Smooth hyperbolicity cones are spectrahedral shadows

Tim Netzer, Raman Sanyal— 2012

Focus Area 1: High-complexity Geometry 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.

TitelSmooth hyperbolicity cones are spectrahedral shadows
VerfasserTim Netzer, Raman Sanyal
Erschienen inMath. Prog. B, special issue `Lifts of Convex Sets in Optimization', accepted for publication
Größe oder Länge8 pages