Two Regularization Methods for the Variational Inequality Problem over the Set of Solutions of the Generalized Mixed Equilibrium Problem
In this work, we consider bilevel problems: variational inequality problems over the set of solutions of the generalized mixed equilibrium problems. Two new inertial extragradient methods are proposed for solving these problems. Under appropriate conditions, we prove strong convergence theorems for...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/16/2981 |
| _version_ | 1797431980061622272 |
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| author | Yanlai Song Omar Bazighifan |
| author_facet | Yanlai Song Omar Bazighifan |
| author_sort | Yanlai Song |
| collection | DOAJ |
| description | In this work, we consider bilevel problems: variational inequality problems over the set of solutions of the generalized mixed equilibrium problems. Two new inertial extragradient methods are proposed for solving these problems. Under appropriate conditions, we prove strong convergence theorems for the proposed methods by the regularization technique. Finally, some numerical examples are provided to show the efficiency of the proposed algorithms. |
| first_indexed | 2024-03-09T09:53:11Z |
| format | Article |
| id | doaj.art-b82070397a804d02881f0f5c0e3be45b |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T09:53:11Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-b82070397a804d02881f0f5c0e3be45b2023-12-01T23:58:00ZengMDPI AGMathematics2227-73902022-08-011016298110.3390/math10162981Two Regularization Methods for the Variational Inequality Problem over the Set of Solutions of the Generalized Mixed Equilibrium ProblemYanlai Song0Omar Bazighifan1College of Science, Zhongyuan University of Technology, Zhengzhou 450007, ChinaSection of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, ItalyIn this work, we consider bilevel problems: variational inequality problems over the set of solutions of the generalized mixed equilibrium problems. Two new inertial extragradient methods are proposed for solving these problems. Under appropriate conditions, we prove strong convergence theorems for the proposed methods by the regularization technique. Finally, some numerical examples are provided to show the efficiency of the proposed algorithms.https://www.mdpi.com/2227-7390/10/16/2981Hilbert spacestrong convergencemonotone operatorregularization methodTseng’s extragradient method |
| spellingShingle | Yanlai Song Omar Bazighifan Two Regularization Methods for the Variational Inequality Problem over the Set of Solutions of the Generalized Mixed Equilibrium Problem Mathematics Hilbert space strong convergence monotone operator regularization method Tseng’s extragradient method |
| title | Two Regularization Methods for the Variational Inequality Problem over the Set of Solutions of the Generalized Mixed Equilibrium Problem |
| title_full | Two Regularization Methods for the Variational Inequality Problem over the Set of Solutions of the Generalized Mixed Equilibrium Problem |
| title_fullStr | Two Regularization Methods for the Variational Inequality Problem over the Set of Solutions of the Generalized Mixed Equilibrium Problem |
| title_full_unstemmed | Two Regularization Methods for the Variational Inequality Problem over the Set of Solutions of the Generalized Mixed Equilibrium Problem |
| title_short | Two Regularization Methods for the Variational Inequality Problem over the Set of Solutions of the Generalized Mixed Equilibrium Problem |
| title_sort | two regularization methods for the variational inequality problem over the set of solutions of the generalized mixed equilibrium problem |
| topic | Hilbert space strong convergence monotone operator regularization method Tseng’s extragradient method |
| url | https://www.mdpi.com/2227-7390/10/16/2981 |
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