Abstract
This paper deals with multiobjective programming in which the objective functions are nonsymmetric distances (derived from different gauges) to the points of a fixed finite subset of ℝn. It emphasizes the case in which the gauges are polyhedral. In this framework the following result is known: if the gauges are polyhedral, then each Pareto optimum is the solution to a Fermat—Weber problem with strictly positive coefficients. We give a new proof of this result, and we show that it is useful in finding the whole set of efficient points of a location problem with polyhedral gauges. Also, we characterize polyhedral gauges in terms of a property of their subdifferential.
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Durier, R. On Pareto optima, the Fermat-Weber problem, and polyhedral gauges. Mathematical Programming 47, 65–79 (1990). https://doi.org/10.1007/BF01580853
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DOI: https://doi.org/10.1007/BF01580853