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

Francisco J. Aragón Artacho; Yair Censor; Aviv Gibali

doi:10.1080/10556788.2018.1504049

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

Francisco J. Aragón Artacho
, Yair Censor
, Aviv Gibali

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	875-889
Number of pages	15
Journal	Optimization Methods and Software
Volume	34
Issue number	4
DOIs	https://doi.org/10.1080/10556788.2018.1504049
State	Published - 4 Jul 2019

Bibliographical note

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

Keywords

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

ASJC Scopus subject areas

Software
Control and Optimization
Applied Mathematics

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10.1080/10556788.2018.1504049

Cite this

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Y1 - 2019/7/4

N2 - 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.

AB - 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.

KW - Douglas–Rachford

KW - feasibility problems

KW - r-sets-Douglas–Rachford operator

KW - reflections

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ER -

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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