The Douglas-Rachford algorithm in the absence of convexity

Title: The Douglas-Rachford algorithm in the absence of convexity
Creator: Borwein, Jonathan M.; Sims, Brailey
Relation: Fixed-Point Algorithms for Inverse Problems in Science and Engineering p. 93-109
Relation: Springer Optimization and its Applications 49
Publisher Link: http://dx.doi.org/10.1007/978-1-4419-9569-8_6
Publisher: Springer
Resource Type: book chapter
Date: 2011
Description: 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.
Subject: non convex feasibility problem; fixed point theory; dynamical system; iteration
Identifier: http://hdl.handle.net/1959.13/1038186
Identifier: uon:13520
Identifier: ISBN:9781441995681
Rights: The original publication is available at www.springerlink.com
Language: eng
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