Optimality Conditions and Scalarization of Approximate Quasi Weak Efficient Solutions for Vector Equilibrium Problem
This paper is devoted to the investigation of optimality conditions for approximate quasi weak efficient solutions for a class of vector equilibrium problem (VEP). First, a necessary optimality condition for approximate quasi weak efficient solutions to VEP is established by utilizing the separation...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/1063251 |
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| _version_ | 1832566348095422464 |
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| author | Yameng Zhang Guolin Yu Wenyan Han |
| author_facet | Yameng Zhang Guolin Yu Wenyan Han |
| author_sort | Yameng Zhang |
| collection | DOAJ |
| description | This paper is devoted to the investigation of optimality conditions for approximate quasi weak efficient solutions for a class of vector equilibrium problem (VEP). First, a necessary optimality condition for approximate quasi weak efficient solutions to VEP is established by utilizing the separation theorem with respect to the quasirelative interior of convex sets and the properties of the Clarke subdifferential. Second, the concept of approximate pseudoconvex function is introduced and its existence is verified by a concrete example. Under the assumption of introduced convexity, a sufficient optimality condition for VEP in sense of approximate quasi weak efficiency is also presented. Finally, by using Tammer’s function and the directed distance function, the scalarization theorems of the approximate quasi weak efficient solutions of the VEP are proposed. |
| format | Article |
| id | doaj-art-82f89ef574a14204abdf0d7b1f27ce93 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-82f89ef574a14204abdf0d7b1f27ce932025-02-03T01:04:27ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/10632511063251Optimality Conditions and Scalarization of Approximate Quasi Weak Efficient Solutions for Vector Equilibrium ProblemYameng Zhang0Guolin Yu1Wenyan Han2Institute of Applied Mathematics, North Minzu University, Yinchuan 750021, ChinaInstitute of Applied Mathematics, North Minzu University, Yinchuan 750021, ChinaInstitute of Applied Mathematics, North Minzu University, Yinchuan 750021, ChinaThis paper is devoted to the investigation of optimality conditions for approximate quasi weak efficient solutions for a class of vector equilibrium problem (VEP). First, a necessary optimality condition for approximate quasi weak efficient solutions to VEP is established by utilizing the separation theorem with respect to the quasirelative interior of convex sets and the properties of the Clarke subdifferential. Second, the concept of approximate pseudoconvex function is introduced and its existence is verified by a concrete example. Under the assumption of introduced convexity, a sufficient optimality condition for VEP in sense of approximate quasi weak efficiency is also presented. Finally, by using Tammer’s function and the directed distance function, the scalarization theorems of the approximate quasi weak efficient solutions of the VEP are proposed.http://dx.doi.org/10.1155/2020/1063251 |
| spellingShingle | Yameng Zhang Guolin Yu Wenyan Han Optimality Conditions and Scalarization of Approximate Quasi Weak Efficient Solutions for Vector Equilibrium Problem Complexity |
| title | Optimality Conditions and Scalarization of Approximate Quasi Weak Efficient Solutions for Vector Equilibrium Problem |
| title_full | Optimality Conditions and Scalarization of Approximate Quasi Weak Efficient Solutions for Vector Equilibrium Problem |
| title_fullStr | Optimality Conditions and Scalarization of Approximate Quasi Weak Efficient Solutions for Vector Equilibrium Problem |
| title_full_unstemmed | Optimality Conditions and Scalarization of Approximate Quasi Weak Efficient Solutions for Vector Equilibrium Problem |
| title_short | Optimality Conditions and Scalarization of Approximate Quasi Weak Efficient Solutions for Vector Equilibrium Problem |
| title_sort | optimality conditions and scalarization of approximate quasi weak efficient solutions for vector equilibrium problem |
| url | http://dx.doi.org/10.1155/2020/1063251 |
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