A Multi-Step Inertial Proximal Peaceman-Rachford Splitting Method for Separable Convex Programming

Abstract

In this paper, we propose a multi-step inertial proximal Peaceman-Rachford splitting method (abbreviated as MIP-PRSM) for solving the two-block separable convex optimization problems with linear constraints, which is a unified framework for such Peaceman-Rachford splitting methods (PRSM)-based improved algorithms with inertial step. Furthermore, we establish the global convergence of the MIP-PRSM under some assumptions. Finally, some numerical experimental results on the least squares semidefinite programming (LSSP), LASSO, the convex quadratic programming problem (CQPP), total variation (TV) based denoising and medical image reconstruction problems demonstrate the efficiency of the proposed method.