Contractibility of the efficient set in strictly quasiconcave vector maximization
type: Item
instance of: scholarly article
title: Contractibility of the efficient set in strictly quasiconcave vector maximization
zbMATH Open document ID: 1009.90101
DOI: 10.1023/A:1017527329601
author: R. Smith
published in: Journal of Optimization Theory and Applications
publication date: 2002-08-12T00:00:00Z
review text: \textit{E. J. Sun} [ibid. 89, 475-481 (1996; Zbl 0851.90108)] has shown that the efficient set of a vector maximization problem with convex compact feasible set and any finite number of continuous strictly quasiconcave objective functions, at least one of which is strongly quasiconcave, is connected. In this paper it is shown that, under the same assumptions, the Pareto set is contractible. Even though the given proof cannot be extended to the general case where all objective functions are continuous and strictly quasiconcave, it is conjectured that the Pareto set is contractible also in this case.
reviewed by: Kathrin Klamroth
Mathematics Subject Classification ID: 90C29
zbMATH DE Number: 1779067
zbMATH Keywords: vector optimization
zbMATH Keywords: connectedness
zbMATH Keywords: contractability
MaRDI profile type: Publication
cites work: On the connectedness of the efficient set for strictly quasiconvex vector minimization problems
cites work: Q3710333
cites work: Connectedness of the efficient set for three-objective quasiconcave maximization problems
cites work: Connectedness of the efficient set in strictly quasiconcave vector maximization
cites work: Connectedness of the efficient solution sets for a strictly path quasiconvex programming problem
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cites work: The structure of the efficient frontier of finite-dimensional completely-shaded sets
full work available at URL: a:1017527329601
OpenAlex ID: W28695241
description: scientific article; zbMATH DE number 1779067