Department of Mathematics
A proximal strictly contractive Peaceman-Rachford splitting method for convex programming with applications to imaging
© 2015 Society for Industrial and Applied Mathematics.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.
Contraction, Convergence rate, Convex programming, Image processing, Peaceman–Rachford splitting method
Source Publication Title
SIAM Journal on Imaging Sciences
Society for Industrial and Applied Mathematics
Li, Xinxin, and Xiaoming Yuan. "A proximal strictly contractive Peaceman-Rachford splitting method for convex programming with applications to imaging." SIAM Journal on Imaging Sciences 8.2 (2015): 1332-1365.