# Distance between a polytope and a point

How to calculate the distance between a convex polytope and a point?
Polytope is specified as the solution to the system of linear inequalities.

I'm looking for the method that is computationally efficient.

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Have you considered the methods described at en.wikipedia.org/wiki/Quadratic_programming ? – Mariano Suárez-Alvarez Feb 25 '11 at 15:08
Correct me if I'm wrong. Using QD I can find a point from the polytope which is the closest one to the given point. If this polytope is given by a system of linear equalities then I can use Lagrange Multiplier with multiple constraints to solve QD and this can be done by solving linear system of equations with $n+m$ variables. The complexity of this method is $O((n+m)^{3})$ – Tomek Tarczynski Feb 25 '11 at 17:58
Of course instead of QD I should write QP... – Tomek Tarczynski Feb 25 '11 at 18:04