Location problems with different norms for different points

摘要

Given a finite set A = {a(1),..., a(n)} in a linear space X, we consider two problems. The first problem consists of finding the points minimizing the maximum distance to the points in A; the second problem looks for the points that minimize the average distance to the points in A. In both cases, we assume that the distances at different points are defined asd(x, a(i)) = parallel to x - a(i)parallel to(i), for i = 1,..., n,with norms parallel to.parallel to(i) defined on X. The use of different norms to measure distances from different points allows us to extend some results that hold in the single-norm case, while some strange and rather unexpected facts arise in the general case.