A note on the equivalence of operator splitting methods

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.