Given a set of $n$ points $v_1,\ldots,v_n$ in $R^d$, find a point $p$ such that $\sum_{i=1}^n w_i d(p,v_i)$ is minimized, where $w_i$ is the weight of $v_i$, which may be positive or negative.
Is there any known result for this problem. It seems the problem has been considered in graphs (one, two). What about in $R^d$ ? Due to the negative weights, the problem is not convex any more.