Condition number and eccentricity of a closed convex cone (Q2879607)

The paper is the last part of a~triptych initiated by the authors in [Set-Valued Var. Anal. 18, No. 2, 205--231 (2010; Zbl 1198.46011)] and continued in [Set-Valued Var. Anal. 18, No. 3--4, 483--511 (2010; Zbl 1217.46047)], and is concerned with the condition number of a~closed convex cone in~\(\mathbb R^n\). The condition number refers to the ratio between the circumradius and the inradius. The eccentricity of a~closed convex cone is also examined; this is a~coefficient that measures to which extent the circumcenter differs from the incenter. Some extremality issues concerning inradii and circumradii are discussed.