6533b7d3fe1ef96bd125fe02
RESEARCH PRODUCT
On Pareto optima, the Fermat-Weber problem, and polyhedral gauges
R. Duriersubject
Fermat's Last TheoremMathematical optimizationHigh Energy Physics::LatticeGeneral MathematicsNumerical analysisPareto principleSubderivativeWeber problemLocation theorySet (abstract data type)High Energy Physics::TheoryMultiobjective programmingSoftwareMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1990-05-01 | Mathematical Programming |