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Douglas-Rachford method is a splitting algorithm for finding a zero of thesum of two maximal monotone operators. Weak convergence in this method to asolution of the underlying monotone inclusion problem in the general caseremained an open problem for 30 years and was prove by the author 7 year ago.The proof presented at that occasion was cluttered with technicalities becausewe considered the inexact version with summable errors. The aim of this note isto present a streamlined proof of this result.

A simplified proof of weak convergence in Douglas-Rachford method to a solution of the unnderlying inclusion problem