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.

翻译：我们提出了一种简单高效的加速技术，适用于任意方法在计算点到凸多面体（定义为有限点集的凸包）的欧几里得投影时，特别是当多面体中的点数远大于空间维度的情况。该技术通过将任意给定方法应用于原始多面体的“小”子多面体，并逐步移动该子多面体，直到给定点在子多面体上的投影与其在原始多面体上的投影重合。数值实验结果表明，所提出的加速技术具有高效性。尤其值得注意的是，计算时间的减少随着多面体点数的增加而增大，且对于某些方法，该减少与点数成正比。在论文的第二部分，我们还将该加速技术直接推广至计算两个凸多面体（定义为有限点集的凸包）之间距离的任意方法中。