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arXiv · 2504.10302

Nonnegativity of signomials with Newton simplex over $\mathcal{A}$-convex sets

Gennadiy Averkov·Jonas Ellwanger·Thorsten Theobald·Timo de Wolff
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Abstract

We study a class of signomials whose positive support is the set of vertices of a simplex and which may have several negative support points in the simplex. Various groups of authors have provided an exact characterization for the global nonnegativity of a signomial in this class in terms of circuit signomials and that characterization provides a tractable nonnegativity test. We generalize this characterization to the constrained nonnegativity over a set $X$ under an additional convexity precondition in the exponential moment space. This provides a tractable nonnegativity test over $X$ for the class in terms of a power cone program. Our proof methods rely on a variant of the convex cone of constrained SAGE signomials (sums of arithmetic-geometric exponentials) and the duality theory.

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Gennadiy Averkov, Jonas Ellwanger, Thorsten Theobald, Timo de Wolff. 2025-04-14. Nonnegativity of signomials with Newton simplex over $\mathcal{A}$-convex sets. https://arxiv.org/abs/2504.10302

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