Searching for critical angles in a convex cone
Alberto Seeger | Iusem, Alfredo N.
Convex cones | critical angles
The concept of antipodality related to a convex cone in a finite dimensional space has been explored in detail in a recent work of ours. The antipodality problem consists of finding a pair of unit vectors in K achieving the maximal angle of the cone. Our attention is now focused not just in the maximal angle, but in the angular specterum of the cone, consisting of all the angles satisfying the stationarity condition associated to the maximization problem of determining the maximal angle. In the case of a polyhedral cone, the angular spectrum is finite.Among other results, we obtain an upper bound for the cardinality of the spectrum of a polyhedral cone. We also discuss the link between the angular spectrum of K and that of the positive polar cone of K.