Minimal hyperbolic polynomials and ranks of homogeneous cones
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866918055933640704 |
|---|---|
| author | Gouveia, João Ito, Masaru Lourenço, Bruno F. |
| author_facet | Gouveia, João Ito, Masaru Lourenço, Bruno F. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03860 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minimal hyperbolic polynomials and ranks of homogeneous cones Gouveia, João Ito, Masaru Lourenço, Bruno F. Optimization and Control Algebraic Geometry Metric Geometry 52A20, 14P10 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. |
| title | Minimal hyperbolic polynomials and ranks of homogeneous cones |
| topic | Optimization and Control Algebraic Geometry Metric Geometry 52A20, 14P10 |
| url | https://arxiv.org/abs/2404.03860 |