A Relaxed Inertial Tseng’s Extragradient Method for Solving Split Variational Inequalities with Multiple Output Sets
Recently, the split inverse problem has received great research attention due to its several applications in diverse fields. In this paper, we study a new class of split inverse problems called the split variational inequality problem with multiple output sets. We propose a new Tseng extragradient m...
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| Format: | Article |
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MDPI AG
2023-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/2/386 |
| _version_ | 1797438981787353088 |
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| author | Timilehin Opeyemi Alakoya Oluwatosin Temitope Mewomo |
| author_facet | Timilehin Opeyemi Alakoya Oluwatosin Temitope Mewomo |
| author_sort | Timilehin Opeyemi Alakoya |
| collection | DOAJ |
| description | Recently, the split inverse problem has received great research attention due to its several applications in diverse fields. In this paper, we study a new class of split inverse problems called the split variational inequality problem with multiple output sets. We propose a new Tseng extragradient method, which uses self-adaptive step sizes for approximating the solution to the problem when the cost operators are pseudomonotone and non-Lipschitz in the framework of Hilbert spaces. We point out that while the cost operators are non-Lipschitz, our proposed method does not involve any linesearch procedure for its implementation. Instead, we employ a more efficient self-adaptive step size technique with known parameters. In addition, we employ the relaxation method and the inertial technique to improve the convergence properties of the algorithm. Moreover, under some mild conditions on the control parameters and without the knowledge of the operators’ norm, we prove that the sequence generated by our proposed method converges strongly to a minimum-norm solution to the problem. Finally, we apply our result to study certain classes of optimization problems, and we present several numerical experiments to demonstrate the applicability of our proposed method. Several of the existing results in the literature in this direction could be viewed as special cases of our results in this study. |
| first_indexed | 2024-03-09T11:46:15Z |
| format | Article |
| id | doaj.art-21ab97e9f09b42569094f5c2c0efc0ba |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T11:46:15Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj.art-21ab97e9f09b42569094f5c2c0efc0ba2023-11-30T23:21:28ZengMDPI AGMathematics2227-73902023-01-0111238610.3390/math11020386A Relaxed Inertial Tseng’s Extragradient Method for Solving Split Variational Inequalities with Multiple Output SetsTimilehin Opeyemi Alakoya0Oluwatosin Temitope Mewomo1School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban 4041, South AfricaSchool of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban 4041, South AfricaRecently, the split inverse problem has received great research attention due to its several applications in diverse fields. In this paper, we study a new class of split inverse problems called the split variational inequality problem with multiple output sets. We propose a new Tseng extragradient method, which uses self-adaptive step sizes for approximating the solution to the problem when the cost operators are pseudomonotone and non-Lipschitz in the framework of Hilbert spaces. We point out that while the cost operators are non-Lipschitz, our proposed method does not involve any linesearch procedure for its implementation. Instead, we employ a more efficient self-adaptive step size technique with known parameters. In addition, we employ the relaxation method and the inertial technique to improve the convergence properties of the algorithm. Moreover, under some mild conditions on the control parameters and without the knowledge of the operators’ norm, we prove that the sequence generated by our proposed method converges strongly to a minimum-norm solution to the problem. Finally, we apply our result to study certain classes of optimization problems, and we present several numerical experiments to demonstrate the applicability of our proposed method. Several of the existing results in the literature in this direction could be viewed as special cases of our results in this study.https://www.mdpi.com/2227-7390/11/2/386split inverse problemsnon-Lipschitz operatorspseudomonotone operatorsTseng’s extragradient methodrelaxation and inertial techniques |
| spellingShingle | Timilehin Opeyemi Alakoya Oluwatosin Temitope Mewomo A Relaxed Inertial Tseng’s Extragradient Method for Solving Split Variational Inequalities with Multiple Output Sets Mathematics split inverse problems non-Lipschitz operators pseudomonotone operators Tseng’s extragradient method relaxation and inertial techniques |
| title | A Relaxed Inertial Tseng’s Extragradient Method for Solving Split Variational Inequalities with Multiple Output Sets |
| title_full | A Relaxed Inertial Tseng’s Extragradient Method for Solving Split Variational Inequalities with Multiple Output Sets |
| title_fullStr | A Relaxed Inertial Tseng’s Extragradient Method for Solving Split Variational Inequalities with Multiple Output Sets |
| title_full_unstemmed | A Relaxed Inertial Tseng’s Extragradient Method for Solving Split Variational Inequalities with Multiple Output Sets |
| title_short | A Relaxed Inertial Tseng’s Extragradient Method for Solving Split Variational Inequalities with Multiple Output Sets |
| title_sort | relaxed inertial tseng s extragradient method for solving split variational inequalities with multiple output sets |
| topic | split inverse problems non-Lipschitz operators pseudomonotone operators Tseng’s extragradient method relaxation and inertial techniques |
| url | https://www.mdpi.com/2227-7390/11/2/386 |
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