Arcwise connectedness of closed efficient point sets
type: Item
instance of: scholarly article
title: Arcwise connectedness of closed efficient point sets
zbMATH Open document ID: 0966.90070
author: E. K. Makarov
author: Wen Song
author: N. N. Rachkovskij
published in: Journal of Mathematical Analysis and Applications
publication date: 2000-11-22T00:00:00Z
review text: One of the most important problems of vector optimization is to investigate the structure of efficient point sets. For various applications, the possibility of continuous moving from one optimal solution to any other along optimal alternatives only is of special interest. This possibility is guaranteed if the efficient set is arcwise connected or at least connected. In this paper the authors prove that the efficient point set \(\text{Max} (Q\mid K)\) of a compact convex set \(Q\subset X\) in a Hausdorff topological vector space \(X\) ordered by a closed convex cone \(K\subset X\) is arcwise connected if the set \(\text{Max} (Q\mid K)\) is closed.
reviewed by: Paulo Mbunga
Mathematics Subject Classification ID: 90C29
zbMATH DE Number: 1497250
zbMATH Keywords: arcwise connectedness
zbMATH Keywords: \(F\)-point
zbMATH Keywords: vector optimization
zbMATH Keywords: efficient point sets
MaRDI profile type: Publication
full work available at URL: jmaa.2000.6814
OpenAlex ID: W1979892529
cites work: The structure of admissible points with respect to cone dominance
cites work: Q5341488
cites work: Connectedness of the efficient set for three-objective quasiconcave maximization problems
cites work: Q4848988
cites work: Connectedness of efficient solution sets for set-valued maps in normed spaces
cites work: Connectedness of the efficient solution set of a convex vector optimization in normed spaces
cites work: Connectedness of the efficient set in strictly quasiconcave vector maximization
cites work: Q3701188
cites work: Connectedness of the efficient point sets in quasiconcave vector maximization
cites work: Contractibility of efficient point sets in normed spaces
cites work: Connectedness of the set of nondominated outcomes in multicriteria optimization
cites work: Some results about nondominated solutions
cites work: Q4742579
cites work: Q3710333
cites work: A note on connectivity of efficient solution sets
cites work: Connectivity of efficient solution sets in vector optimization of set-valued mappings
cites work: On the connectivity of efficient point sets
cites work: On the connectedness of the efficient set for strictly quasiconvex vector minimization problems
cites work: Quasiconcave vector maximization: Connectedness of the sets of Pareto- optimal and weak Pareto-optimal alternatives
DOI: 10.1006/JMAA.2000.6814
description: scientific article; zbMATH DE number 1497250