A Reflected Forward-Backward Splitting Method for Monotone Inclusions Involving Lipschitzian Operators

In this paper, we propose a novel splitting method for finding a zero point of the sum of two monotone operators where one of them is Lipschizian. The weak convergence the method is proved in real Hilbert spaces. Applying the proposed method to composite monotone inclusions involving parallel sums y...

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Veröffentlicht in:Set-valued and variational analysis Jg. 29; H. 1; S. 163 - 174
Hauptverfasser: Cevher, Volkan, Vũ, Bằng Công
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Dordrecht Springer Netherlands 01.03.2021
Springer Nature B.V
Schlagworte:
Analysis
Hilbert space
Inclusions
Mathematics
Mathematics and Statistics
Noise reduction
Operators
Optimization
Splitting
Cocoercive
Monotone inclusion
Primal-dual algorithm
Monotone operator
Duality
Forward-backward algorithm
Forward-backward-forward method
90C25
Operator splitting
Composite operator
49M29
49M27
47H05
ISSN:1877-0533, 1877-0541
Online-Zugang:Volltext
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Zusammenfassung:In this paper, we propose a novel splitting method for finding a zero point of the sum of two monotone operators where one of them is Lipschizian. The weak convergence the method is proved in real Hilbert spaces. Applying the proposed method to composite monotone inclusions involving parallel sums yields a new primal-dual splitting which is different from the existing methods. Connections to existing works are clearly stated. We also provide an application of the proposed method to the image denoising by the total variation.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1877-0533
1877-0541
DOI:10.1007/s11228-020-00542-4