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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Bibliographic Details
Published in:Set-Valued and Variational Analysis Vol. 17; no. 4; pp. 389 - 408
Main Author: Zheng, Xi Yin
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.12.2009
Subjects:
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 Access:Get full text
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Summary: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