The single-facility network location problem on general networks is considered in which cost is any nondecreasing convex function of distances. The notion of treelike segment is introduced and is shown to be useful for solving the problem. Namely, the location problem is solved by solving convex subproblems on these treelike segments. Moreover, the algorithm accommodates a wide variety of side constraints. Its complexity for a network of n nodes and m arcs equals $O(mn\sp 2(n+g(n)))$, where g($\cdot)$ is the complexity of evaluating the cost function at one point.
Reviewer: W.Stanczak