Proximal Point Methods for Solving Mixed Variational Inequalities on the Hadamard Manifolds
We use the auxiliary principle technique to suggest and analyze a proximal point method for solving the mixed variational inequalities on the Hadamard manifold. It is shown that the convergence of this proximal point method needs only pseudomonotonicity, which is a weaker condition than monotonicity...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/657278 |
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| _version_ | 1849402467318497280 |
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| author | Muhammad Aslam Noor Khalida Inayat Noor |
| author_facet | Muhammad Aslam Noor Khalida Inayat Noor |
| author_sort | Muhammad Aslam Noor |
| collection | DOAJ |
| description | We use the auxiliary principle technique to suggest and analyze a proximal point method for
solving the mixed variational inequalities on the Hadamard manifold. It is shown that the convergence of this proximal point method needs only pseudomonotonicity, which is a weaker condition than monotonicity. Some special cases are also considered. Results can be viewed as refinement and improvement of previously known results. |
| format | Article |
| id | doaj-art-82be05891d9a4018a3fde18094fa16ac |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-82be05891d9a4018a3fde18094fa16ac2025-08-20T03:37:31ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/657278657278Proximal Point Methods for Solving Mixed Variational Inequalities on the Hadamard ManifoldsMuhammad Aslam Noor0Khalida Inayat Noor1Mathematics Department, COMSATS Institute of Information Technology, Islamabad 44000, PakistanMathematics Department, COMSATS Institute of Information Technology, Islamabad 44000, PakistanWe use the auxiliary principle technique to suggest and analyze a proximal point method for solving the mixed variational inequalities on the Hadamard manifold. It is shown that the convergence of this proximal point method needs only pseudomonotonicity, which is a weaker condition than monotonicity. Some special cases are also considered. Results can be viewed as refinement and improvement of previously known results.http://dx.doi.org/10.1155/2012/657278 |
| spellingShingle | Muhammad Aslam Noor Khalida Inayat Noor Proximal Point Methods for Solving Mixed Variational Inequalities on the Hadamard Manifolds Journal of Applied Mathematics |
| title | Proximal Point Methods for Solving Mixed Variational Inequalities on the Hadamard Manifolds |
| title_full | Proximal Point Methods for Solving Mixed Variational Inequalities on the Hadamard Manifolds |
| title_fullStr | Proximal Point Methods for Solving Mixed Variational Inequalities on the Hadamard Manifolds |
| title_full_unstemmed | Proximal Point Methods for Solving Mixed Variational Inequalities on the Hadamard Manifolds |
| title_short | Proximal Point Methods for Solving Mixed Variational Inequalities on the Hadamard Manifolds |
| title_sort | proximal point methods for solving mixed variational inequalities on the hadamard manifolds |
| url | http://dx.doi.org/10.1155/2012/657278 |
| work_keys_str_mv | AT muhammadaslamnoor proximalpointmethodsforsolvingmixedvariationalinequalitiesonthehadamardmanifolds AT khalidainayatnoor proximalpointmethodsforsolvingmixedvariationalinequalitiesonthehadamardmanifolds |