Finding the closest point to a sets of discrete points
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.