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On Pareto optima, the Fermat-Weber problem, and polyhedral gauges. (English) Zbl 0706.90066

This paper deals with problems of scalarization in vector optimization, in the framework of location theory with respect to objective functions involving polyhedral gauges. A nice concept (namely, the so-called diff- max property) is developed and used to prove that each Pareto optimum is properly efficient (in other words, each Pareto optimum is the solution to a Fermat-Weber problem, with strictly positive coefficients).

This concept is also used to characterize polyhedral gauges. Finally, practical rules are given in order to obtain the whole set of efficient points of a location problem involving polyhedral gauges. However, an efficient implementation of the described procedure does not seem very easy.

Reviewer: P.Loridan

MSC:
90C29Multi-objective programming; goal programming
90B85Continuous location
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