A Proximal Strictly Contractive Peaceman--Rachford Splitting Method for Convex Programming with Applications to Imaging

A strictly contractive Peaceman-Rachford splitting method was proposed recently for solving separable convex programming problems. In this paper we further discuss a proximal version of this method, where a subproblem at each iteration is regularized by a proximal point term. The resulting regularized subproblem thus may have closed-form or easily computable solutions, especially in some interesting applications such as a class of sparse and low-rank optimization models. We establish the worst-case convergence rate measured by the iteration complexity in both the ergodic and nonergodic senses for the new algorithm. Some applications arising in image processing are tested to demonstrate the efficiency of the new algorithm.