On the connectedness of the set of weakly efficient points of a vector optimization problem in locally convex spaces
type: Item
instance of: scholarly article
title: On the connectedness of the set of weakly efficient points of a vector optimization problem in locally convex spaces
zbMATH Open document ID: 0674.90090
DOI: 10.1007/BF01102345
published in: Journal of Optimization Theory and Applications
publication date: 1990-01-01T00:00:00Z
review text: In vector optimization, topological properties of the set of efficient and weak efficient points are of interest. We study the connectedness of the set \(E^ w\) of all weakly efficient points of a subset Z of a locally convex space X with respect to a continuous mapping p: \(X\to Y\), Y locally convex and partially ordered by a closed, convex cone with nonempty interior. Under the general assumptions that Z is convex and closed and that p is a pointwise quasiconvex mapping (i.e., a generalizd quasiconvex concept), the set \(E^ w\) is connected, if the lower level- sets of p are compact. Furthermore, we show some connectedness results on the efficient points and the efficient and weakly efficient outcomes. The considerations of this paper extend the previous results of \textit{E. U. Choo} and \textit{D. R. Atkis} [ibid. 36, 203-220 (1982; Zbl 0452.90076); Manage Sci. 29, 250-255 (1983; Zbl 0519.90082)] and \textit{A. R. Warburton} [J. Optimization Theory Appl. 40, 537-557 (1983; Zbl 0496.90073)]. Moreover, some examples in vector approximation are given.
Mathematics Subject Classification ID: 90C31
Mathematics Subject Classification ID: 90C48
Mathematics Subject Classification ID: 26B25
zbMATH DE Number: 4104738
zbMATH Keywords: generalized convex mappings
zbMATH Keywords: vector optimization
zbMATH Keywords: weak efficient points
zbMATH Keywords: locally convex space
zbMATH Keywords: closed convex cone
zbMATH Keywords: pointwise quasiconvex mapping
zbMATH Keywords: lower level-sets
zbMATH Keywords: connectedness results
zbMATH Keywords: vector approximation
author: Siegfried Helbig
reviewed by: Siegfried Helbig
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4104738