Sets of efficient points in a normed space
type: Item
instance of: scholarly article
title: Sets of efficient points in a normed space
zbMATH Open document ID: 0605.49020
DOI: 10.1016/0022-247X(86)90237-4
author: Roland Durier
author: Christian Michelot
published in: Journal of Mathematical Analysis and Applications
publication date: 1986-01-01T00:00:00Z
review text: The paper deals with efficient solutions of a multiobjective programming problem in a normed space; the objective functions to be minimized are distances to every point of a compact subset. We give a geometrical description of the sets of strictly efficient, efficient and weakly efficient points which looks like a description of the convex hull. It makes use of a family of cones, which play the role of halfspaces in the Euclidean case. Topological properties of these cones are developed. The above description leads to hull and closure properties of sets of efficiency. In addition the two-dimensional case is emphasized in connection with location theory where more precise results are obtained. In particular, when the space is strictly convex or polyhedral, the description of the sets of efficiency provides a geometrical construction of these sets.
Mathematics Subject Classification ID: 49K27
Mathematics Subject Classification ID: 52A07
Mathematics Subject Classification ID: 90C31
Mathematics Subject Classification ID: 46B99
zbMATH DE Number: 3977805
zbMATH Keywords: hull and closure properties
zbMATH Keywords: sets of efficiency
zbMATH Keywords: location theory
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3977805