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.
- symmetric tensors
- nonnegative forms
- polynomial and tensor optimization