A Primal-dual Backward Reflected Forward Splitting Algorithm for Structured Monotone Inclusions
We propose a primal-dual backward reflected forward splitting method for solving structured primal-dual monotone inclusions in real Hilbert spaces. The algorithm allows to use the inexact computations of Lipschitzian and cocoercive operators. The strong convergence of the generated iterative sequenc...
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| Published in: | Acta mathematica vietnamica Vol. 49; no. 2; pp. 159 - 172 |
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| Abstract | We propose a primal-dual backward reflected forward splitting method for solving structured primal-dual monotone inclusions in real Hilbert spaces. The algorithm allows to use the inexact computations of Lipschitzian and cocoercive operators. The strong convergence of the generated iterative sequence is proved under the strong monotonicity condition, whilst the weak convergence is formally proved under several conditions used in the literature. An application to a structured minimization problem is provided. |
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| AbstractList | We propose a primal-dual backward reflected forward splitting method for solving structured primal-dual monotone inclusions in real Hilbert spaces. The algorithm allows to use the inexact computations of Lipschitzian and cocoercive operators. The strong convergence of the generated iterative sequence is proved under the strong monotonicity condition, whilst the weak convergence is formally proved under several conditions used in the literature. An application to a structured minimization problem is provided. |
| Author | Papadimitriou, Dimitri Nhâm, Vũ Xuân Bằng, Vũ Công |
| Author_xml | – sequence: 1 givenname: Vũ Công surname: Bằng fullname: Bằng, Vũ Công organization: Belgium Research Center (BeRC), Huawei – sequence: 2 givenname: Dimitri surname: Papadimitriou fullname: Papadimitriou, Dimitri organization: Belgium Research Center (BeRC), Huawei – sequence: 3 givenname: Vũ Xuân surname: Nhâm fullname: Nhâm, Vũ Xuân email: nhamvx@utt.edu.vn organization: University of Transport Technology |
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| Copyright | Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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| Keywords | Forward-backward Cocoercive Monotone inclusion Primal-dual algorithm Monotone operator Duality Lipschitz Backward-forward 90C25 Operator splitting Composite operator 49M29 49M27 47H05 |
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Signal Process. doi: 10.1109/TSP.2014.2331614 |
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| Title | A Primal-dual Backward Reflected Forward Splitting Algorithm for Structured Monotone Inclusions |
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