The $\mathcal{ S}$-cone provides a common framework for cones of polynomials or exponential sums which establish non-negativity upon the arithmetic-geometric inequality, in particular for sums of non-negative circuit polynomials (SONC) or sums of arithmetic-geometric exponentials (SAGE). In this paper, we study the $\mathcal{ S}$-cone and its dual from the viewpoint of second-order representability. Extending results of Averkov and of Wang and Magron on the primal SONC cone, we provide explicit generalized second-order descriptions for rational $\mathcal{ S}$-cones and theirs duals.
Categories: math.OC