Efficiency in constrained continuous location

We present a geometrical characterization of the efficient, weakly efficient and strictly efficient points for multiobjective location problems in presence of convex constraints and when distances are measured by an arbitrary norm. These results, established for a compact set of demand points, generalize similar characterizations previously obtained for unconstrained problems. They are used to show that, in planar problems, the set of constrained weakly efficient points always coincides with the closest projection of the set of unconstrained weakly efficient points onto the feasible set. This projection property which is known previously only for strictly convex norms, allows us easily construct all the weakly efficient points and provides a useful localization property for efficient and strictly efficient points.