A Cyclic Douglas–Rachford Iteration Scheme

Jonathan M. Borwein () and Matthew K. Tam ()
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Jonathan M. Borwein: University of Newcastle
Matthew K. Tam: University of Newcastle

Journal of Optimization Theory and Applications, 2014, vol. 160, issue 1, No 1, 29 pages

Abstract: 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.

Keywords: Douglas–Rachford method; Convex feasibility problem; Projections; Firmly nonexpansive map; Nonexpansive map; Asymptotic regularity; Fixed points; Parallelization (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-013-0381-x

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