Locating an undesirable facility by generalized cutting planes

We address the problem of locating an undesirable facility within a compact set by minimizing a strictly decreasing boundedly lower subdifferentiable function of the squared Euclidean distances to a set of fixed points. Using (generalized) cutting planes, the resolution of this problem is reduced to solving a sequence of maxmin problems. These maxmin problems have a clear geometrical interpretation, which enables to solve them sequentially by means of an on-line enumeration of the vertices of polyhedra in higher dimensions.