On the convergence rate of Douglas–Rachford operator splitting method

Abstract

© 2014, Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society. This note provides a simple proof of a worst-case convergence rate measured by the iteration complexity for the Douglas–Rachford operator splitting method for finding a root of the sum of two maximal monotone set-valued operators. The accuracy of an iterate to the solution set is measured by the residual of a characterization of the original problem, which is different from conventional measures such as the distance to the solution set.