Minimal hyperbolic polynomials and ranks of homogeneous cones

2024/04/05 by João Gouveia, Gouveia, João, Masaru Ito +3
Mathematics · #14P10 #52A20 #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematical functions and polynomials #Mathematics and Applications #Metric Geometry (math.MG) #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2404.03860

openalex publication_date 2024/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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