Two continuous location problems are considered, namely the point- objective problem and the Weber problem, with the purpose of locating a new facility with respect to a set of fixed facilities. First, some properties of the set of quasi-efficient points are given for the point- objective problem. Then, by using the Hausdorff distance, the authors prove that the efficient set under a polyhedral (or block) norm tends to the convex hull of the fixed facilities for a sequence of polyhedral norms converging to a round norm.
Secondly, for the Weber problem with polyhedral norms, it is proved that a finite set of intersection points belonging to the convex hull of the fixed facilities always contains an optimal location and that this set tends to the convex hull as previously.