SIAM Journal on Optimization, Volume 30, Issue 3, Page 2251-2271, January 2020.
We propose a methodology for studying the performance of common splitting methods through semidefinite programming. We prove tightness of the methodology and demonstrate its value by presenting two applications of it. First, we use the methodology as a tool for computer-assisted proofs to prove tight analytical contraction factors for Douglas--Rachford splitting that are likely too complicated for a human to find bare-handed. Second, we use the methodology as an algorithmic tool to computationally select the optimal splitting method parameters by solving a series of semidefinite programs.

中文翻译：

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操作员拆分性能估计：紧缩因子和最佳参数选择

SIAM优化杂志，第30卷，第3期，第2251-2271页，2020年1月。
我们提出了一种通过半定规划研究常用拆分方法性能的方法。我们通过介绍该方法的两个应用来证明该方法的紧密性并证明其价值。首先，我们使用该方法学作为计算机辅助证明的工具，以证明道格拉斯-拉奇福德分裂的严格分析收缩因子，这对于人类来说很难找到徒手。其次，我们使用该方法作为一种算法工具，通过求解一系列半定程序，从计算上选择最佳的分裂方法参数。