Hyperbolicity cones are amenable

Abstract Amenability is a notion of facial exposedness for convex cones that stronger than being facially dual complete (or ‘nice’) which is, in turn, merely exposed. Hyperbolicity are family algebraically structured closed contain all spectrahedral (linear sections positive semidefinite cones) as special cases. It known amenable. We establish hyperbolicity As part the argument, we show any face cone cone. corollary, intersection two cones, not necessarily sharing common relative interior point,