A modified projection and contraction method for solving a variational inequality problem in Hilbert spaces
In this paper, we proposed a modified projection and contraction method for solving a variational inequality problem in Hilbert spaces. In the existing projection and contraction methods for solving the variational inequality problem, the sequence $ \{\beta_n\} $ has a similar computation manner, wh...
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AIMS Press
2025-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025279 |
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| author | Limei Xue Jianmin Song Shenghua Wang |
| author_facet | Limei Xue Jianmin Song Shenghua Wang |
| author_sort | Limei Xue |
| collection | DOAJ |
| description | In this paper, we proposed a modified projection and contraction method for solving a variational inequality problem in Hilbert spaces. In the existing projection and contraction methods for solving the variational inequality problem, the sequence $ \{\beta_n\} $ has a similar computation manner, which is computed in a self-adaptive manner, but the sequence $ \{\beta_n\} $ in our method is a sequence of numbers in (0, 1) given in advance, which is the main difference of our method with the existing projection and contraction methods. A line search is used to deal with the unknown Lipschitz constant of the mapping. The strong convergence of the proposed method is proved under certain conditions. Finally, some numerical examples are presented to illustrate the effectiveness of our method and compare the computation results with some related methods in the literature. The numerical results show that our method has an obvious competitive advantage compared with the related methods. |
| format | Article |
| id | doaj-art-9df3120b7f8545f3a7a9fe56777cbca1 |
| institution | OA Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-9df3120b7f8545f3a7a9fe56777cbca12025-08-20T02:26:19ZengAIMS PressAIMS Mathematics2473-69882025-03-011036128614310.3934/math.2025279A modified projection and contraction method for solving a variational inequality problem in Hilbert spacesLimei Xue0Jianmin Song1Shenghua Wang2School of Mathematics and Science, Hebei GEO University, Shijiazhuang, 050031, ChinaSchool of Mathematics and Science, Hebei GEO University, Shijiazhuang, 050031, ChinaDepartment of Mathematics and Physics, North China Electric Power University, Baoding 071003, ChinaIn this paper, we proposed a modified projection and contraction method for solving a variational inequality problem in Hilbert spaces. In the existing projection and contraction methods for solving the variational inequality problem, the sequence $ \{\beta_n\} $ has a similar computation manner, which is computed in a self-adaptive manner, but the sequence $ \{\beta_n\} $ in our method is a sequence of numbers in (0, 1) given in advance, which is the main difference of our method with the existing projection and contraction methods. A line search is used to deal with the unknown Lipschitz constant of the mapping. The strong convergence of the proposed method is proved under certain conditions. Finally, some numerical examples are presented to illustrate the effectiveness of our method and compare the computation results with some related methods in the literature. The numerical results show that our method has an obvious competitive advantage compared with the related methods.https://www.aimspress.com/article/doi/10.3934/math.2025279variational inequalityprojection methodgolden ratiohilbert space |
| spellingShingle | Limei Xue Jianmin Song Shenghua Wang A modified projection and contraction method for solving a variational inequality problem in Hilbert spaces AIMS Mathematics variational inequality projection method golden ratio hilbert space |
| title | A modified projection and contraction method for solving a variational inequality problem in Hilbert spaces |
| title_full | A modified projection and contraction method for solving a variational inequality problem in Hilbert spaces |
| title_fullStr | A modified projection and contraction method for solving a variational inequality problem in Hilbert spaces |
| title_full_unstemmed | A modified projection and contraction method for solving a variational inequality problem in Hilbert spaces |
| title_short | A modified projection and contraction method for solving a variational inequality problem in Hilbert spaces |
| title_sort | modified projection and contraction method for solving a variational inequality problem in hilbert spaces |
| topic | variational inequality projection method golden ratio hilbert space |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025279 |
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