Pick $n$ points $p_1,\dots, p_n$ in a closed convex planar set $S$ that maximize $\sum_{i,j=1}^n\|p_i-p_j\|^2$.
- Is there a name and/or more general broadly studied formulation of this problem?
- I can get to pretty good and similar solutions via gradient search. Can global optima be found numerically?
- Are optima even known for $S$ a disk? Numerical experiments suggest it the optimum is uniform placement around the boundary.
