On the convergence of a modified algorithm for the spherical facility location problem

We study the spherical facility location problem which is a more realistic model than the Euclidean facilities location. We present a modified algorithm for this problem, whcih has the following good properties: (a) it is very easy to initialize the algorithm with an arbitrary point as its starting point; (b) Under suitable assumptions, it is proved that the algorithm globally converges to a global minimizer of the problem.