- Title
- Adaptive Douglas-Rachford splitting algorithm for the sum of two operators
- Creator
- Dao, Minh N.; Phan, Hung M.
- Relation
- ARC.DP160101537 http://purl.org/au-research/grants/arc/DP160101537
- Relation
- SIAM Journal on Optimization Vol. 29, Issue 4, p. 2697-2724
- Publisher Link
- http://dx.doi.org/10.1137/18M121160X
- Publisher
- Society for Industrial and Applied Mathematics (SIAM)
- Resource Type
- journal article
- Date
- 2019
- Description
- The Douglas-Rachford algorithm is a classical and powerful splitting method for minimizing the sum of two convex functions and, more generally, finding a zero of the sum of two maximally monotone operators. Although this algorithm is well understood when the involved operators are monotone or strongly monotone, the convergence theory for weakly monotone settings is far from being complete. In this paper, we propose an adaptive Douglas-Rachford splitting algorithm for the sum of two operators, one of which is strongly monotone while the other one is weakly monotone. With appropriately chosen parameters, the algorithm converges globally to a fixed point from which we derive a solution of the problem. When one operator is Lipschitz continuous, we prove global linear convergence, which sharpens recent known results.
- Subject
- Douglas-Rachford algorithm; Fejer monotonicity; global convergence; inclusion problem; linear convergence; Lipschitz continuity; strong monotonicity; weak monotonicity
- Identifier
- http://hdl.handle.net/1959.13/1413763
- Identifier
- uon:36669
- Identifier
- ISSN:1052-6234
- Rights
- © 2019 Society for Industrial and Applied Mathematics. This work is distributed under the Creative Commons Attribution 4.0 Licence (http://creativecommons.org/licenses/by/4.0/).
- Language
- eng
- Full Text
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