Numerical Results on Computing the Vector in the Convex Hull of a Finite Set of Points Having Minimal Length

Abstract

In some applications it is necessary to determine the vector x* in the convex hull of a given finite point set having minimal length.

We describe an algorithm solving this problem for point sets in the n—dimensional Euclidean space. The algorithm is divided into two steps. In the first step decides the algorithm whether the origin is contained in the convex hull or not. If the origin is not contained in the convex hull, then x* is an element of the boundary. Thus in the second step the boundary is subdivided into its facets, and the original problem is reduced into a finite number of problems of the same type, each within one dimension less and with a reduced number of points.

Moreover we describe a variation of the second step accelerating the algorithm in many cases.