On New Classes of Nonnegative Symmetric Tensors
本文提出了三类新的非负对称张量及其扩展，它们构成对称张量空间中的凸锥，并讨论了在多项式与张量优化中的应用，附有数值实验。
In this paper we introduce three new classes of nonnegative forms (or equivalently, symmetric tensors) and their extensions. The newly identified nonnegative symmetric tensors constitute distinctive convex cones in the space of general symmetric tensors (order six or above). For the special case of quartic forms, they collapse into the set of convex quartic homogeneous polynomial functions. We discuss the properties and applications of the new classes of nonnegative symmetric tensors in the context of polynomial and tensor optimization. Numerical experiments for solving certain polynomial optimization models based on the new classes of nonnegative symmetric tensors are presented.