Smooth hyperbolicity cones are spectrahedral shadows

被引：7

作者：

Netzer, Tim ^{[1
]}

Sanyal, Raman ^{[2
]}

机构：

[1] Univ Leipzig, D-04109 Leipzig, Germany

[2] Free Univ Berlin, Fachbereich Math & Informat, Berlin, Germany

来源：

MATHEMATICAL PROGRAMMING | 2015年 / 153卷 / 01期

基金：

欧洲研究理事会;

关键词：

Hyperbolic polynomials; Hyperbolicity cones; Spectrahedra; Spectrahedral shadows; sdp-representable; POLYNOMIALS; REPRESENTATION; INEQUALITY;

D O I：

10.1007/s10107-014-0744-6

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

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.

引用

页码：213 / 221

页数：9

共 19 条

[1] Hyperbolic polynomials and convex analysis [J].