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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 http://en.wikipedia.org/wiki/Quadratic_programming ?2011-02-25
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    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})$2011-02-25
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    Of course instead of QD I should write QP...2011-02-25

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