Smooth hyperbolicity cones are second-order cone representable
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916989912481792 |
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| author | Scheiderer, Claus |
| author_facet | Scheiderer, Claus |
| contents | Netzer and Sanyal proved that every smooth hyperbolicity cone is a spectrahedral shadow. We generalize and sharpen this result at the same time, by showing that every Nash-smooth hyperbolicity cone is even second-order cone representable (socr). The result is proved as a consequence of our second theorem, according to which every compact convex semialgebraic set with Nash-smooth boundary of strict positive curvature is socr. The proof uses the technique of tensor evaluation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_17121 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Smooth hyperbolicity cones are second-order cone representable Scheiderer, Claus Algebraic Geometry Optimization and Control 14P99 (Primary), 90C25 (Secondary) Netzer and Sanyal proved that every smooth hyperbolicity cone is a spectrahedral shadow. We generalize and sharpen this result at the same time, by showing that every Nash-smooth hyperbolicity cone is even second-order cone representable (socr). The result is proved as a consequence of our second theorem, according to which every compact convex semialgebraic set with Nash-smooth boundary of strict positive curvature is socr. The proof uses the technique of tensor evaluation. |
| title | Smooth hyperbolicity cones are second-order cone representable |
| topic | Algebraic Geometry Optimization and Control 14P99 (Primary), 90C25 (Secondary) |
| url | https://arxiv.org/abs/2509.17121 |