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Iteration complexity of an inexact Douglas-Rachford method and of a Douglas-Rachford-Tseng’s F-B four-operator splitting method for solving monotone inclusions
- Source :
- Numerical Algorithms. 82:263-295
- Publication Year :
- 2018
- Publisher :
- Springer Science and Business Media LLC, 2018.
-
Abstract
- In this paper, we propose and study the iteration complexity of an inexact Douglas-Rachford splitting (DRS) method and a Douglas-Rachford-Tseng’s forward-backward (F-B) splitting method for solving two-operator and four-operator monotone inclusions, respectively. The former method (although based on a slightly different mechanism of iteration) is motivated by the recent work of J. Eckstein and W. Yao, in which an inexact DRS method is derived from a special instance of the hybrid proximal extragradient (HPE) method of Solodov and Svaiter, while the latter one combines the proposed inexact DRS method (used as an outer iteration) with a Tseng’s F-B splitting-type method (used as an inner iteration) for solving the corresponding subproblems. We prove iteration complexity bounds for both algorithms in the pointwise (non-ergodic) as well as in the ergodic sense by showing that they admit two different iterations: one that can be embedded into the HPE method, for which the iteration complexity is known since the work of Monteiro and Svaiter, and another one which demands a separate analysis. Finally, we perform simple numerical experiments to show the performance of the proposed methods when compared with other existing algorithms.
- Subjects :
- Pointwise
021103 operations research
Applied Mathematics
Numerical analysis
0211 other engineering and technologies
Separate analysis
010103 numerical & computational mathematics
02 engineering and technology
01 natural sciences
Operator splitting
Monotone polygon
Simple (abstract algebra)
Theory of computation
Ergodic theory
Applied mathematics
0101 mathematics
Mathematics
Subjects
Details
- ISSN :
- 15729265 and 10171398
- Volume :
- 82
- Database :
- OpenAIRE
- Journal :
- Numerical Algorithms
- Accession number :
- edsair.doi...........b25d619bb3d4347537c162e3ae2aa56f