The convex ordered median problem is a generalization of the median, the k‐centrum or the center problem. The task of the associated inverse problem is to change edge lengths at minimum cost such that a given vertex becomes an optimal solution of the location problem, i.e., an ordered median. It is shown that the problem is NP‐hard even if the underlying network is a tree and the ordered median problem is convex and either the vertex weights are all equal to 1 or the underlying problem is the k‐centrum problem. For the special case of the inverse unit weight k‐centrum problem a polynomial time algorithm is developed.
