An iteration scheme for monotone operators in Hilbert spaces

TL;DR

This paper introduces an iteration method for finding zeros of maximal monotone operators in Hilbert spaces, ensuring strong convergence to solutions or divergence otherwise, with applications to convex minimization.

Contribution

It proposes a new iteration scheme that guarantees strong convergence for maximal monotone operators in Hilbert spaces, including convex functional minimization.

Findings

Iterates converge strongly to a solution when one exists.

If no solution exists, iterates tend to infinity.

Application to strongly convergent convex minimization schemes.

Abstract

We give an iteration scheme for finding zeros of maximal monotone operators in Hilbert spaces. We assume that the operator is defined in the whole space. The iterates converge strongly to a solution if there exists any, otherwise they tend to infinity. As an application we get a strongly convergent minimization scheme for convex functionals in Hilbert spaces.