A note on the paper by Eckstein and Svaiter on "General projective splitting methods for sums of maximal monotone operators"

TL;DR

This paper refines a general splitting framework for maximal monotone operators by removing restrictive assumptions, broadening its applicability in infinite-dimensional Hilbert spaces.

Contribution

It provides a technical result that eliminates the need for the sum of operators to be maximal monotone and for the space to be finite-dimensional.

Findings

Framework now applicable in infinite-dimensional spaces

Removes previous assumptions on maximal monotonicity of the sum

Enhances flexibility of splitting methods for monotone operators

Abstract

In their recent SIAM J. Control Optim. paper from 2009, J. Eckstein and B.F. Svaiter proposed a very general and flexible splitting framework for finding a zero of the sum of finitely many maximal monotone operators. In this short note, we provide a technical result that allows for the removal of Eckstein and Svaiter's assumption that the sum of the operators be maximal monotone or that the underlying Hilbert space be finite-dimensional.