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 semialgebraic sets that are parametrized by families of tropical hypersurfaces. As an application, we give sufficient conditions for equality between the sonc-cone and the sparse nonnegativity cone for generic support sets, and we describe a semialgebraic stratification of the boundary of the sonc-cone in the univariate case.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.