Ok, first off, I have never taken linear algebra (still in college) so keep in mind that my only exposure the matrices has been from the lasts days in calc class where they basically say "Oh, and btw, this is a matrix!".

So here is the problem. I have a matrix of weighted points, we can call that M. and a function that given two point coordinates will give the weighted distance (it is a non-euclidean distance measurement). With this data, I need to be able to find a set of points such that for that set size, each point not contained in the set is at a minimum distance to its closest set point.

Right now, I'm just doing a Monte Carlo simulation where I just keep taking random points from the matrix, calculate their average distance, and repeat, saving off the best one. This works, but It would be nice to have an absolute answer (in a relatively short amount of time).

Brute force is out of the question. I could do up to 4 with a brute force approach, after that, with 5 it would take days. (I need to be able to do up to 20 points).

Now here is where the linear algebra comes in. I was told that this problem could be solved using a least squares approach (or a non-linear least squares) However, I am having a tough time actually understand least squares, and also seeing how it would give me the best answer in a relatively short amount of time (Hours of processing power is acceptable, days is not).

So any help would be much appreciated!