Computational cost of the Fekete problem I: The Forces Method on the 2-sphere

Here, we study the computational complexity of the Fekete point problem. Namely, we give an exhaustive description of the main properties of an algorithm for the minimization of the logarithmic potential energy on the 2-sphere, and we characterize the probability distribution of the cost of the different minima. In particular, we show that a local minimum can be found with an average cost of about O(N2.8)O(N2.8).