The $\mathcal{S}$-cone and a primal-dual view on second-order representability
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2020
- DOI:
- 10.48550/arXiv.2003.09495
- arXiv:
- arXiv:2003.09495
- Bibcode:
- 2020arXiv200309495N
- Keywords:
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- Mathematics - Optimization and Control;
- 14P05;
- 90C30 (Primary);
- 52A20;
- 12D15 (Secondary)
- E-Print:
- Minor revision, 19 pages, 4 figures