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We describe a generalization of the Sums-of-AM/GM Exponential (SAGE)relaxation methodology for obtaining bounds on constrained signomial andpolynomial optimization problems. Our approach leverages the fact that relativeentropy based SAGE certificates conveniently and transparently blend withconvex duality, in a manner that Sums-of-Squares certificates do not. This moregeneral approach not only retains key properties of ordinary SAGE relaxations(e.g. sparsity preservation), but also inspires a novel perspective-basedmethod of solution recovery. We illustrate the utility of our methodology witha range of examples from the global optimization literature, along with apublicly available software package.

Signomial and Polynomial Optimization via Relative Entropy and Partial Dualization