The Peaceman–Rachford splitting method (PRSM) is a preferred method for solving the two-block separable convex minimization problems with linear constraints at present. In this paper, we propose an inertial generalized proximal PRSM (abbreviated as IGPRSM) to improve computing efficiency, which unify the ideas of inertial proximal point and linearization technique. Both subproblems are linearized by positive semi-definite proximal matrices, and we explain why the matrix cannot be indefinite. The global convergence and the worst-case asymptotic iteration complexity are derived theoretically via the variational inequality framework. Numerical experiments on LASSO, total variation (TV) based denoising models and image decomposition problems are presented to show the effectiveness of the introduced method even compared with the state-of-the-art methods.

目前，Peaceman-Rachford分裂方法（PRSM）是解决具有线性约束的两块可分离凸极小化问题的首选方法。在本文中，我们提出了一种惯性广义近端PRSM（简称为IGPRSM）以提高计算效率，从而将惯性近端点和线性化技术的思想统一起来。两个子问题都通过正半定近邻矩阵线性化，我们解释了为什么矩阵不能定为不定式。理论上，通过变分不等式框架得出了全局收敛性和最坏情况下的渐近迭代复杂度。LASSO的数值实验，