Dehomogenization for completely positive tensors

Jiawang Nie, Xindong Tang, Zi Yang, Suhan Zhong

Research output: Contribution to journalJournal articlepeer-review


A real symmetric tensor is completely positive (CP) if it is a sum of symmetric tensor powers of nonnegative vectors. We propose a dehomogenization approach for studying CP tensors. This gives new Moment-SOS relaxations for CP tensors. Detection for CP tensors and the linear conic optimization with CP tensor cones can be solved more efficiently by the dehomogenization approach.

Original languageEnglish
Pages (from-to)340-363
Number of pages24
JournalNumerical Algebra, Control and Optimization
Issue number2
Early online date1 Jan 2023
Publication statusPublished - Jun 2023

Scopus Subject Areas

  • Algebra and Number Theory
  • Control and Optimization
  • Applied Mathematics

User-Defined Keywords

  • Tensor
  • complete positivity
  • dehomogenization
  • moment
  • semidefinite relaxation


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