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The Douglas-Rachford (DR) algorithm is an iterative procedure that usessequential reflections onto convex sets and which has become popular for convexfeasibility problems. In this paper we propose a structural generalization thatallows to use $r$-sets-DR operators in a cyclic fashion. We prove convergenceand present numerical illustrations of the potential advantage of suchoperators with $r>2$ over the classical $2$-sets-DR operators in a cyclicalgorithm.

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