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
1. Verfasser: Zheng, Xi Yin
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Dordrecht Springer Netherlands 01.12.2009
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ISSN:1877-0533, 1572-932X, 1877-0541
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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.
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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Keywords 90C30
49J53
Pareto solution
90C29
Weak Pareto solution
Banach space
Vector optimization
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Snippet 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...
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SubjectTerms Analysis
Mathematics
Mathematics and Statistics
Optimization
Title Pareto Solutions of Polyhedral-valued Vector Optimization Problems in Banach Spaces
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Volume 17
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