In this note we address the problem of determining the point in ℝn that minimizes the variance of its Euclidean distance to a given random vector. This problem may have no global and many local optimal solutions. However, by exploring the behavior of the objective function V at infinity, the search of an ϵ-optimal solution is reduced to a bounded set, within which standard global optimization techniques may be used. Furthermore, we show how to exploit the structure of the problem to obtain sharp bounds in a Branch and Bound scheme, which is crucial when the mere evaluation of V is time-consuming.
