I'm trying to solve the Thomson Problem, i.e we have $N$ repelling point charges on a (hyper)sphere of dimension $m$ and we want to determine which configuration gives the lowest energy.
We thus want to minimize $E=\sum_{i
I want to apply gradient descent to it (as part of a local optimization routien in a genetic algorithm), so I need the gradient of $E$, however $E$ depends on $N$ points, and each point has $m-1$ (hyper)spherical components. How could I calculate $\nabla E$ ?