Optimality and Duality for Multiobjective Fractional Programming Involving Nonsmooth Generalized (ℱ,b,ϕ,ρ,θ)-Univex Functions
We establish properly efficient necessary and sufficient optimality conditions for multiobjective fractional programming involving nonsmooth generalized (ℱ,b,ϕ,ρ,θ)-univex functions. Utilizing the necessary optimality conditions, we formulate the parametric dual model and establish some duality resu...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2013/284046 |
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| _version_ | 1832550752475676672 |
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| author | Jen-Chwan Liu Chun-Yu Liu |
| author_facet | Jen-Chwan Liu Chun-Yu Liu |
| author_sort | Jen-Chwan Liu |
| collection | DOAJ |
| description | We establish properly efficient necessary and sufficient optimality conditions for multiobjective fractional programming involving nonsmooth generalized (ℱ,b,ϕ,ρ,θ)-univex functions. Utilizing the necessary optimality conditions, we formulate the parametric dual model and establish some duality results in the framework of generalized (ℱ,b,ϕ,ρ,θ)-univex functions. |
| format | Article |
| id | doaj-art-40d11bbc98654d699d7b5848d07ec99c |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-40d11bbc98654d699d7b5848d07ec99c2025-02-03T06:05:55ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252013-01-01201310.1155/2013/284046284046Optimality and Duality for Multiobjective Fractional Programming Involving Nonsmooth Generalized (ℱ,b,ϕ,ρ,θ)-Univex FunctionsJen-Chwan Liu0Chun-Yu Liu1Department of Mathematics and Science, National Taiwan Normal University, Linkou Campus, Renai Road, Section 1, Linkou Shiang, Taipei 24499, TaiwanDepartment of Mathematics, National Central University, Zhongli, Taoyuan, TaiwanWe establish properly efficient necessary and sufficient optimality conditions for multiobjective fractional programming involving nonsmooth generalized (ℱ,b,ϕ,ρ,θ)-univex functions. Utilizing the necessary optimality conditions, we formulate the parametric dual model and establish some duality results in the framework of generalized (ℱ,b,ϕ,ρ,θ)-univex functions.http://dx.doi.org/10.1155/2013/284046 |
| spellingShingle | Jen-Chwan Liu Chun-Yu Liu Optimality and Duality for Multiobjective Fractional Programming Involving Nonsmooth Generalized (ℱ,b,ϕ,ρ,θ)-Univex Functions International Journal of Mathematics and Mathematical Sciences |
| title | Optimality and Duality for Multiobjective Fractional Programming Involving Nonsmooth Generalized (ℱ,b,ϕ,ρ,θ)-Univex Functions |
| title_full | Optimality and Duality for Multiobjective Fractional Programming Involving Nonsmooth Generalized (ℱ,b,ϕ,ρ,θ)-Univex Functions |
| title_fullStr | Optimality and Duality for Multiobjective Fractional Programming Involving Nonsmooth Generalized (ℱ,b,ϕ,ρ,θ)-Univex Functions |
| title_full_unstemmed | Optimality and Duality for Multiobjective Fractional Programming Involving Nonsmooth Generalized (ℱ,b,ϕ,ρ,θ)-Univex Functions |
| title_short | Optimality and Duality for Multiobjective Fractional Programming Involving Nonsmooth Generalized (ℱ,b,ϕ,ρ,θ)-Univex Functions |
| title_sort | optimality and duality for multiobjective fractional programming involving nonsmooth generalized f b ϕ ρ θ univex functions |
| url | http://dx.doi.org/10.1155/2013/284046 |
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