On Slater's condition and finite convergence of the Douglas-Rachford algorithm for solving convex feasibility problems in Euclidean spaces
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Publication:288232
DOI10.1007/S10898-015-0373-5zbMATH Open1345.90065arXiv1504.06969OpenAlexW1901524206MaRDI QIDQ288232
Author name not available (Why is that?)
Publication date: 25 May 2016
Published in: (Search for Journal in Brave)
Abstract: The Douglas-Rachford algorithm is a classical and very successful method for solving optimization and feasibility problems. In this paper, we provide novel conditions sufficient for finite convergence in the context of convex feasibility problems. Our analysis builds upon, and considerably extends, pioneering work by Spingarn. Specifically, we obtain finite convergence in the presence of Slater's condition in the affine-polyhedral and in a hyperplanar-epigraphical case. Various examples illustrate our results. Numerical experiments demonstrate the competitiveness of the Douglas-Rachford algorithm for solving linear equations with a positivity constraint when compared to the method of alternating projections and the method of reflection-projection.
Full work available at URL: https://arxiv.org/abs/1504.06969
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