In this article, we propose a geometric programming method in order to compute lower bounds for real polynomials. We provide new sufficient conditions for polynomials to be nonnegative as well as to have a sum of binomial squares representation. These criteria rely on the coefficients and the support of a polynomial and generalize all previous ones by Lasserre, Ghasemi, Marshall, Fidalgo and Ko...

This paper presents the application of geometric programming for combined high-level and low-level architecture parameter exploration. This paper builds an geometric programming framework for reconfigurable architectures, and presents a full delay and area model of an FPGA. This optimization allows high-level architectural parameter selection and the transistor sizing to be done concurrently. T...

This paper derives new algorithms for signomial programming, a generalization of geometric programming. The algorithms are based on a generic principle for optimization called the MM algorithm. In this setting, one can apply the geometric-arithmetic mean inequality and a supporting hyperplane inequality to create a surrogate function with parameters separated. Thus, unconstrained signomial prog...

We trace progress and thinking about the Strominger-Yau-Zaslow conjecture since its introduction in 1996. In particular, we aim to explain how the conjecture led to the algebro-geometric program developed by myself and Siebert, whose objective is to explain mirror symmetry by studying degenerations of Calabi-Yau manifolds. We end by outlining how tropical curves arise in the mirror symmetry story.