- Title
- Computing the resolvent of the sum of operators with application to best approximation problems
- Creator
- Dao, Minh N.; Phan, Hung M.
- Relation
- ARC.160101537 http://purl.org/au-research/grants/arc/DP160101537
- Relation
- Optimization Letters Vol. 14, p. 1193-1205
- Publisher Link
- http://dx.doi.org/10.1007/s11590-019-01432-x
- Publisher
- Springer
- Resource Type
- journal article
- Date
- 2019
- Description
- We propose a flexible approach for computing the resolvent of the sum of weakly monotone operators in real Hilbert spaces. This relies on splitting methods where strong convergence is guaranteed. We also prove linear convergence under Lipschitz continuity assumption. The approach is then applied to computing the proximity operator of the sum of weakly convex functions, and particularly to finding the best approximation to the intersection of convex sets.
- Subject
- Best approximation; Douglas–Rachford algorithm; Linear convergence; Operator splitting; Peaceman–Rachford algorithm; Projector
- Identifier
- http://hdl.handle.net/1959.13/1447793
- Identifier
- uon:43234
- Identifier
- ISSN:1862-4472
- 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/s11590-019-01432-x
- Language
- eng
- Full Text
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