A Relaxed Self-Adaptive Projection Algorithm for Solving the Multiple-Sets Split Equality Problem
In this article, we introduce a relaxed self-adaptive projection algorithm for solving the multiple-sets split equality problem. Firstly, we transfer the original problem to the constrained multiple-sets split equality problem and a fixed point equation system is established. Then, we show the equiv...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2020/6183214 |
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| _version_ | 1832554559773343744 |
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| author | Haitao Che Haibin Chen |
| author_facet | Haitao Che Haibin Chen |
| author_sort | Haitao Che |
| collection | DOAJ |
| description | In this article, we introduce a relaxed self-adaptive projection algorithm for solving the multiple-sets split equality problem. Firstly, we transfer the original problem to the constrained multiple-sets split equality problem and a fixed point equation system is established. Then, we show the equivalence of the constrained multiple-sets split equality problem and the fixed point equation system. Secondly, we present a relaxed self-adaptive projection algorithm for the fixed point equation system. The advantage of the self-adaptive step size is that it could be obtained directly from the iterative procedure. Furthermore, we prove the convergence of the proposed algorithm. Finally, several numerical results are shown to confirm the feasibility and efficiency of the proposed algorithm. |
| format | Article |
| id | doaj-art-3ee69dae74fa4af0b3d5fc92e0820fc4 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-3ee69dae74fa4af0b3d5fc92e0820fc42025-02-03T05:51:14ZengWileyJournal of Function Spaces2314-88962314-88882020-01-01202010.1155/2020/61832146183214A Relaxed Self-Adaptive Projection Algorithm for Solving the Multiple-Sets Split Equality ProblemHaitao Che0Haibin Chen1School of Mathematics and Information Science, Weifang University, Weifang, Shandong, ChinaSchool of Management Science, Qufu Normal University, Rizhao, Shandong, ChinaIn this article, we introduce a relaxed self-adaptive projection algorithm for solving the multiple-sets split equality problem. Firstly, we transfer the original problem to the constrained multiple-sets split equality problem and a fixed point equation system is established. Then, we show the equivalence of the constrained multiple-sets split equality problem and the fixed point equation system. Secondly, we present a relaxed self-adaptive projection algorithm for the fixed point equation system. The advantage of the self-adaptive step size is that it could be obtained directly from the iterative procedure. Furthermore, we prove the convergence of the proposed algorithm. Finally, several numerical results are shown to confirm the feasibility and efficiency of the proposed algorithm.http://dx.doi.org/10.1155/2020/6183214 |
| spellingShingle | Haitao Che Haibin Chen A Relaxed Self-Adaptive Projection Algorithm for Solving the Multiple-Sets Split Equality Problem Journal of Function Spaces |
| title | A Relaxed Self-Adaptive Projection Algorithm for Solving the Multiple-Sets Split Equality Problem |
| title_full | A Relaxed Self-Adaptive Projection Algorithm for Solving the Multiple-Sets Split Equality Problem |
| title_fullStr | A Relaxed Self-Adaptive Projection Algorithm for Solving the Multiple-Sets Split Equality Problem |
| title_full_unstemmed | A Relaxed Self-Adaptive Projection Algorithm for Solving the Multiple-Sets Split Equality Problem |
| title_short | A Relaxed Self-Adaptive Projection Algorithm for Solving the Multiple-Sets Split Equality Problem |
| title_sort | relaxed self adaptive projection algorithm for solving the multiple sets split equality problem |
| url | http://dx.doi.org/10.1155/2020/6183214 |
| work_keys_str_mv | AT haitaoche arelaxedselfadaptiveprojectionalgorithmforsolvingthemultiplesetssplitequalityproblem AT haibinchen arelaxedselfadaptiveprojectionalgorithmforsolvingthemultiplesetssplitequalityproblem AT haitaoche relaxedselfadaptiveprojectionalgorithmforsolvingthemultiplesetssplitequalityproblem AT haibinchen relaxedselfadaptiveprojectionalgorithmforsolvingthemultiplesetssplitequalityproblem |