The dual cone of sums of non-negative circuit polynomials

Abstract

For a non-empty, finite subset $\mathcal{A}\subseteq {\mathbb{N}}_0^n$, denote by $C_{\text{sonc}}(\mathcal{A})\in \mathbb{R}[x_1,\dots ,x_n]$ the cone of sums of non-negative circuit polynomials with support $\mathcal{A}$. We derive a representation of the dual cone $(C_{\text{sonc}}(\mathcal{A}){)}^{\ast }$ and deduce a resulting optimality criterion for the use of sums of non-negative circuit polynomials in polynomial optimization.

Revised version, 14 pages