Modified Inertial Subgradient Extragradient Method with Regularization for Variational Inequality and Null Point Problems
The paper develops a modified inertial subgradient extragradient method to find a solution to the variational inequality problem over the set of common solutions to the variational inequality and null point problems. The proposed method adopts a nonmonotonic stepsize rule without any linesearch proc...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/14/2367 |
| _version_ | 1797433339329642496 |
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| author | Yanlai Song Omar Bazighifan |
| author_facet | Yanlai Song Omar Bazighifan |
| author_sort | Yanlai Song |
| collection | DOAJ |
| description | The paper develops a modified inertial subgradient extragradient method to find a solution to the variational inequality problem over the set of common solutions to the variational inequality and null point problems. The proposed method adopts a nonmonotonic stepsize rule without any linesearch procedure. We describe how to incorporate the regularization technique and the subgradient extragradient method; then, we establish the strong convergence of the proposed method under some appropriate conditions. Several numerical experiments are also provided to verify the efficiency of the introduced method with respect to previous methods. |
| first_indexed | 2024-03-09T10:15:38Z |
| format | Article |
| id | doaj.art-aea0f7f0cfd24dcf9b0b72c1ad3a2ff3 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T10:15:38Z |
| publishDate | 2022-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-aea0f7f0cfd24dcf9b0b72c1ad3a2ff32023-12-01T22:24:22ZengMDPI AGMathematics2227-73902022-07-011014236710.3390/math10142367Modified Inertial Subgradient Extragradient Method with Regularization for Variational Inequality and Null Point ProblemsYanlai Song0Omar Bazighifan1College of Science, Zhongyuan University of Technology, Zhengzhou 450007, ChinaSection of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Rome, ItalyThe paper develops a modified inertial subgradient extragradient method to find a solution to the variational inequality problem over the set of common solutions to the variational inequality and null point problems. The proposed method adopts a nonmonotonic stepsize rule without any linesearch procedure. We describe how to incorporate the regularization technique and the subgradient extragradient method; then, we establish the strong convergence of the proposed method under some appropriate conditions. Several numerical experiments are also provided to verify the efficiency of the introduced method with respect to previous methods.https://www.mdpi.com/2227-7390/10/14/2367Hilbert spacestrong convergenceregularization methodsubgradient extragradient methodmonotone operator |
| spellingShingle | Yanlai Song Omar Bazighifan Modified Inertial Subgradient Extragradient Method with Regularization for Variational Inequality and Null Point Problems Mathematics Hilbert space strong convergence regularization method subgradient extragradient method monotone operator |
| title | Modified Inertial Subgradient Extragradient Method with Regularization for Variational Inequality and Null Point Problems |
| title_full | Modified Inertial Subgradient Extragradient Method with Regularization for Variational Inequality and Null Point Problems |
| title_fullStr | Modified Inertial Subgradient Extragradient Method with Regularization for Variational Inequality and Null Point Problems |
| title_full_unstemmed | Modified Inertial Subgradient Extragradient Method with Regularization for Variational Inequality and Null Point Problems |
| title_short | Modified Inertial Subgradient Extragradient Method with Regularization for Variational Inequality and Null Point Problems |
| title_sort | modified inertial subgradient extragradient method with regularization for variational inequality and null point problems |
| topic | Hilbert space strong convergence regularization method subgradient extragradient method monotone operator |
| url | https://www.mdpi.com/2227-7390/10/14/2367 |
| work_keys_str_mv | AT yanlaisong modifiedinertialsubgradientextragradientmethodwithregularizationforvariationalinequalityandnullpointproblems AT omarbazighifan modifiedinertialsubgradientextragradientmethodwithregularizationforvariationalinequalityandnullpointproblems |