- Title
- Linear convergence of the generalized Douglas-Rachford algorithm for feasibility problems
- Creator
- Dao, Minh N.; Phan, Hung M.
- Relation
- ARC.DP160101537 http://purl.org/au-research/grants/arc/DP160101537
- Relation
- Journal of Global Optimization Vol. 72, Issue 3, p. 443-474
- Publisher Link
- http://dx.doi.org/10.1007/s10898-018-0654-x
- Publisher
- Springer
- Resource Type
- journal article
- Date
- 2018
- Description
- In this paper, we study the generalized Douglas-Rachford algorithm and its cyclic variants which include many projection-type methods such as the classical Douglas-Rachford algorithm and the alternating projection algorithm. Specifically, we establish several local linear convergence results for the algorithm in solving feasibility problems with finitely many closed possibly nonconvex sets under different assumptions. Our findings not only relax some regularity conditions but also improve linear convergence rates in the literature. In the presence of convexity, the linear convergence is global.
- Subject
- affine-hull regularity; cyclic algorithm; generalized Douglas-Rachford algorithm; linear convergence; linear regularity; strong regularity
- Identifier
- http://hdl.handle.net/1959.13/1447836
- Identifier
- uon:43245
- Identifier
- ISSN:0925-5001
- Rights
- This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s10898-018-0654-x
- Language
- eng
- Full Text
- Reviewed
- Hits: 650
- Visitors: 674
- Downloads: 33
| Thumbnail | File | Description | Size | Format | |||
|---|---|---|---|---|---|---|---|
| View Details Download | ATTACHMENT02 | Author final version | 472 KB | Adobe Acrobat PDF | View Details Download |