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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Vydáno v:Abstract and Applied Analysis Ročník 2013; číslo 2013; s. 904 - 913-795
Hlavní autoři: Qinghai, He, Kong, Weili
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cairo, Egypt Hindawi Limiteds 01.01.2013
Hindawi Puplishing Corporation
Hindawi Publishing Corporation
John Wiley & Sons, Inc
Wiley
Témata:
Banach spaces
Decision theory
Game theory
Heuristic
Mathematical optimization
Mathematical research
Optimization
Pareto efficiency
Polyhedra
ISSN:1085-3375, 1687-0409
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1085-3375
1687-0409
DOI:10.1155/2013/619206