The cyclic Douglas–Rachford algorithm with r-sets-Douglas–Rachford operators

Francisco J. Aragón Artacho, Yair Censor, Aviv Gibali

Research output: Contribution to journalArticlepeer-review


The Douglas–Rachford (DR) algorithm is an iterative procedure that uses sequential reflections onto convex sets and which has become popular for convex feasibility problems. In this paper we propose a structural generalization that allows to use r-sets-DR operators in a cyclic fashion. We prove convergence and present numerical illustrations of the potential advantage of such operators with r>2 over the classical 2-sets-DR operators in a cyclic algorithm.

Original languageEnglish
Pages (from-to)875-889
Number of pages15
JournalOptimization Methods and Software
Issue number4
StatePublished - 4 Jul 2019

Bibliographical note

Funding Information:
The f irst author was supported by MINECO of Spain and ERDF of EU, as part of the Ramón y Cajal program (RYC-2013-13327) and the Grant MTM2014-59179-C2-1-P. The second author’s work was supported by research grant no. 2013003 of the United States-Israel Binational Science Foundation (BSF). The third author’s work was supported by the EU FP7 IRSES program STREVCOMS, grant no. PIRSES-GA-2013-612669.

Publisher Copyright:
© 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.


  • Douglas–Rachford
  • feasibility problems
  • r-sets-Douglas–Rachford operator
  • reflections

ASJC Scopus subject areas

  • Software
  • Control and Optimization
  • Applied Mathematics


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