Solution of location problems with radial cost functions

The solution of the Cooper location problem min {A figure is presented} where r_i is the radial (Euclidean) distance between the ith given location (a_i, b_i and the center (x, y) to be located is further investigated. The iterative mehtod given by Cooper (which includes the well known Weiszfeld procedure for n = 1) was previously amended using semi-intuitive arguments. In the present work a better proof is offered for the results given before. Furthermore, using the same line of argument, a broader group of problems previously mentioned by Katz and others can be efficiently solved. These are the problems min {A figure is presented} where ψ_i are non-decreasing functions of the Euclidean distances. The method is also extended to solve similar problems in E^K with K> 2. Apart from the theoretical account, computational experience is reported for the three dimensional Cooper problem with differet values of n. Computational results of the min {A figure is presented} which is a different member of the Katz class of problems, are also presented.