期刊
SIAM JOURNAL ON OPTIMIZATION
卷 29, 期 4, 页码 2697-2724出版社
SIAM PUBLICATIONS
DOI: 10.1137/18M121160X
关键词
Douglas-Rachford algorithm; Fejer monotonicity; global convergence; inclusion problem; linear convergence; Lipschitz continuity; strong monotonicity; weak monotonicity
资金
- Australian Research Council (ARC) [DP160101537]
- Priority Research Centre for Computer-Assisted Research Mathematics and its Applications (CARMA) at the University of Newcastle
- Autodesk, Inc.
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.
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