Smooth hyperbolicity cones are spectrahedral shadows

• 成果类型: Article
• 署名作者: Netzer, Tim; Sanyal, Raman
• 署名单位: Leipzig University; Free University of Berlin
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-014-0744-6
• 发表日期: 2015
• 页码: 213-221
• 关键词: Polynomials; REPRESENTATION; INEQUALITY

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.