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arXiv · 1905.04776

The algebraic boundary of the sonc cone

Jens Forsgård·Timo de Wolff
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Abstract

In this article, we explore the connections between nonnegativity, the theory of $A$-discriminants, and tropical geometry. For an integral support set $A \subset \mathbb{Z}^n$, we cover the boundary of the sonc-cone by semi-algebraic sets that are parametrized by families of tropical hypersurfaces. As an application, we characterization generic support sets for which the sonc-cone is equal to the sparse nonnegativity cone, and we describe a semi-algebraic stratification of the boundary of the sonc-cone in the univariate case.

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Jens Forsgård, Timo de Wolff. 2021-08-20. The algebraic boundary of the sonc cone. https://arxiv.org/abs/1905.04776

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