  We present a simple and efficient acceleration technique for an arbitrary
method for computing the Euclidean projection of a point onto a convex
polytope, defined as the convex hull of a finite number of points, in the case
when the number of points in the polytope is much greater than the dimension of
the space. The technique consists in applying any given method to a "small"
subpolytope of the original polytope and gradually shifting it, till the
projection of the given point onto the subpolytope coincides with its
projection onto the original polytope. The results of numerical experiments
demonstrate the high efficiency of the proposed acceleration technique. In
particular, they show that the reduction of computation time increases with an
increase of the number of points in the polytope and is proportional to this
number for some methods. In the second part of the paper, we also discuss a
straightforward extension of the proposed acceleration technique to the case of
arbitrary methods for computing the distance between two convex polytopes,
defined as the convex hulls of finite sets of points.
