Tensor absolute value equations

Shouqiang Du, Liping Zhang, Chiyu Chen, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

46 Citations (Scopus)


This paper is concerned with solving some structured multi-linear systems, which are called tensor absolute value equations. This kind of absolute value equations is closely related to tensor complementarity problems and is a generalization of the well-known absolute value equations in the matrix case. We prove that tensor absolute value equations are equivalent to some special structured tensor complementary problems. Some sufficient conditions are given to guarantee the existence of solutions for tensor absolute value equations. We also propose a Levenberg-Marquardt-type algorithm for solving some given tensor absolute value equations and preliminary numerical results are reported to indicate the efficiency of the proposed algorithm.

Original languageEnglish
Pages (from-to)1695-1710
Number of pages16
JournalScience China Mathematics
Issue number9
Publication statusPublished - 1 Sept 2018


  • 15A48
  • 15A69
  • 65K05
  • 90C20
  • 90C30
  • absolute value equations
  • Levenberg-Marquardt method
  • M-tensors
  • tensor complementarity problem

ASJC Scopus subject areas

  • General Mathematics


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