Given four lines in $3D$ (represented as a couple of points), I want to find the point in space which minimizes the sum of distances between this point and every line.
I'm trying to find a way to formulate this as a problem of Least Square, but I'm not quite sure as to how I should. I'm currently trying to use the definition of distance provided at: http://mathworld.wolfram.com/Point-LineDistance3-Dimensional.html
Any ideas?