Sublinear circuits and the constrained signomial nonnegativity problem

Abstract Conditional Sums-of-AM/GM-Exponentials (conditional SAGE) is a decomposition method to prove nonnegativity of signomial or polynomial over some subset X real space. In this article, we undertake the first structural analysis conditional SAGE signomials for convex sets . We introduce -circuits finite $${\mathcal {A}}\subset {\mathbb {R}}^n$$ A ⊂ R n , which generalize simplicial circuits affine-linear matroid induced by {A}}$$ constrained setting. The serve as main tool in our and exhibit particularly rich combinatorial properties polyhedral case set comprised one-dimensional cones suitable fans. framework transparently reveals when an -nonnegative AM/GM-exponential can fact be further decomposed sum simpler signomials. develop duality theory with connections geometry that are according geometric mean. This provides optimal power cone reconstruction polyhedral. conjunction notion reduced -circuits, facilitates characterization extreme rays cones. Since under logarithmic variable substitutions give polynomials, results also have implications nonnegative polynomials optimization.