A modified strictly contractive peaceman-rachford splitting method for multi-block separable convex programming

Abstract

We propose a modified splitting method for a linearly constrained minimization model whose objective function is the sum of three convex functions without coupled variables. Our work is mainly inspired by the recently proposed strictly contractive Peaceman-Rachford splitting method (SC-PRSM) for a two-block separable convex minimization model. For the new method, we prove its convergence and estimate its convergence rates measured by iteration complexity in the nonergodic sense. We also test the SC-PRSM on the continuous resource allocation problem, and the numerical results show that our method has a competitive performance with the direct extension of ADMM which usually works well in practice but may fail to converge in theory.