关于算子分裂方法等价性的注记
A note on the equivalence of operator splitting methods
摘要：
本文全面讨论了分裂方法之间的等价性。过去几十年来，人们一直在研究这些等价关系，事实上，这些等价关系已被证明非常有用。在本文中，我们调查已知的结果，也提出了新的。特别是，我们提供了简化的ADMM和Douglas-Rachford方法的等价性和ADMM与中间更新的乘法器和Escherman-Rachford方法的等价性的证明。还考虑了其他分裂方法。
英文摘要：
This paper provides a comprehensive discussion of the equivalences between splitting methods. These equivalences have been studied over the past few decades and, in fact, have proven to be very useful. In this paper, we survey known results and also present new ones. In particular, we provide simplified proofs of the equivalence of the ADMM and the Douglas-Rachford method and the equivalence of the ADMM with intermediate update of multipliers and the Peaceman-Rachford method. Other splitting methods are also considered.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
