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The cyclic Douglas–Rachford algorithm with r-sets-Douglas–Rachford operators |
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| Authors: | Francisco J Aragón Artacho Aviv Gibali |
| Affiliation: | 1. Department of Mathematics, University of Alicante, Alicante, Spain;2. Department of Mathematics, ORT Braude College, Karmiel, Israel;3. The Center for Mathematics and Scientific Computation, University of Haifa, Haifa, Israel |
| 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 |