Generalized AOR Method for Solving Absolute Complementarity Problems
We introduce and consider a new class of complementarity problems, which is called the absolute value complementarity problem. We establish the equivalence between the absolute complementarity problems and the fixed point problem using the projection operator. This alternative equivalent formulation...
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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/10.1155/2012/743861 |
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| _version_ | 1832561961104048128 |
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| author | Muhammad Aslam Noor Javed Iqbal Khalida Inayat Noor E. Al-Said |
| author_facet | Muhammad Aslam Noor Javed Iqbal Khalida Inayat Noor E. Al-Said |
| author_sort | Muhammad Aslam Noor |
| collection | DOAJ |
| description | We introduce and consider a new class of complementarity problems, which is called the absolute value complementarity problem. We establish the equivalence between the absolute complementarity problems and the fixed point problem using the projection operator. This alternative equivalent formulation is used to discuss the existence of a solution of the absolute value complementarity problem. A generalized AOR method is suggested and analyzed for solving the absolute the complementarity problems. We discuss the convergence of generalized AOR method for the L-matrix. Several examples are given to illustrate the implementation and efficiency of the method. Results are very encouraging and may stimulate further research in this direction. |
| format | Article |
| id | doaj-art-19044080003f487a86b763cf4013cfdd |
| 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-19044080003f487a86b763cf4013cfdd2025-02-03T01:23:44ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/743861743861Generalized AOR Method for Solving Absolute Complementarity ProblemsMuhammad Aslam Noor0Javed Iqbal1Khalida Inayat Noor2E. Al-Said3Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Chak Shahzad, Islamabad 44000, PakistanDepartment of Mathematics, COMSATS Institute of Information Technology, Park Road, Chak Shahzad, Islamabad 44000, PakistanDepartment of Mathematics, COMSATS Institute of Information Technology, Park Road, Chak Shahzad, Islamabad 44000, PakistanMathematics Department, College of Science, King Saud University, Riyadh 11451, Saudi ArabiaWe introduce and consider a new class of complementarity problems, which is called the absolute value complementarity problem. We establish the equivalence between the absolute complementarity problems and the fixed point problem using the projection operator. This alternative equivalent formulation is used to discuss the existence of a solution of the absolute value complementarity problem. A generalized AOR method is suggested and analyzed for solving the absolute the complementarity problems. We discuss the convergence of generalized AOR method for the L-matrix. Several examples are given to illustrate the implementation and efficiency of the method. Results are very encouraging and may stimulate further research in this direction.http://dx.doi.org/10.1155/2012/743861 |
| spellingShingle | Muhammad Aslam Noor Javed Iqbal Khalida Inayat Noor E. Al-Said Generalized AOR Method for Solving Absolute Complementarity Problems Journal of Applied Mathematics |
| title | Generalized AOR Method for Solving Absolute Complementarity Problems |
| title_full | Generalized AOR Method for Solving Absolute Complementarity Problems |
| title_fullStr | Generalized AOR Method for Solving Absolute Complementarity Problems |
| title_full_unstemmed | Generalized AOR Method for Solving Absolute Complementarity Problems |
| title_short | Generalized AOR Method for Solving Absolute Complementarity Problems |
| title_sort | generalized aor method for solving absolute complementarity problems |
| url | http://dx.doi.org/10.1155/2012/743861 |
| work_keys_str_mv | AT muhammadaslamnoor generalizedaormethodforsolvingabsolutecomplementarityproblems AT javediqbal generalizedaormethodforsolvingabsolutecomplementarityproblems AT khalidainayatnoor generalizedaormethodforsolvingabsolutecomplementarityproblems AT ealsaid generalizedaormethodforsolvingabsolutecomplementarityproblems |