Minimal Hyperbolic Polynomials and Ranks of Homogeneous Cones

João Gouveia; Masaru Ito; Bruno F. Lourenço

Abstract

The starting point of this paper is the computation of minimal hyperbolic polynomials of duals of cones arising from chordal sparsity patterns. From that, we investigate the relation between ranks of homogeneous cones and their minimal polynomials. Along the way, we answer in the negative a question posed in an earlier paper and show examples of homogeneous cones that cannot be realized as rank-one generated (ROG) hyperbolicity cones.

Author information

Contact details are reproduced from the original publication and may be historical.

João Gouveia

CMUC, Dept. of Mathematics, University of Coimbra, Coimbra, Portugal

jgouveia@mat.uc.pt

Masaru Ito

Dept. of Mathematics, College of Science and Technology, Nihon University, Tokyo, Japan

ito.masaru@nihon-u.ac.jp

Bruno F. Lourenço

Dept. of Fundamental Statistical Mathematics, Institute of Statistical Mathematics, Kyoto University, Kyoto, Japan

bruno@ism.ac.jp

Keywords

Hyperbolic polynomial
homogeneous cone
hyperbolicity cone
chordal graphs
minimal polynomial

Mathematics Subject Classification

52A20, 14P10, 05C50

Suggested citation

J. Gouveia, M. Ito, B. F. Lourenço. “Minimal Hyperbolic Polynomials and Ranks of Homogeneous Cones.” Journal of Convex Analysis 33 (2026), No. 1&2, 227–242.