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arXiv · 2003.09495

The $\mathcal{S}$-cone and a primal-dual view on second-order representability

Helen Naumann·Thorsten Theobald
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Abstract

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.

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Helen Naumann, Thorsten Theobald. 2020-03-20. The $\mathcal{S}$-cone and a primal-dual view on second-order representability. https://arxiv.org/abs/2003.09495

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