A Note on the Paper by Eckstein and Svaiter on “General Projective Splitting Methods for Sums of Maximal Monotone Operators”

Abstract

In their recent paper from 2009 [SIAM J. Control Optim., 48 (2009), pp. 787–811], 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.