The general one center location problem deals with the location of a point in a real normed space X in order to minimize an objective function G which depends on the distances to a finite number of centers and on initial costs. The function G is defined by G(x) = γ(c1+w1‖x–a1‖,…,cn+wn‖x–an‖), where a1…,an are n given points in X, w1,…,wn are positive numbers, c1…,c1 are nonnegative initial costs and γ is a monotone norm on ℝn. A geometrical description of the set of optimal solutions to the problem minx∈XG(x) is provided. The peculiar role of the minisum problem, where γ is the l1-norm, is emphasized and the minimax problem, where γ is the lx-norm, is used to illustrate the general geometrical description.
