Average distance constants for polygons in spaces with non-positive curvature

Abstract

In this paper we show that the average distance constant of a general polygon which is a subset of an Af-space with non-positive curvature can be expressed as the extreme value of either of two nonlinear programs and discuss the practical application of one of these nonlinear programs for the determination of the average distance constant for a polygon in general, and in particular for a planar triangle.