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

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Title: The cyclic Douglas–Rachford algorithm with r-sets-Douglas–Rachford operators
Authors: Aragón Artacho, Francisco Javier | Censor, Yair | Gibali, Aviv
Research Group/s: Laboratorio de Optimización (LOPT)
Center, Department or Service: Universidad de Alicante. Departamento de Matemáticas
Keywords: Douglas–Rachford | Reflections | Feasibility problems | r-sets-Douglas–Rachford operator
Knowledge Area: Estadística e Investigación Operativa
Issue Date: 2019
Publisher: Taylor & Francis
Citation: Optimization Methods and Software. 2019, 34(4): 875-889. doi:10.1080/10556788.2018.1504049
Abstract: 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.
Sponsor: The first 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.
ISSN: 1055-6788 (Print) | 1029-4937 (Online)
DOI: 10.1080/10556788.2018.1504049
Language: eng
Type: info:eu-repo/semantics/article
Rights: © 2018 Informa UK Limited, trading as Taylor & Francis Group
Peer Review: si
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Appears in Collections:Research funded by the EU
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