On the convergence rate of Douglas–Rachford operator splitting method

Bingsheng He*, Xiaoming Yuan

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

45 Citations (Scopus)


This note provides a simple proof of a worst-case convergence rate measured by the iteration complexity for the Douglas–Rachford operator splitting method for finding a root of the sum of two maximal monotone set-valued operators. The accuracy of an iterate to the solution set is measured by the residual of a characterization of the original problem, which is different from conventional measures such as the distance to the solution set.

Original languageEnglish
Pages (from-to)715-722
Number of pages8
JournalMathematical Programming
Issue number2
Early online date11 Sept 2014
Publication statusPublished - Nov 2015

Scopus Subject Areas

  • Software
  • Mathematics(all)

User-Defined Keywords

  • Convergence rate
  • Douglas–Rachford operator splitting method


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