2025/04/14 by Averkov, Gennadiy, Ellwanger, Jonas, Jonas Ellwanger +4
Engineering · Mathematics · #05E14 #12D10 #14P05 #52A20 #90C23 #Advanced Numerical Analysis Techniques #Advanced Optimization Algorithms Research #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2504.10302
openalex publication_date 2025/04/14 · openalex created_date 2025/10/14 · openalex updated_date 2026/08/01
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.