The $p$-principal points of a random variable $X$ with finite second moment are those $p$ points in $ℝ$ minimizing the expected squared distance from $X$ to the closest point. Although the determination of principal points involves in general the resolution of a multiextremal optimization problem, existing procedures in the literature provide just a local optimum. In this paper we show that standard Global Optimization techniques can be applied.

The p-principal points of a random variable X with finite second moment are those p points in $ℝ$ minimizing the expected squared distance from X to the closest point. Although the determination of principal points involves in general the resolution of a multiextremal optimization problem, existing procedures in the literature provide just a local optimum. In this paper we show that standard Global Optimization techniques can be applied.