For a non-empty, finite subset A⊆ N0n $\mathcal{A} \subseteq \mathbb{N}_0^n$ let C sonc (𝒜) ∈ ℝ[ x 1 , . . . , x n ] be the cone of sums of non-negative circuit polynomials with support 𝒜. We derive a representation of the dual cone ( C sonc (𝒜)) ∗ and deduce an optimality criterion for sums of non-negative circuit polynomials in polynomial optimization.

中文翻译：

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非负电路多项式和的对偶圆锥

对于非空的有限子集A⊆N0n $ \ mathcal {A} \ subseteq \ mathbb {N} _0 ^ n $，令C sonc（𝒜）∈ℝ[x 1，。。。，xn]为具有支持𝒜的非负电路多项式之和的圆锥。我们推导了对偶圆锥（C sonc（𝒜））∗的表示，并为多项式优化中的非负电路多项式之和得出了最优准则。