On the Complexity of the Projective Splitting and Spingarn’s Methods for the Sum of Two Maximal Monotone Operators

In this work, we study the pointwise and ergodic iteration complexity of a family of projective splitting methods proposed by Eckstein and Svaiter, for finding a zero of the sum of two maximal monotone operators. As a consequence of the complexity analysis of the projective splitting methods, we obtain complexity bounds for the two-operator case of Spingarn’s partial inverse method. We also present inexact variants of two specific instances of this family of algorithms and derive corresponding convergence rate results.