A note on "On Pareto optima, the Fermat-Weber problem, and polyhedral gauges"
A note on "On Pareto optima, the Fermat-Weber problem, and polyhedral gauges"
We show by counterexample that one of the results in the paper "On Pareto optima, the FermatWeber problem, and polyhedral gauges", by R. Durier, Mathematical 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.
Fermat, Location theory, Multiobjective programming, Scalarization, Weber problems
435-438
Fliege, Jörg
54978787-a271-4f70-8494-3c701c893d98
1999
Fliege, Jörg
54978787-a271-4f70-8494-3c701c893d98
Fliege, Jörg
(1999)
A note on "On Pareto optima, the Fermat-Weber problem, and polyhedral gauges".
Mathematical Programming, Series B, 84 (2), .
(doi:10.1007/s101070050030).
Abstract
We show by counterexample that one of the results in the paper "On Pareto optima, the FermatWeber problem, and polyhedral gauges", by R. Durier, Mathematical 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.
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Published date: 1999
Keywords:
Fermat, Location theory, Multiobjective programming, Scalarization, Weber problems
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Local EPrints ID: 482539
URI: http://eprints.soton.ac.uk/id/eprint/482539
ISSN: 0025-5610
PURE UUID: 4b786616-732e-42ef-8e0e-f7b492bd6f7c
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Date deposited: 10 Oct 2023 16:48
Last modified: 06 Jun 2024 01:46
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