Riley Murray: Signomial and Polynomial Nonnegativity via Relative Entropy and Partial Dualization
(Abstract:) In this talk we provide a tutorial on the Sums-of-AM/GM Exponential (SAGE) proof system for signomial and polynomial nonnegativity. Special attention is paid to recent developments for certifying nonnegativity over proper subsets of $n$-dimensional real space. In the signomial case, these developments further the connection between SAGE certificates and convex duality. The same phenomenon can be understood in the polynomial case by considering convexity with respect to the geometric mean. By focusing on the signomial case, we speak to concepts such as formal proofs of nonnegativity (i.e. addressing the limitations of floating point arithmetic), and the extent to which circuits (a-la SONC polynomials) play a role in the broader theory.