Structure of Pareto Solutions of Generalized 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 or the union of finitely many generalized polyhedra. Dropping the compactness assumption, we establish some results on structu...

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Bibliographic Details
Published in:Abstract and Applied Analysis Vol. 2013; no. 2013; pp. 904 - 913-795
Main Authors: Qinghai, He, Kong, Weili
Format: Journal Article
Language:English
Published: Cairo, Egypt Hindawi Limiteds 01.01.2013
Hindawi Puplishing Corporation
Hindawi Publishing Corporation
John Wiley & Sons, Inc
Wiley
Subjects:
Banach spaces
Decision theory
Game theory
Heuristic
Mathematical optimization
Mathematical research
Optimization
Pareto efficiency
Polyhedra
ISSN:1085-3375, 1687-0409
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 or the union of finitely many generalized polyhedra. Dropping the compactness assumption, we establish some results on structure of the weak Pareto solution set, Pareto solution set, weak Pareto optimal value set, and Pareto optimal value set of (SVOP) and on connectedness of Pareto solution set and Pareto optimal value set of (SVOP). In particular, we improved and generalize, Arrow, Barankin, and Blackwell’s classical results in Euclidean spaces and Zheng and Yang’s results in general Banach spaces.
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ISSN:1085-3375
1687-0409
DOI:10.1155/2013/619206