Finding the closest point to a sets of discrete points In a paper I am reviewing, the authors define the following problem and construct an algorithm. They give no further references and I suspect it has appeared somewhere in the literature before.

Let $P_1,\ldots,P_n$ be sets of points in a space with a metric $d$. Define the distance to a set as 
    $$\operatorname{dist}(x, P_i) = \min\{ d(x,p) \,|\, x \in P_i\}.$$
The problem is to compute
    $$\min_x \sum_{i=1}^n \operatorname{dist}(x, P_i).$$
What is the name of this problem? Has it been discussed in the literature? What if $d(x,P_i) = ||x - P_i||_2?$
It is called p-Median and is known to be NP-hard.
Refer to the following paper for more info: 


  O. Kariv and S. Hakimi, “An Algorithmic Approach to Network Location
  Problems. II: The p-MEDIANS,” SIAM Journal on Applied Mathematics,
  vol. 37, no. 3, pp. 539–560, December 1979.