The Douglas–Rachford algorithm for the case of the sphere and the line

Joël Benoist ()

Journal of Global Optimization, 2015, vol. 63, issue 2, 363-380

Abstract: In this paper, we solve a conjecture proposed by Borwein and Sims (Fixed-point algorithms for inverse problems in science and engineering, Springer optimization and its applications, 2011 ) in a Hilbert space setting. For the simple non-convex example of the sphere and the line, the sequence of Douglas–Rachford iterates converges in norm to a point of the intersection except when the initial value belongs to the hyperplane of symmetry. Copyright Springer Science+Business Media New York 2015

Keywords: Hilbert space; Douglas–Rachford algorithm; Global convergence; Lyapunov function (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (9)

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DOI: 10.1007/s10898-015-0296-1

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