In a n-dimensional space, I want to divide a set of m points into v (non-empty) subsets. I want to minimize the sum of the pairwise Euclidean distances between the centroids of the resulting subsets.

It seems to me that this is related to K-mean clustering but that in this case, I want the resulting centroids to be as close as possible from each other.

What is the correct name for this problem ? Is there a known algorithm to solve it (excluding brute force) ?