The Douglas–Rachford Algorithm in the Absence of Convexity

Jonathan M. Borwein () and Brailey Sims
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Jonathan M. Borwein: University of Newcastle

Chapter Chapter 6 in Fixed-Point Algorithms for Inverse Problems in Science and Engineering, 2011, pp 93-109 from Springer

Abstract: Abstract The Douglas–Rachford iteration scheme, introduced half a century ago in connection with nonlinear heat flow problems, aims to find a point common to two or more closed constraint sets. Convergence of the scheme is ensured when the sets are convex subsets of a Hilbert space, however, despite the absence of satisfactory theoretical justification, the scheme has been routinely used to successfully solve a diversity of practical problems in which one or more of the constraints involved is non-convex. As a first step toward addressing this deficiency, we provide convergence results for a prototypical non-convex two-set scenario in which one of the sets is the Euclidean sphere.

Keywords: Non-convex feasibility problem; Fixed point theory; Dynamical system; Iteration (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4419-9569-8_6

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DOI: 10.1007/978-1-4419-9569-8_6

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