- Title
- The Douglas–Rachford algorithm in the affine-convex case
- Creator
- Bauschke, Heinz; Dao, Minh; Moursi, Walaa
- Date
- 2016
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/185539
- Identifier
- vital:16692
- Identifier
-
https://doi.org/10.1016/j.orl.2016.03.010
- Identifier
- ISBN:0167-6377
- Abstract
- The Douglas–Rachford algorithm is a simple yet effective method for solving convex feasibility problems. However, if the underlying constraints are inconsistent, then the convergence theory is incomplete. We provide convergence results when one constraint is an affine subspace. As a consequence, we extend a result by Spingarn from halfspaces to general closed convex sets admitting least-squares solutions.
- Publisher
- Ithaca: Elsevier B.V
- Relation
- Operations research letters Vol. 44, no. 3 (2016), p. 379-382
- Rights
- All metadata describing materials held in, or linked to, the repository is freely available under a CC0 licence
- Rights
- Copyright Elsevier
- Subject
- Algorithms; Computational geometry; Convergence; Convex feasibility problem; Convexity; Douglas–Rachford splitting operator; Feasibility; Least squares method; Least-squares solution; Operations research; Spingarn’s method; Subspaces; 4901 Applied mathematics
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