Condition number and eccentricity of a closed convex cone

Abstract

We discuss some extremality issues concerning the circumradius, the inradius, and the condition number of a closed convex cone in $\mathsf{R}^n$. The condition number refers to the ratio between the circumradius and the inradius. We also study the eccentricity of a closed convex cone, which is a coefficient that measures to which extent the circumcenter differs from the incenter.