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arXiv · 2404.14440

Convex Ternary Quartics Are SOS-Convex

Amir Ali Ahmadi·Grigoriy Blekherman·Pablo A. Parrilo
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Abstract

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.

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Amir Ali Ahmadi, Grigoriy Blekherman, Pablo A. Parrilo. 2024-04-19. Convex Ternary Quartics Are SOS-Convex. https://arxiv.org/abs/2404.14440

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