Complexity of the relaxed Peaceman–Rachford splitting method for the sum of two maximal strongly monotone operators
研究了松弛Peaceman-Rachford分裂方法求解单调包含问题，扩展了迭代收敛结果，并建立了松弛参数在特定区间内的点态和遍历收敛速率，同时给出参数区间外迭代可能不收敛的例子。
This paper considers the relaxed Peaceman-Rachford (PR) splitting method for finding an approximate solution of a monotone inclusion whose underlying operator consists of the sum of two maximal strongly monotone operators. Using general results obtained in the setting of a non-Euclidean hybrid proximal extragradient framework, we extend a previous convergence result on the iterates generated by the relaxed PR splitting method, as well as establish new pointwise and ergodic convergence rate results for the method whenever an associated relaxation parameter is within a certain interval. An example is also discussed to demonstrate that the iterates may not converge when the relaxation parameter is outside this interval.