Inertial projection and contraction algorithms for variational inequalities
In this article, we introduce an inertial projection and contraction algorithm by combining inertial type algorithms with the projection and contraction algorithm for solving a variational inequality in a Hilbert space H . In addition, we propose a modified version of our algorithm to find a common...
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| Published in | Journal of global optimization Vol. 70; no. 3; pp. 687 - 704 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.03.2018
Springer Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
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| Abstract | In this article, we introduce an inertial projection and contraction algorithm by combining inertial type algorithms with the projection and contraction algorithm for solving a variational inequality in a Hilbert space
H
. In addition, we propose a modified version of our algorithm to find a common element of the set of solutions of a variational inequality and the set of fixed points of a nonexpansive mapping in
H
. We establish weak convergence theorems for both proposed algorithms. Finally, we give the numerical experiments to show the efficiency and advantage of the inertial projection and contraction algorithm. |
|---|---|
| AbstractList | In this article, we introduce an inertial projection and contraction algorithm by combining inertial type algorithms with the projection and contraction algorithm for solving a variational inequality in a Hilbert space H. In addition, we propose a modified version of our algorithm to find a common element of the set of solutions of a variational inequality and the set of fixed points of a nonexpansive mapping in H. We establish weak convergence theorems for both proposed algorithms. Finally, we give the numerical experiments to show the efficiency and advantage of the inertial projection and contraction algorithm. In this article, we introduce an inertial projection and contraction algorithm by combining inertial type algorithms with the projection and contraction algorithm for solving a variational inequality in a Hilbert space H . In addition, we propose a modified version of our algorithm to find a common element of the set of solutions of a variational inequality and the set of fixed points of a nonexpansive mapping in H . We establish weak convergence theorems for both proposed algorithms. Finally, we give the numerical experiments to show the efficiency and advantage of the inertial projection and contraction algorithm. |
| Audience | Academic |
| Author | Cho, Y. J. Zhong, L. L. Dong, Q. L. Rassias, Th. M. |
| Author_xml | – sequence: 1 givenname: Q. L. surname: Dong fullname: Dong, Q. L. organization: College of Science, Civil Aviation University of China, Tianjin Key Lab for Advanced Signal Processing, Civil Aviation University of China – sequence: 2 givenname: Y. J. surname: Cho fullname: Cho, Y. J. email: yjcho@gnu.ac.kr organization: Department of Mathematics Education and RINS, Gyeongsang National University, Center for General Education, China Medical University – sequence: 3 givenname: L. L. surname: Zhong fullname: Zhong, L. L. organization: Tianjin Key Lab for Advanced Signal Processing, Civil Aviation University of China – sequence: 4 givenname: Th. M. surname: Rassias fullname: Rassias, Th. M. organization: Department of Mathematics, National Technical University of Athens |
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| Copyright | Springer Science+Business Media New York 2017 COPYRIGHT 2018 Springer Journal of Global Optimization is a copyright of Springer, (2017). All Rights Reserved. |
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| SubjectTerms | Algorithms Computer Science Fixed points (mathematics) Hilbert space Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Portfolio management Projection Real Functions Signal processing |
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| Title | Inertial projection and contraction algorithms for variational inequalities |
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