The algebraic boundary of the sonc cone

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.

arXiv comment33 pages

Cited by in corpus (2)

• Global Optimization via the Dual SONC Cone and Linear Programming
• Real Zeros of SONC Polynomials