Multiobjective Fractional Programming Involving Generalized Semilocally V-Type I-Preinvex and Related Functions
We study a nonlinear multiple objective fractional programming with inequality constraints where each component of functions occurring in the problem is considered semidifferentiable along its own direction instead of the same direction. New Fritz John type necessary and Karush-Kuhn-Tucker type nece...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2014/496149 |
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| _version_ | 1850106492412231680 |
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| author | Hachem Slimani Shashi Kant Mishra |
| author_facet | Hachem Slimani Shashi Kant Mishra |
| author_sort | Hachem Slimani |
| collection | DOAJ |
| description | We study a nonlinear multiple objective fractional programming with inequality
constraints where each component of functions occurring in the
problem is considered semidifferentiable along its own direction instead of
the same direction. New Fritz John type necessary and Karush-Kuhn-Tucker
type necessary and sufficient efficiency conditions are obtained for a feasible
point to be weakly efficient or efficient. Furthermore, a general Mond-Weir
dual is formulated and weak and strong duality results are proved using
concepts of generalized semilocally V-type I-preinvex functions. This contribution
extends earlier results of Preda
(2003), Mishra et al. (2005), Niculescu
(2007), and Mishra and Rautela (2009), and generalizes results obtained in the literature on
this topic. |
| format | Article |
| id | doaj-art-2e5e366c013541a1b06024da99be1863 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-2e5e366c013541a1b06024da99be18632025-08-20T02:38:49ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252014-01-01201410.1155/2014/496149496149Multiobjective Fractional Programming Involving Generalized Semilocally V-Type I-Preinvex and Related FunctionsHachem Slimani0Shashi Kant Mishra1LaMOS Research Unit, Computer Science Department, University of Bejaia, 06000 Bejaia, AlgeriaDepartment of Mathematics, Faculty of Science, Banaras Hindu University, Varanasi 221005, IndiaWe study a nonlinear multiple objective fractional programming with inequality constraints where each component of functions occurring in the problem is considered semidifferentiable along its own direction instead of the same direction. New Fritz John type necessary and Karush-Kuhn-Tucker type necessary and sufficient efficiency conditions are obtained for a feasible point to be weakly efficient or efficient. Furthermore, a general Mond-Weir dual is formulated and weak and strong duality results are proved using concepts of generalized semilocally V-type I-preinvex functions. This contribution extends earlier results of Preda (2003), Mishra et al. (2005), Niculescu (2007), and Mishra and Rautela (2009), and generalizes results obtained in the literature on this topic.http://dx.doi.org/10.1155/2014/496149 |
| spellingShingle | Hachem Slimani Shashi Kant Mishra Multiobjective Fractional Programming Involving Generalized Semilocally V-Type I-Preinvex and Related Functions International Journal of Mathematics and Mathematical Sciences |
| title | Multiobjective Fractional Programming Involving Generalized Semilocally V-Type I-Preinvex and Related Functions |
| title_full | Multiobjective Fractional Programming Involving Generalized Semilocally V-Type I-Preinvex and Related Functions |
| title_fullStr | Multiobjective Fractional Programming Involving Generalized Semilocally V-Type I-Preinvex and Related Functions |
| title_full_unstemmed | Multiobjective Fractional Programming Involving Generalized Semilocally V-Type I-Preinvex and Related Functions |
| title_short | Multiobjective Fractional Programming Involving Generalized Semilocally V-Type I-Preinvex and Related Functions |
| title_sort | multiobjective fractional programming involving generalized semilocally v type i preinvex and related functions |
| url | http://dx.doi.org/10.1155/2014/496149 |
| work_keys_str_mv | AT hachemslimani multiobjectivefractionalprogramminginvolvinggeneralizedsemilocallyvtypeipreinvexandrelatedfunctions AT shashikantmishra multiobjectivefractionalprogramminginvolvinggeneralizedsemilocallyvtypeipreinvexandrelatedfunctions |