Pareto Solutions of Polyhedral-valued Vector Optimization Problems in Banach Spaces
In general Banach spaces, we consider a vector optimization problem (SVOP) in which the objective is a set-valued mapping whose graph is the union of finitely many polyhedra. We establish some results on structure and connectedness of the weak Pareto solution set, Pareto solution set, weak Pareto op...
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| Veröffentlicht in: | Set-Valued and Variational Analysis Jg. 17; H. 4; S. 389 - 408 |
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01.12.2009
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| Abstract | In general Banach spaces, we consider a vector optimization problem (SVOP) in which the objective is a set-valued mapping whose graph is the union of finitely many polyhedra. We establish some results on structure and connectedness of the weak Pareto solution set, Pareto solution set, weak Pareto optimal value set and Pareto optimal value set of (SVOP). In particular, we improve and generalize Arrow, Barankin and Blackwell’s classical results on linear vector optimization problems in Euclidean spaces. |
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| AbstractList | In general Banach spaces, we consider a vector optimization problem (SVOP) in which the objective is a set-valued mapping whose graph is the union of finitely many polyhedra. We establish some results on structure and connectedness of the weak Pareto solution set, Pareto solution set, weak Pareto optimal value set and Pareto optimal value set of (SVOP). In particular, we improve and generalize Arrow, Barankin and Blackwell’s classical results on linear vector optimization problems in Euclidean spaces. |
| Author | Zheng, Xi Yin |
| Author_xml | – sequence: 1 givenname: Xi Yin surname: Zheng fullname: Zheng, Xi Yin email: xyzheng@ynu.edu.cn organization: Department of Mathematics, Yunnan University |
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| Title | Pareto Solutions of Polyhedral-valued Vector Optimization Problems in Banach Spaces |
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