Carathéodory number of homogeneous convex cones

• 成果类型: Article; Early Access
• 署名作者: Chua, Chek Beng
• 署名单位: Nanyang Technological University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610; 1436-4646
• DOI: 10.1007/s10107-026-02411-8
• 发表日期: 2026-08-04
• 关键词: Homogeneous cone; Spectrahedral representation; Carath & eacute; odory number

摘要

We study the Carath & eacute;odory number of homogeneous convex cones via their spectrahedral representations. A characterization of homogeneous convex cones whose ranks match their Carath & eacute;odory numbers is given. This characterization is then used to show that a homogeneous convex cone is selfdual if and only if its rank matches the Carath & eacute;odory numbers of both its closure and its dual cone. It is further used to show that the only sparse spectrahedral cones that are homogeneous convex cones are those described by homogeneous chordal graphs.