A recursive algorithm for finding the minimum norm point in a polytope and a pair of closest points in two polytopes

For a given pair of finite point set P and Q in some Euclidean space the authors consider two problems: Problem 1 of finding the minimum Euclidean norm point in the convex hull of P and Problem 2 of finding a minimum Euclidean distance pair of points in the convex hulls of P and Q. They propose a finite recursive algorithm for these problems. The algorithm is not based on the simplicial decomposition of convex sets and does not require to solve systems of linear equations.