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The Cyclic Douglas-Rachford Algorithm with r-sets-Douglas-Rachford Operators

Francisco J. Aragón Artacho (francisco.aragon***at***ua.es)
Yair Censor (yair***at***math.haifa.ac.il)
Aviv Gibali (avivg***at***braude.ac.il)

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.

Keywords: Douglas–Rachford; reflections; feasibility problems; r-sets-Douglas-Rachford operator.

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Citation: Optimization Methods and Software, accepted for publication.

Download: [PDF]

Entry Submitted: 07/19/2018
Entry Accepted: 07/19/2018
Entry Last Modified: 07/19/2018

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