Inverse minimax circle location problem with variable coordinates

Traditionally, the minimax circle location problems concern finding a circle C in the plane such that the maximum distance from the given points to the circumference of the circle is minimized. The radius of the circle can be fixed or variable. In this paper we consider the inverse case, that is: a circle C with radius r0 is given and we want to modify the coordinate of existing points with the minimum cost such that the given circle becomes optimal. Mathematical models and some properties of the cases that circle C becomes optimal with comparing to all other circles, and circle C becomes the best circle with comparing to the circles with radius r0 are presented.