The minisum location problem is well-known and had extensively been studied in the case of the unknown location being situated somewhere in the plane.
Also the accompanying Weiszfeld iteration [3] is nowadays well understood, even for noneuclidean distances [2,3]. We introduce
as a side condition that the unknown optimal location point may only lie on some given curve in the plane. For a piece at a straight line and for a circle numerical methods are developed and numerical examples got by them are given
