Modified Inertial Forward–Backward Algorithm in Banach Spaces and Its Application
In this paper, we present a new modified inertial forward–backward algorithm for finding a common solution of the quasi-variational inclusion problem and the variational inequality problem in a <i>q</i>-uniformly smooth Banach space. The proposed algorithm is based on descent, splitting...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/12/1365 |
| _version_ | 1827689868927434752 |
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| author | Yanlai Song Mihai Postolache |
| author_facet | Yanlai Song Mihai Postolache |
| author_sort | Yanlai Song |
| collection | DOAJ |
| description | In this paper, we present a new modified inertial forward–backward algorithm for finding a common solution of the quasi-variational inclusion problem and the variational inequality problem in a <i>q</i>-uniformly smooth Banach space. The proposed algorithm is based on descent, splitting and inertial ideas. Under suitable assumptions, we prove that the sequence generated by the iterative algorithm converges strongly to the unique solution of the abovementioned problems. Numerical examples are also given to demonstrate our results. |
| first_indexed | 2024-03-10T10:27:33Z |
| format | Article |
| id | doaj.art-97c21d7f9a69417e8ae8cdbf21b335cd |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T10:27:33Z |
| publishDate | 2021-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-97c21d7f9a69417e8ae8cdbf21b335cd2023-11-21T23:54:26ZengMDPI AGMathematics2227-73902021-06-01912136510.3390/math9121365Modified Inertial Forward–Backward Algorithm in Banach Spaces and Its ApplicationYanlai Song0Mihai Postolache1College of Science, Zhongyuan University of Technology, Zhengzhou 450007, ChinaDepartment of General Education, China Medical University, Taichung 40402, TaiwanIn this paper, we present a new modified inertial forward–backward algorithm for finding a common solution of the quasi-variational inclusion problem and the variational inequality problem in a <i>q</i>-uniformly smooth Banach space. The proposed algorithm is based on descent, splitting and inertial ideas. Under suitable assumptions, we prove that the sequence generated by the iterative algorithm converges strongly to the unique solution of the abovementioned problems. Numerical examples are also given to demonstrate our results.https://www.mdpi.com/2227-7390/9/12/1365hybrid steepest decent methodforward–backward methodquasi-variational inclusion problemBanach spacevariational inequality problem |
| spellingShingle | Yanlai Song Mihai Postolache Modified Inertial Forward–Backward Algorithm in Banach Spaces and Its Application Mathematics hybrid steepest decent method forward–backward method quasi-variational inclusion problem Banach space variational inequality problem |
| title | Modified Inertial Forward–Backward Algorithm in Banach Spaces and Its Application |
| title_full | Modified Inertial Forward–Backward Algorithm in Banach Spaces and Its Application |
| title_fullStr | Modified Inertial Forward–Backward Algorithm in Banach Spaces and Its Application |
| title_full_unstemmed | Modified Inertial Forward–Backward Algorithm in Banach Spaces and Its Application |
| title_short | Modified Inertial Forward–Backward Algorithm in Banach Spaces and Its Application |
| title_sort | modified inertial forward backward algorithm in banach spaces and its application |
| topic | hybrid steepest decent method forward–backward method quasi-variational inclusion problem Banach space variational inequality problem |
| url | https://www.mdpi.com/2227-7390/9/12/1365 |
| work_keys_str_mv | AT yanlaisong modifiedinertialforwardbackwardalgorithminbanachspacesanditsapplication AT mihaipostolache modifiedinertialforwardbackwardalgorithminbanachspacesanditsapplication |