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
Schlagworte:
Analysis
Mathematics
Mathematics and Statistics
Optimization
90C30
49J53
Pareto solution
90C29
Weak Pareto solution
Banach space
Vector optimization
ISSN:1877-0533, 1572-932X, 1877-0541
Online-Zugang:Volltext
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Beschreibung
Zusammenfassung: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.
ISSN:1877-0533
1572-932X
1877-0541
DOI:10.1007/s11228-009-0120-5