A modified subgradient extragradient method with non-monotonic step sizes for solving quasimonotone variational inequalities
In this work, we propose a self-adaptive projection method for solving variational inequalities with Lipschitz continuous and quasimonotone mapping (or Lipschitz continuous mapping without monotonicity) in real Hilbert space. Using the technique of double inertial steps into a single projection meth...
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| Published in: | Computational & applied mathematics Vol. 43; no. 4 |
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| Main Authors: | , , , , |
| Format: | Journal Article |
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| Abstract | In this work, we propose a self-adaptive projection method for solving variational inequalities with Lipschitz continuous and quasimonotone mapping (or Lipschitz continuous mapping without monotonicity) in real Hilbert space. Using the technique of double inertial steps into a single projection method, we give weak and strong convergence theorems of the proposed algorithm. The results obtained in this paper extend some recent results in the literature. |
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| AbstractList | In this work, we propose a self-adaptive projection method for solving variational inequalities with Lipschitz continuous and quasimonotone mapping (or Lipschitz continuous mapping without monotonicity) in real Hilbert space. Using the technique of double inertial steps into a single projection method, we give weak and strong convergence theorems of the proposed algorithm. The results obtained in this paper extend some recent results in the literature. |
| ArticleNumber | 198 |
| Author | Dung, Vu Tien Li, Xiao-Huan Van Long, Luong Van Thang, Hoang Thong, Duong Viet |
| Author_xml | – sequence: 1 givenname: Duong Viet orcidid: 0000-0003-1753-7237 surname: Thong fullname: Thong, Duong Viet organization: Faculty of Mathematical Economics, National Economics University – sequence: 2 givenname: Xiao-Huan surname: Li fullname: Li, Xiao-Huan organization: School of Mathematics and Statistics, Shandong University of Technology – sequence: 3 givenname: Vu Tien surname: Dung fullname: Dung, Vu Tien email: duzngvt@gmail.com organization: University of Science, Vietnam National University – sequence: 4 givenname: Hoang orcidid: 0000-0002-8764-3521 surname: Van Thang fullname: Van Thang, Hoang organization: Faculty of Mathematical Economics, National Economics University – sequence: 5 givenname: Luong orcidid: 0000-0003-4991-093X surname: Van Long fullname: Van Long, Luong organization: Faculty of Mathematical Economics, National Economics University |
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| Cites_doi | 10.1007/s10957-010-9650-0 10.1007/s10957-010-9757-3 10.1090/S0002-9904-1967-11761-0 10.1186/s13660-023-02981-7 10.1007/BF00941468 10.1007/s10589-014-9659-7 10.1007/978-1-4419-9467-7 10.1007/s10957-012-0055-0 10.1007/s10898-022-01152-0 10.1007/s10915-021-01751-1 10.1016/j.cam.2023.115099 10.1016/j.ejor.2020.04.035 10.1109/TNN.2006.879774 10.1080/02331934.2018.1522636 10.1007/s00186-022-00780-2 10.1080/02331934.2010.539689 10.1007/s10957-017-1214-0 10.1080/10556788.2010.551536 10.1137/14097238X 10.1007/BF00940531 10.1007/s10589-020-00217-8 10.1007/978-3-642-56886-2 10.1007/s10957-013-0494-2 10.1080/02331934.2016.1271800 10.1023/A:1011253113155 10.1007/s10559-015-9768-z 10.1108/JED-08-2021-0135 10.1007/s10957-018-1351-0 10.1080/02331934.2016.1239266 10.1007/s11081-020-09593-w 10.1007/s11081-022-09713-8 10.1007/s11075-023-01674-y 10.1007/s10898-021-01083-2 10.1080/02331934.2022.2123241 |
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| Keywords | 65K15 47J20 linear convergence rate Quasimonotone mapping 90C25 47H09 Quasimonotone variational inequality Non-monotone mapping Lipschitz continuity |
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| SubjectTerms | Algorithms Applications of Mathematics Computational Mathematics and Numerical Analysis Hilbert space Inequalities Mapping Mathematical Applications in Computer Science Mathematical Applications in the Physical Sciences Mathematics Mathematics and Statistics |
| Title | A modified subgradient extragradient method with non-monotonic step sizes for solving quasimonotone variational inequalities |
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