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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| Format: | Article |
| Language: | English |
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MDPI AG
2018-11-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/10/11/563 |
| _version_ | 1798002741310652416 |
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| author | Chunxiang Zong Yuchao Tang Yeol Je Cho |
| author_facet | Chunxiang Zong Yuchao Tang Yeol Je Cho |
| author_sort | Chunxiang Zong |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T11:58:05Z |
| format | Article |
| id | doaj.art-fd9e70a82c1a48b1a2c3f47527d1a768 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-11T11:58:05Z |
| publishDate | 2018-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-fd9e70a82c1a48b1a2c3f47527d1a7682022-12-22T04:25:05ZengMDPI AGSymmetry2073-89942018-11-01101156310.3390/sym10110563sym10110563Convergence Analysis of an Inexact Three-Operator Splitting AlgorithmChunxiang Zong0Yuchao Tang1Yeol Je Cho2Department of Mathematics, NanChang University, Nanchang 330031, ChinaDepartment of Mathematics, NanChang University, Nanchang 330031, ChinaSchool of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, ChinaThe 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.https://www.mdpi.com/2073-8994/10/11/563inexact three-operator splitting algorithmnonexpansive operatorfixed point |
| spellingShingle | Chunxiang Zong Yuchao Tang Yeol Je Cho Convergence Analysis of an Inexact Three-Operator Splitting Algorithm Symmetry inexact three-operator splitting algorithm nonexpansive operator fixed point |
| title | Convergence Analysis of an Inexact Three-Operator Splitting Algorithm |
| title_full | Convergence Analysis of an Inexact Three-Operator Splitting Algorithm |
| title_fullStr | Convergence Analysis of an Inexact Three-Operator Splitting Algorithm |
| title_full_unstemmed | Convergence Analysis of an Inexact Three-Operator Splitting Algorithm |
| title_short | Convergence Analysis of an Inexact Three-Operator Splitting Algorithm |
| title_sort | convergence analysis of an inexact three operator splitting algorithm |
| topic | inexact three-operator splitting algorithm nonexpansive operator fixed point |
| url | https://www.mdpi.com/2073-8994/10/11/563 |
| work_keys_str_mv | AT chunxiangzong convergenceanalysisofaninexactthreeoperatorsplittingalgorithm AT yuchaotang convergenceanalysisofaninexactthreeoperatorsplittingalgorithm AT yeoljecho convergenceanalysisofaninexactthreeoperatorsplittingalgorithm |