The cyclic Douglas–Rachford algorithm with r-sets-Douglas–Rachford operators. (4th July 2019)

• Record Type: Journal Article
• Authors: Aragón Artacho, Francisco J.; Censor, Yair; Gibali, Aviv
• Is Part Of: Optimization methods and software. Volume 34:Number 4(2019)
• Page Start: 875
• Page End: 889
• Publication Date: 2019-07-04
• Subjects: Douglas–Rachford -- reflections -- feasibility problems -- r-sets-Douglas–Rachford operator; 65K05 -- 90C25; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2018.1504049
• Languages: English
• ISSNs: 1055-6788

Abstract

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.