Convex Ternary Quartics Are SOS-Convex
Optimization and Control
2024-04-24 v1 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.2404.14440,
title = {Convex Ternary Quartics Are SOS-Convex},
author = {Amir Ali Ahmadi and Grigoriy Blekherman and Pablo A. Parrilo},
journal= {arXiv preprint arXiv:2404.14440},
year = {2024}
}
Comments
15 pages