Minimal hyperbolic polynomials and ranks of homogeneous cones

João Gouveia; Masaru Ito; Bruno F. Lourenço

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arXiv · 2404.03860

Minimal hyperbolic polynomials and ranks of homogeneous cones

João Gouveia·Masaru Ito·Bruno F. Lourenço

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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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João Gouveia, Masaru Ito, Bruno F. Lourenço. 2024-04-05. Minimal hyperbolic polynomials and ranks of homogeneous cones. https://arxiv.org/abs/2404.03860

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