Further Application of H-Differentiability to Generalized Complementarity Problems Based on Generalized Fisher-Burmeister Functions
We study nonsmooth generalized complementarity problems based on the generalized Fisher-Burmeister function and its generalizations, denoted by GCP(f,g) where f and g are H-differentiable. We describe H-differentials of some GCP functions based on the generalized Fisher-Burmeister function and its g...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/468065 |
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| author | Wei-Zhe Gu Mohamed A. Tawhid |
| author_facet | Wei-Zhe Gu Mohamed A. Tawhid |
| author_sort | Wei-Zhe Gu |
| collection | DOAJ |
| description | We study nonsmooth generalized complementarity problems based on the generalized Fisher-Burmeister function and its generalizations, denoted by GCP(f,g) where f and g are H-differentiable. We describe H-differentials of some GCP functions based on the generalized Fisher-Burmeister function and its generalizations, and their merit functions. Under appropriate conditions on the H-differentials of f and g, we show that a local/global minimum of a merit function (or a “stationary point” of a merit function) is coincident with the solution of the given generalized complementarity problem. When specializing GCP(f,g) to the nonlinear complementarity problems, our results not only give new results but also extend/unify various similar results proved for C1, semismooth, and locally Lipschitzian. |
| format | Article |
| id | doaj-art-7e4e6f3be2f34f7d98f9b8453517aa14 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-7e4e6f3be2f34f7d98f9b8453517aa142025-02-03T05:57:49ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/468065468065Further Application of H-Differentiability to Generalized Complementarity Problems Based on Generalized Fisher-Burmeister FunctionsWei-Zhe Gu0Mohamed A. Tawhid1Department of Mathematics, School of Science, Tianjin University, Tianjin 300072, ChinaDepartment of Mathematics and Statistics, Faculty of Science, Thompson Rivers University, Kamloops, BC, V2C 0C8, CanadaWe study nonsmooth generalized complementarity problems based on the generalized Fisher-Burmeister function and its generalizations, denoted by GCP(f,g) where f and g are H-differentiable. We describe H-differentials of some GCP functions based on the generalized Fisher-Burmeister function and its generalizations, and their merit functions. Under appropriate conditions on the H-differentials of f and g, we show that a local/global minimum of a merit function (or a “stationary point” of a merit function) is coincident with the solution of the given generalized complementarity problem. When specializing GCP(f,g) to the nonlinear complementarity problems, our results not only give new results but also extend/unify various similar results proved for C1, semismooth, and locally Lipschitzian.http://dx.doi.org/10.1155/2014/468065 |
| spellingShingle | Wei-Zhe Gu Mohamed A. Tawhid Further Application of H-Differentiability to Generalized Complementarity Problems Based on Generalized Fisher-Burmeister Functions Abstract and Applied Analysis |
| title | Further Application of H-Differentiability to Generalized Complementarity Problems Based on Generalized Fisher-Burmeister Functions |
| title_full | Further Application of H-Differentiability to Generalized Complementarity Problems Based on Generalized Fisher-Burmeister Functions |
| title_fullStr | Further Application of H-Differentiability to Generalized Complementarity Problems Based on Generalized Fisher-Burmeister Functions |
| title_full_unstemmed | Further Application of H-Differentiability to Generalized Complementarity Problems Based on Generalized Fisher-Burmeister Functions |
| title_short | Further Application of H-Differentiability to Generalized Complementarity Problems Based on Generalized Fisher-Burmeister Functions |
| title_sort | further application of h differentiability to generalized complementarity problems based on generalized fisher burmeister functions |
| url | http://dx.doi.org/10.1155/2014/468065 |
| work_keys_str_mv | AT weizhegu furtherapplicationofhdifferentiabilitytogeneralizedcomplementarityproblemsbasedongeneralizedfisherburmeisterfunctions AT mohamedatawhid furtherapplicationofhdifferentiabilitytogeneralizedcomplementarityproblemsbasedongeneralizedfisherburmeisterfunctions |