- 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
- Full Text
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