New Inertial Relaxed CQ Algorithms for Solving Split Feasibility Problems in Hilbert Spaces
The split feasibility problem SFP has received much attention due to its various applications in signal processing and image reconstruction. In this paper, we propose two inertial relaxed CQ algorithms for solving the split feasibility problem in real Hilbert spaces according to the previous experie...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/6624509 |
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| _version_ | 1850214317348093952 |
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| author | Haiying Li Yulian Wu Fenghui Wang |
| author_facet | Haiying Li Yulian Wu Fenghui Wang |
| author_sort | Haiying Li |
| collection | DOAJ |
| description | The split feasibility problem SFP has received much attention due to its various applications in signal processing and image reconstruction. In this paper, we propose two inertial relaxed CQ algorithms for solving the split feasibility problem in real Hilbert spaces according to the previous experience of applying inertial technology to the algorithm. These algorithms involve metric projections onto half-spaces, and we construct new variable step size, which has an exact form and does not need to know a prior information norm of bounded linear operators. Furthermore, we also establish weak and strong convergence of the proposed algorithms under certain mild conditions and present a numerical experiment to illustrate the performance of the proposed algorithms. |
| format | Article |
| id | doaj-art-8530d33296944f61aad7b74954cce3df |
| institution | OA Journals |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-8530d33296944f61aad7b74954cce3df2025-08-20T02:08:57ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/66245096624509New Inertial Relaxed CQ Algorithms for Solving Split Feasibility Problems in Hilbert SpacesHaiying Li0Yulian Wu1Fenghui Wang2College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, ChinaCollege of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, ChinaDepartment of Mathematics, Luoyang Normal University, Luoyang 471934, ChinaThe split feasibility problem SFP has received much attention due to its various applications in signal processing and image reconstruction. In this paper, we propose two inertial relaxed CQ algorithms for solving the split feasibility problem in real Hilbert spaces according to the previous experience of applying inertial technology to the algorithm. These algorithms involve metric projections onto half-spaces, and we construct new variable step size, which has an exact form and does not need to know a prior information norm of bounded linear operators. Furthermore, we also establish weak and strong convergence of the proposed algorithms under certain mild conditions and present a numerical experiment to illustrate the performance of the proposed algorithms.http://dx.doi.org/10.1155/2021/6624509 |
| spellingShingle | Haiying Li Yulian Wu Fenghui Wang New Inertial Relaxed CQ Algorithms for Solving Split Feasibility Problems in Hilbert Spaces Journal of Mathematics |
| title | New Inertial Relaxed CQ Algorithms for Solving Split Feasibility Problems in Hilbert Spaces |
| title_full | New Inertial Relaxed CQ Algorithms for Solving Split Feasibility Problems in Hilbert Spaces |
| title_fullStr | New Inertial Relaxed CQ Algorithms for Solving Split Feasibility Problems in Hilbert Spaces |
| title_full_unstemmed | New Inertial Relaxed CQ Algorithms for Solving Split Feasibility Problems in Hilbert Spaces |
| title_short | New Inertial Relaxed CQ Algorithms for Solving Split Feasibility Problems in Hilbert Spaces |
| title_sort | new inertial relaxed cq algorithms for solving split feasibility problems in hilbert spaces |
| url | http://dx.doi.org/10.1155/2021/6624509 |
| work_keys_str_mv | AT haiyingli newinertialrelaxedcqalgorithmsforsolvingsplitfeasibilityproblemsinhilbertspaces AT yulianwu newinertialrelaxedcqalgorithmsforsolvingsplitfeasibilityproblemsinhilbertspaces AT fenghuiwang newinertialrelaxedcqalgorithmsforsolvingsplitfeasibilityproblemsinhilbertspaces |