- Title
- The Douglas–Rachford algorithm for a hyperplane and a doubleton
- Creator
- Bauschke, Heinz; Dao, Minh; Lindstrom, Scott
- Date
- 2019
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/185557
- Identifier
- vital:16691
- Identifier
-
https://doi.org/10.1007/s10898-019-00744-7
- Identifier
- ISBN:0925-5001
- Abstract
- The Douglas–Rachford algorithm is a popular algorithm for solving both convex and nonconvex feasibility problems. While its behaviour is settled in the convex inconsistent case, the general nonconvex inconsistent case is far from being fully understood. In this paper, we focus on the most simple nonconvex inconsistent case: when one set is a hyperplane and the other a doubleton (i.e., a two-point set). We present a characterization of cycling in this case which—somewhat surprisingly—depends on whether the ratio of the distance of the points to the hyperplane is rational or not. Furthermore, we provide closed-form expressions as well as several concrete examples which illustrate the dynamical richness of this algorithm.
- Publisher
- New York: Springer US
- Relation
- Journal of global optimization Vol. 74, no. 1 (2019), p. 79-93
- Rights
- All metadata describing materials held in, or linked to, the repository is freely available under a CC0 licence
- Rights
- Copyright Springer
- Subject
- Algorithms; Computer Science; Hyperplanes; Mathematics; Mathematics - Optimization and Control; Mathematics and Statistics; Operations Research/Decision Theory; Optimization; Projectors; Real Functions; 4602 Artificial intelligence; 4901 Applied mathematics; 4903 Numerical and computational mathematics
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