论文标题
$ \ MATHCAL {S} $ - 圆锥和二阶表示的原始二次视图
The $\mathcal{S}$-cone and a primal-dual view on second-order representability
论文作者
论文摘要
$ \ MATHCAL {S} $ - 锥为多项式或指数总和提供了一个共同的框架，这些框架在算术几何不平等上建立了非负性，尤其是对于非阴性电路多项式（SONC）或算术 - 几点质量指数（SAGE）的总和。在本文中，我们从二阶表示的角度研究了$ \ Mathcal {s} $ - 圆锥体及其双重。扩展了Averkov和Wang and Magron在原始SONC锥上的结果，我们为有理$ \ Mathcal {s} $ - 圆锥体及其双重的二阶说明了明确的二阶描述。
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.
