On new classes of nonnegative symmetric tensors

Bilian Chen, Simai He, Zhening Li, Shuzhong Zhang

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


In this paper we introduce three new classes of nonnegative forms (or equivalently, symmetric tensors) and their extensions. The newly identified nonnegative symmetric tensors consti- tute 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 (US)
Pages (from-to)292-318
Number of pages27
JournalSIAM Journal on Optimization
Issue number1
StatePublished - 2017


  • Nonnegative forms
  • Polynomial and tensor optimization
  • Symmetric tensors

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