Performance comparisons show that the presented method is competitive, efficient and practical with the compared ones.