Convex Ternary Quartics Are SOS-Convex
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909178023378944 |
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| author | Ahmadi, Amir Ali Blekherman, Grigoriy Parrilo, Pablo A. |
| author_facet | Ahmadi, Amir Ali Blekherman, Grigoriy Parrilo, Pablo A. |
| contents | We prove that convex ternary quartic forms are sum-of-squares-convex (sos-convex). This result is in a meaningful sense the ``convex analogue'' a celebrated theorem of Hilbert from 1888, where he proves that nonnegative ternary quartic forms are sums of squares. We show by an appropriate construction that exploiting the structure of the Hessian matrix is crucial in any possible proof of our result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_14440 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convex Ternary Quartics Are SOS-Convex Ahmadi, Amir Ali Blekherman, Grigoriy Parrilo, Pablo A. Optimization and Control Algebraic Geometry We prove that convex ternary quartic forms are sum-of-squares-convex (sos-convex). This result is in a meaningful sense the ``convex analogue'' a celebrated theorem of Hilbert from 1888, where he proves that nonnegative ternary quartic forms are sums of squares. We show by an appropriate construction that exploiting the structure of the Hessian matrix is crucial in any possible proof of our result. |
| title | Convex Ternary Quartics Are SOS-Convex |
| topic | Optimization and Control Algebraic Geometry |
| url | https://arxiv.org/abs/2404.14440 |