Strict Efficiency in Vector Optimization with Nearly Convexlike Set-Valued Maps
The concept of the well posedness for a special scalar problem is linked with strictly efficient solutions of vector optimization problem involving nearly convexlike set-valued maps. Two scalarization theorems and two Lagrange multiplier theorems for strict efficiency in vector optimization involvin...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/570918 |
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| _version_ | 1832556162516516864 |
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| author | Xiaohong Hu Zhimiao Fang Yunxuan Xiong |
| author_facet | Xiaohong Hu Zhimiao Fang Yunxuan Xiong |
| author_sort | Xiaohong Hu |
| collection | DOAJ |
| description | The concept of the well posedness for a special scalar problem is linked with strictly efficient solutions of vector optimization problem involving nearly convexlike set-valued maps. Two scalarization theorems and two Lagrange multiplier theorems for strict efficiency in vector optimization involving nearly convexlike set-valued maps are established. A dual is proposed and duality results are obtained in terms of strictly efficient solutions. A new type of saddle point, called strict saddle point, of an appropriate set-valued Lagrange map is introduced and is used to characterize strict efficiency. |
| format | Article |
| id | doaj-art-d21ecc97709a4aae8ade158c2472fba3 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d21ecc97709a4aae8ade158c2472fba32025-02-03T05:46:14ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/570918570918Strict Efficiency in Vector Optimization with Nearly Convexlike Set-Valued MapsXiaohong Hu0Zhimiao Fang1Yunxuan Xiong2Department of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Chongqing 400065, ChinaChongqing Police College, Chongqing 401331, ChinaBasic Course Department, Nanchang Institute of Science and Technology, Nanchang 330108, ChinaThe concept of the well posedness for a special scalar problem is linked with strictly efficient solutions of vector optimization problem involving nearly convexlike set-valued maps. Two scalarization theorems and two Lagrange multiplier theorems for strict efficiency in vector optimization involving nearly convexlike set-valued maps are established. A dual is proposed and duality results are obtained in terms of strictly efficient solutions. A new type of saddle point, called strict saddle point, of an appropriate set-valued Lagrange map is introduced and is used to characterize strict efficiency.http://dx.doi.org/10.1155/2013/570918 |
| spellingShingle | Xiaohong Hu Zhimiao Fang Yunxuan Xiong Strict Efficiency in Vector Optimization with Nearly Convexlike Set-Valued Maps Abstract and Applied Analysis |
| title | Strict Efficiency in Vector Optimization with Nearly Convexlike Set-Valued Maps |
| title_full | Strict Efficiency in Vector Optimization with Nearly Convexlike Set-Valued Maps |
| title_fullStr | Strict Efficiency in Vector Optimization with Nearly Convexlike Set-Valued Maps |
| title_full_unstemmed | Strict Efficiency in Vector Optimization with Nearly Convexlike Set-Valued Maps |
| title_short | Strict Efficiency in Vector Optimization with Nearly Convexlike Set-Valued Maps |
| title_sort | strict efficiency in vector optimization with nearly convexlike set valued maps |
| url | http://dx.doi.org/10.1155/2013/570918 |
| work_keys_str_mv | AT xiaohonghu strictefficiencyinvectoroptimizationwithnearlyconvexlikesetvaluedmaps AT zhimiaofang strictefficiencyinvectoroptimizationwithnearlyconvexlikesetvaluedmaps AT yunxuanxiong strictefficiencyinvectoroptimizationwithnearlyconvexlikesetvaluedmaps |