CP-Rays in Simplicial Cones

Abstract

In classical mathematics, interest in the concept of regularity of a triangle, is mainly centered on the property that for every interior point of the triangle, its orthogonal projection on the line containing each side must lie in the relative interior of that side. We generalize the concept of regularity using this property, and extend this work to simplicial cones in R^n, and derive very efficient necessary and sufficient conditions for this property to hold in them. We show that these concepts have important ramifications in algorithmic studies of the linear complementarity problem. We relate our results to other well known properties of square matrices.