Generalized Peaceman-Rachford splitting method for multiple-block separable convex programming with applications to robust PCA

The Peaceman-Rachford splitting method (PRSM) is an efficient approach for two-block separable convex programming. In this paper we extend this method to the general case where the objective function consists of the sum of multiple convex functions without coupled variables, and present a generalized PRSM. Theoretically, we prove global convergence of the new method and establish the worst-case convergence rate measured by the iteration complexity in the ergodic sense for the new method. Numerically, its efficiency is illustrated by synthetic data about the robust principal component analysis (PCA) model with noisy and incomplete information.