SIAM Journal on Control and Optimization, Vol.48, No.4, 2513-2515, 2009
A NOTE ON THE PAPER BY ECKSTEIN AND SVAITER ON "GENERAL PROJECTIVE SPLITTING METHODS FOR SUMS OF MAXIMAL MONOTONE OPERATORS"
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.
Keywords:firmly nonexpansive mapping;maximal monotone operator;nonexpansive mapping;proximal algorithm;splitting algorithm