ϵ-Henig Saddle Points and Duality of Set-Valued Optimization Problems in Real Linear Spaces
We study ϵ-Henig saddle points and duality of set-valued optimization problems in the setting of real linear spaces. Firstly, an equivalent characterization of ϵ-Henig saddle point of the Lagrangian set-valued map is obtained. Secondly, under the assumption of the generalized cone subconvexlikeness...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2013/403642 |
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| _version_ | 1832555336272183296 |
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| author | Zhi-Ang Zhou |
| author_facet | Zhi-Ang Zhou |
| author_sort | Zhi-Ang Zhou |
| collection | DOAJ |
| description | We study ϵ-Henig saddle points and duality of set-valued optimization problems in the setting of real linear spaces. Firstly, an equivalent characterization of ϵ-Henig saddle point of the Lagrangian set-valued map is obtained. Secondly, under the assumption of the generalized cone subconvexlikeness of set-valued maps, the relationship between the ϵ-Henig saddle point of the Lagrangian set-valued map and the ϵ-Henig properly efficient element of the set-valued optimization problem is presented. Finally, some duality theorems are given. |
| format | Article |
| id | doaj-art-43c9f1ff3d404988a0a12b3a55c93067 |
| institution | Kabale University |
| issn | 1537-744X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-43c9f1ff3d404988a0a12b3a55c930672025-02-03T05:48:28ZengWileyThe Scientific World Journal1537-744X2013-01-01201310.1155/2013/403642403642ϵ-Henig Saddle Points and Duality of Set-Valued Optimization Problems in Real Linear SpacesZhi-Ang Zhou0College of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, ChinaWe study ϵ-Henig saddle points and duality of set-valued optimization problems in the setting of real linear spaces. Firstly, an equivalent characterization of ϵ-Henig saddle point of the Lagrangian set-valued map is obtained. Secondly, under the assumption of the generalized cone subconvexlikeness of set-valued maps, the relationship between the ϵ-Henig saddle point of the Lagrangian set-valued map and the ϵ-Henig properly efficient element of the set-valued optimization problem is presented. Finally, some duality theorems are given.http://dx.doi.org/10.1155/2013/403642 |
| spellingShingle | Zhi-Ang Zhou ϵ-Henig Saddle Points and Duality of Set-Valued Optimization Problems in Real Linear Spaces The Scientific World Journal |
| title | ϵ-Henig Saddle Points and Duality of Set-Valued Optimization Problems in Real Linear Spaces |
| title_full | ϵ-Henig Saddle Points and Duality of Set-Valued Optimization Problems in Real Linear Spaces |
| title_fullStr | ϵ-Henig Saddle Points and Duality of Set-Valued Optimization Problems in Real Linear Spaces |
| title_full_unstemmed | ϵ-Henig Saddle Points and Duality of Set-Valued Optimization Problems in Real Linear Spaces |
| title_short | ϵ-Henig Saddle Points and Duality of Set-Valued Optimization Problems in Real Linear Spaces |
| title_sort | ϵ henig saddle points and duality of set valued optimization problems in real linear spaces |
| url | http://dx.doi.org/10.1155/2013/403642 |
| work_keys_str_mv | AT zhiangzhou ehenigsaddlepointsanddualityofsetvaluedoptimizationproblemsinreallinearspaces |