Nonnegativity of signomials with Newton simplex over $\mathcal{A}$-convex sets
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| Format: | Preprint |
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2025
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| _version_ | 1866911435853922304 |
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| author | Averkov, Gennadiy Ellwanger, Jonas Theobald, Thorsten de Wolff, Timo |
| author_facet | Averkov, Gennadiy Ellwanger, Jonas Theobald, Thorsten de Wolff, Timo |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_10302 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonnegativity of signomials with Newton simplex over $\mathcal{A}$-convex sets Averkov, Gennadiy Ellwanger, Jonas Theobald, Thorsten de Wolff, Timo Combinatorics Algebraic Geometry Optimization and Control 12D10, 14P05, 52A20, 90C23, 05E14 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. |
| title | Nonnegativity of signomials with Newton simplex over $\mathcal{A}$-convex sets |
| topic | Combinatorics Algebraic Geometry Optimization and Control 12D10, 14P05, 52A20, 90C23, 05E14 |
| url | https://arxiv.org/abs/2504.10302 |