On Sat, Aug 22, 2009 at 8:17 AM, J.-R. Jiang <jrjiang@csie.ncu.edu.tw> wrote:
Problem: Given n lines, determine a point minimizing the summation of the
distances from the point to the n lines.

This is a Least Absolute Deviations problem, which are normally solved by simplex methods; see the Wikipedia page for more details. If an O(n^3) running time is acceptable to you, however, a minimal solution will always be found at the intersection of two of the lines, so you can just check all the intersection points if you like.

Ben