A Cyclic Douglas-Rachford Iteration Scheme

Abstract

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.

22 pages, 7 figures, 4 tables

References in corpus (3)

• Divide and concur: A general approach to constraint satisfaction
• Recent Results on Douglas-Rachford Methods for Combinatorial Optimization Problems
• Global convergence of a non-convex Douglas-Rachford iteration

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