Modified Relaxed CQ Iterative Algorithms for the Split Feasibility Problem
The split feasibility problem models inverse problems arising from phase retrievals problems and intensity-modulated radiation therapy. For solving the split feasibility problem, Xu proposed a relaxed CQ algorithm that only involves projections onto half-spaces. In this paper, we use the dual variab...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/7/2/119 |
| _version_ | 1819160466983747584 |
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| author | Xinglong Wang Jing Zhao Dingfang Hou |
| author_facet | Xinglong Wang Jing Zhao Dingfang Hou |
| author_sort | Xinglong Wang |
| collection | DOAJ |
| description | The split feasibility problem models inverse problems arising from phase retrievals problems and intensity-modulated radiation therapy. For solving the split feasibility problem, Xu proposed a relaxed CQ algorithm that only involves projections onto half-spaces. In this paper, we use the dual variable to propose a new relaxed CQ iterative algorithm that generalizes Xu’s relaxed CQ algorithm in real Hilbert spaces. By using projections onto half-spaces instead of those onto closed convex sets, the proposed algorithm is implementable. Moreover, we present modified relaxed CQ algorithm with viscosity approximation method. Under suitable conditions, global weak and strong convergence of the proposed algorithms are proved. Some numerical experiments are also presented to illustrate the effectiveness of the proposed algorithms. Our results improve and extend the corresponding results of Xu and some others. |
| first_indexed | 2024-12-22T16:56:54Z |
| format | Article |
| id | doaj.art-ac4b9ba2b6f64ed7b5cf5b05bf59a1a7 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-22T16:56:54Z |
| publishDate | 2019-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-ac4b9ba2b6f64ed7b5cf5b05bf59a1a72022-12-21T18:19:26ZengMDPI AGMathematics2227-73902019-01-017211910.3390/math7020119math7020119Modified Relaxed CQ Iterative Algorithms for the Split Feasibility ProblemXinglong Wang0Jing Zhao1Dingfang Hou2College of Air Traffic Management, Civil Aviation University of China, Tianjin 300300, ChinaCollege of Science, Civil Aviation University of China, Tianjin 300300, ChinaCollege of Science, Civil Aviation University of China, Tianjin 300300, ChinaThe split feasibility problem models inverse problems arising from phase retrievals problems and intensity-modulated radiation therapy. For solving the split feasibility problem, Xu proposed a relaxed CQ algorithm that only involves projections onto half-spaces. In this paper, we use the dual variable to propose a new relaxed CQ iterative algorithm that generalizes Xu’s relaxed CQ algorithm in real Hilbert spaces. By using projections onto half-spaces instead of those onto closed convex sets, the proposed algorithm is implementable. Moreover, we present modified relaxed CQ algorithm with viscosity approximation method. Under suitable conditions, global weak and strong convergence of the proposed algorithms are proved. Some numerical experiments are also presented to illustrate the effectiveness of the proposed algorithms. Our results improve and extend the corresponding results of Xu and some others.https://www.mdpi.com/2227-7390/7/2/119split feasibility problemrelaxed CQ algorithmconvergenceHilbert space |
| spellingShingle | Xinglong Wang Jing Zhao Dingfang Hou Modified Relaxed CQ Iterative Algorithms for the Split Feasibility Problem Mathematics split feasibility problem relaxed CQ algorithm convergence Hilbert space |
| title | Modified Relaxed CQ Iterative Algorithms for the Split Feasibility Problem |
| title_full | Modified Relaxed CQ Iterative Algorithms for the Split Feasibility Problem |
| title_fullStr | Modified Relaxed CQ Iterative Algorithms for the Split Feasibility Problem |
| title_full_unstemmed | Modified Relaxed CQ Iterative Algorithms for the Split Feasibility Problem |
| title_short | Modified Relaxed CQ Iterative Algorithms for the Split Feasibility Problem |
| title_sort | modified relaxed cq iterative algorithms for the split feasibility problem |
| topic | split feasibility problem relaxed CQ algorithm convergence Hilbert space |
| url | https://www.mdpi.com/2227-7390/7/2/119 |
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