Smooth hyperbolicity cones are spectrahedral shadows

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 sho...

Full description

Saved in:
Bibliographic Details
Published in:Mathematical programming 2015-10, Vol.153 (1), p.213-221
Main Authors: Netzer, Tim, Sanyal, Raman
Format: Article
Language:English
Subjects:
Algebra
Calculus of Variations and Optimal Control
Optimization
Combinatorics
Cones
Convex analysis
Full Length Paper
Geometry
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical models
Mathematical programming
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Optimization
Partial differential equations
Polynomials
Projection
Shadows
Spectra
Spectral lines
Studies
Theoretical
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-014-0744-6