Strictly semi-positive tensors and the boundedness of tensor complementarity problems

Yisheng Song, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

51 Citations (Scopus)


In this paper, we present the boundedness of solution set of tensor complementarity problem defined by a strictly semi-positive tensor. For strictly semi-positive tensor, we prove that all H+(Z+) -eigenvalues of each principal sub-tensor are positive. We define two new constants associated with H+(Z+) -eigenvalues of a strictly semi-positive tensor. With the help of these two constants, we establish upper bounds of an important quantity whose positivity is a necessary and sufficient condition for a general tensor to be a strictly semi-positive tensor. The monotonicity and boundedness of such a quantity are established too.
Original languageEnglish
Pages (from-to)1407-1426
Number of pages20
JournalOptimization Letters
Issue number7
Publication statusPublished - 1 Oct 2017


  • Eigenvalues
  • Strictly semi-positive tensor
  • Tensor complementarity problem
  • Upper and lower bounds

ASJC Scopus subject areas

  • Control and Optimization


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