The dual cone of sums of non-negative circuit polynomials (1809.07648v2)

Abstract: For a non-empty, finite subset $\mathcal{A} \subseteq \mathbb{N}0^n$, denote by $C{\text{sonc}}(\mathcal{A}) \in \mathbb{R}[x_1, \ldots, x_n]$ the cone of sums of non-negative circuit polynomials with support $\mathcal{A}$. We derive a representation of the dual cone $(C_{\text{sonc}}(\mathcal{A}))^*$ and deduce a resulting optimality criterion for the use of sums of non-negative circuit polynomials in polynomial optimization.