- Title
- A cyclic Douglas-Rachford iteration scheme
- Creator
- Borwein, Jonathan M.; Tam, Matthew K.
- Relation
- ARC
- Relation
- Journal of Optimization Theory and Applications Vol. 160, Issue 1, p. 1-29
- Publisher Link
- http://dx.doi.org/10.1007/s10957-013-0381-x
- Publisher
- Springer New York
- Resource Type
- journal article
- Date
- 2014
- Description
- In this paper, we present two Douglas–Rachford inspired iteration schemes which can be applied directly to N-set convex feasibility problems in Hilbert space. Our main results are weak convergence of the methods to a point whose nearest point projections onto each of the N sets coincide. For affine subspaces, convergence is in norm. Initial results from numerical experiments, comparing our methods to the classical (product-space) Douglas–Rachford scheme, are promising.
- Subject
- Douglas–Rachford method; convex feasibility problem; projections; firmly nonexpansive map; nonexpansive map; asymptotic regularity; fixed points; parallelization
- Identifier
- http://hdl.handle.net/1959.13/1066302
- Identifier
- uon:18073
- Identifier
- ISSN:0022-3239
- Language
- eng
- Reviewed
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