论文标题
SONC的二元性：基于电路证书的进步
The Duality of SONC: Advances in Circuit-based Certificates
论文作者
论文摘要
非负回路（SONC）的总和是非负多项式 /指数总和的子集，近年来已经对其进行了广泛的研究。在本文中，我们构建了SONC锥的子集，我们称之为DSONC锥。 DSONC锥被视为双SONC锥的扩展。可以通过线性编程测试会员资格。我们表明，DSONC锥是一个合适的全维锥体，我们提供了其极端射线的描述，并收集了与SONC锥体相似的几种属性。此外，我们表明DSONC锥体中的功能不能具有真实的零，这表明DSONC锥不会与SONC锥的边界相交。此外，我们讨论了DSONC锥与SOS和SDSOS锥的交集。最后，我们表明电路在DSONC锥的边界中的功能由平衡点确定，因此，这是原始SONC锥中单数点的类似物，并将DSONC锥与热带几何形状相关联。
The cone of sums of nonnegative circuits (SONCs) is a subset of the cone of nonnegative polynomials / exponential sums, which has been studied extensively in recent years. In this article, we construct a subset of the SONC cone which we call the DSONC cone. The DSONC cone can be seen as an extension of the dual SONC cone; membership can be tested via linear programming. We show that the DSONC cone is a proper, full-dimensional cone, we provide a description of its extreme rays, and collect several properties that parallel those of the SONC cone. Moreover, we show that functions in the DSONC cone cannot have real zeros, which yields that DSONC cone does not intersect the boundary of the SONC cone. Furthermore, we discuss the intersection of the DSONC cone with the SOS and SDSOS cones. Finally, we show that circuit functions in the boundary of the DSONC cone are determined by points of equilibria, which hence are the analogues to singular points in the primal SONC cone, and relate the DSONC cone to tropical geometry.
