Suppose there is a set of points $V$ lives on surface of a 2-sphere $V \subset S^2$. One common distance between two points is the haversine distance or great circle distance $d: S^2\times S^2 \to \mathbb{R}$.
And I can define a optimization version of median by $m^* = \textbf{argmin}_{m \in S^2} \sum_{i \in V} |d(i, m)|$. Here $|.|$ is the absolute value.
And my question is how can one efficiently find the $m^*$ given $V$ ?