Hyperbolicity cones are amenable

• 成果类型: Article
• 署名作者: Lourenco, Bruno F.; Roshchina, Vera; Saunderson, James
• 署名单位: Research Organization of Information & Systems (ROIS); Institute of Statistical Mathematics (ISM) - Japan; University of New South Wales Sydney; Monash University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-023-01958-0
• 发表日期: 2024
• 页码: 753-764
• 关键词: exposed cones; INEQUALITY

摘要

Amenability is a notion of facial exposedness for convex cones that is stronger than being facially dual complete (or 'nice') which is, in turn, stronger than merely being facially exposed. Hyperbolicity cones are a family of algebraically structured closed convex cones that contain all spectrahedral cones (linear sections of positive semidefinite cones) as special cases. It is known that all spectrahedral cones are amenable. We establish that all hyperbolicity cones are amenable. As part of the argument, we show that any face of a hyperbolicity cone is a hyperbolicity cone. As a corollary, we show that the intersection of two hyperbolicity cones, not necessarily sharing a common relative interior point, is a hyperbolicity cone.