Smooth Hyperbolicity Cones are Spectrahedral Shadows
Optimization and Control
2012-08-03 v1 Algebraic Geometry
Abstract
Hyperbolicity cones are convex algebraic cones arising from hyperbolic polynomials. A well-understood subclass of hyperbolicity cones is that of spectrahedral cones and it is conjectured that every hyperbolicity cone is spectrahedral. In this paper we prove a weaker version of this conjecture by showing that every smooth hyperbolicity cone is the linear projection of a spectrahedral cone, that is, a spectrahedral shadow.
Keywords
Cite
@article{arxiv.1208.0441,
title = {Smooth Hyperbolicity Cones are Spectrahedral Shadows},
author = {Tim Netzer and Raman Sanyal},
journal= {arXiv preprint arXiv:1208.0441},
year = {2012}
}