Recently, a generalized version of Peaceman-Rachford splitting method (GPRSM) for solving a convex minmization model with a general separable structure has been proposed by \textbf{Sun} et al and its global convergence has been proved. In this paper, we further study theoretical aspects of the generalized Peaceman-Rachford splitting method. We first establish the worst-case $\mathcal{O}(1/t)$ convergence rate for the proposed GPRSM in both the ergodic and a nonergodic senses, then we give some numerical results to demonstrate the convergence rate of the algorithm.
Citation
July 8, 2017