New Double Projection Algorithm for Solving Variational Inequalities
We propose a class of new double projection algorithms for solving variational inequality problem, which can be viewed as a framework of the method of Solodov and Svaiter by adopting a class of new hyperplanes. By the separation property of hyperplane, our method is proved to be globally convergent...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/714397 |
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| _version_ | 1832560998710509568 |
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| author | Lian Zheng |
| author_facet | Lian Zheng |
| author_sort | Lian Zheng |
| collection | DOAJ |
| description | We propose a class of new double projection algorithms for solving variational inequality problem, which can be viewed as a framework of the method of Solodov and Svaiter by adopting a class of new hyperplanes. By the separation property of hyperplane, our method is proved to be globally convergent under very mild assumptions. In addition, we propose a modified version of our algorithm that finds a solution of variational inequality which is also a fixed point of a given nonexpansive mapping. If, in addition, a certain local error bound holds, we analyze the convergence rate of the iterative sequence. Numerical experiments prove that our algorithms are efficient. |
| format | Article |
| id | doaj-art-1a164de8feb442fd90b8bde9d006d3fd |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-1a164de8feb442fd90b8bde9d006d3fd2025-02-03T01:26:12ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/714397714397New Double Projection Algorithm for Solving Variational InequalitiesLian Zheng0Department of Mathematics and Computer Science, Yangtze Normal University, Fuling, Chongqing 408100, ChinaWe propose a class of new double projection algorithms for solving variational inequality problem, which can be viewed as a framework of the method of Solodov and Svaiter by adopting a class of new hyperplanes. By the separation property of hyperplane, our method is proved to be globally convergent under very mild assumptions. In addition, we propose a modified version of our algorithm that finds a solution of variational inequality which is also a fixed point of a given nonexpansive mapping. If, in addition, a certain local error bound holds, we analyze the convergence rate of the iterative sequence. Numerical experiments prove that our algorithms are efficient.http://dx.doi.org/10.1155/2013/714397 |
| spellingShingle | Lian Zheng New Double Projection Algorithm for Solving Variational Inequalities Journal of Applied Mathematics |
| title | New Double Projection Algorithm for Solving Variational Inequalities |
| title_full | New Double Projection Algorithm for Solving Variational Inequalities |
| title_fullStr | New Double Projection Algorithm for Solving Variational Inequalities |
| title_full_unstemmed | New Double Projection Algorithm for Solving Variational Inequalities |
| title_short | New Double Projection Algorithm for Solving Variational Inequalities |
| title_sort | new double projection algorithm for solving variational inequalities |
| url | http://dx.doi.org/10.1155/2013/714397 |
| work_keys_str_mv | AT lianzheng newdoubleprojectionalgorithmforsolvingvariationalinequalities |