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Title of Journal: J Glob Optim

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Abbravation: Journal of Global Optimization

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Springer US

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DOI

10.1007/s00425-005-0060-8

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1573-2916

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On Slater’s condition and finite convergence of th

Authors: Heinz H Bauschke Minh N Dao Dominikus Noll Hung M Phan
Publish Date: 2015/10/13
Volume: 65, Issue: 2, Pages: 329-349
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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 affinepolyhedral and in a hyperplanarepigraphical 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–projectionThe authors thank an anonymous referee for careful reading and constructive comments HHB was partially supported by the Natural Sciences and Engineering Research Council of Canada and by the Canada Research Chair Program MND was partially supported by an NSERC accelerator grant of HHB

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