Minimal energy problems with Riesz potentials

    The sequence of greedy minimizers is constructed recursively, as follows: when $N-1$ points $\{x_1, \ldots, x_{N-1}\}$ have been constructed, $x_N$ is chosen as a point minimizing the potential $$ U_\phi(y) = \sum_1^{N-1} \phi(\|y-x_i\|) $$ over all $y$ in the underlying set. The choice of several initial points can be made randomly, or by some convenient rule. Some interesting underlying sets: spheres, intervals.