On destination optimality in asymmetric distance Fermat-Weber problems

This paper introduces skewed norms, i.e. norms perturbed by a linear function, which are useful for modelling asymmetric distance measures. The Fermat-Weber problem with mixed skewed norms is then considered. Using subdifferential calculus we derive exact conditions for a destination point to be optimal, thereby correcting and completing some recent work on asymmetric distance location problems. Finally the classical dominance theorem is generalized to Fermat-Weber problems with a fixed skewed norm.

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