A Cyclic Douglas–Rachford Iteration Scheme

In this paper, we present two Douglas–Rachford inspired iteration schemes which can be applied directly to N‐set convex feasibility problems in Hilbert space. Our main results are weak convergence of the methods to a point whose nearest point projections onto each of the N sets coincide. For affine subspaces, convergence is in norm. Initial results from numerical experiments, comparing our methods to the classical (product‐space) Douglas–Rachford scheme, are promising.