A note on "On Pareto optima, the Fermat-Weber problem, and polyhedral gauges"

Authors
Fliege, J
Citation
J. Fliege, A note on "On Pareto optima, the Fermat-Weber problem, and polyhedral gauges", MATH PROGR, 84(2), 1999, pp. 435-438
Citations number
5
Categorie Soggetti
Mathematics
Journal title
MATHEMATICAL PROGRAMMING
ISSN journal
00255610 → ACNP
Volume
84
Issue
2
Year of publication
1999
Pages
435 - 438
Database
ISI
SICI code
0025-5610(199902)84:2<435:ANO"PO>2.0.ZU;2-2
Abstract
We show by counterexample that one of the results in the paper "On Pareto o ptima, the Fermat-Weber problem, and polyhedral gauges", by R. Durier, Math ematical Programming 47 (1990), does not hold. The stated characterization of properly efficient points for a scalar location problem is only true in dimension 1 and 2. For higher dimensions, the property stated is necessary, but not sufficient.