Convergence Analysis of an Inexact Three-Operator Splitting Algorithm

The three-operator splitting algorithm is a new splitting algorithm for finding monotone inclusion problems of the sum of three maximally monotone operators, where one is cocoercive. As the resolvent operator is not available in a closed form in the original three-operator splitting algorithm, in th...

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Veröffentlicht in:Symmetry (Basel) Jg. 10; H. 11; S. 563
Hauptverfasser: Zong, Chunxiang, Tang, Yuchao, Cho, Yeol Je
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Basel MDPI AG 01.11.2018
Schlagworte:
Algorithms
Convergence
Convex analysis
Hilbert space
Iterative algorithms
Optimization
Splitting
ISSN:2073-8994, 2073-8994
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Zusammenfassung:The three-operator splitting algorithm is a new splitting algorithm for finding monotone inclusion problems of the sum of three maximally monotone operators, where one is cocoercive. As the resolvent operator is not available in a closed form in the original three-operator splitting algorithm, in this paper, we introduce an inexact three-operator splitting algorithm to solve this type of monotone inclusion problem. The theoretical convergence properties of the proposed iterative algorithm are studied in general Hilbert spaces under mild conditions on the iterative parameters. As a corollary, we obtain general convergence results of the inexact forward-backward splitting algorithm and the inexact Douglas-Rachford splitting algorithm, which extend the existing results in the literature.
Bibliographie:ObjectType-Article-1
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ISSN:2073-8994
2073-8994
DOI:10.3390/sym10110563