A relative-error inexact Spingarn's operator splitting algorithm

We propose a relative-error inexact Spingarn's operator splitting algorithm for solving monotone inclusion problems for finite sums of maximal monotone operators defined in a real Hilbert space. In contrast to projective-splitting type methods, which iterate by means of projections onto separating hyperplanes, the proposed algorithm uses extragradient steps, in the spirit of the Korpelevich and HPE-type methods. We analyze the iteration-complexity of the algorithm, establishing O(1/k) pointwise rate and improved O(1/k) ergodic rate. Additionally, we prove the weak convergence of the iterates to a solution, if any.