FINDING A ZERO OF THE SUM OF TWO MAXIMAL MONOTONE OPERATORS WITH MINIMIZATION PROBLEM

Abstract

The aim of this paper is to construct a new method for finding the zeros of the sum of two maximally monotone mappings in Hilbert spaces. We will define a simple function such that its set of zeros coincide with that of the sum of two maximal monotone operators. Moreover, we will use the Newton-Raphson algorithm to get an approximate zero.In addition, some illustrative examples are given at the end of this paper.