On new classes of nonnegative symmetric tensors

Bilian Chen, Simai He, Zhening Li, Shuzhong Zhang

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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.
Original languageEnglish
Pages (from-to)292-318
JournalSIAM Journal on Optimization
Issue number1
Early online date23 Feb 2017
Publication statusPublished - Mar 2017


  • symmetric tensors
  • nonnegative forms
  • polynomial and tensor optimization


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