Use of projective coordinate descent in the Fekete problem

The problem of minimizing the energy of a system of $N$ points on a sphere in $\mathbb{R}^3$, interacting with the potential $U=\frac1{{r}^{s}}$, $s>0$ , where $r$ is the Euclidean distance between a pair of points, is considered. A method of projective coordinate descent using a fast calculation of the function and the gradient, as well as a second-order coordinate descent method that rapidly approaches the minimum values known from the literature is proposed.