Finding the extreme Z-eigenvalues of tensors via a sequential semidefinite programming method

Shenglong Hu, Zheng Hai Huang, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

24 Citations (Scopus)


In this paper, we first introduce the tensor conic linear programming (TCLP), which is a generalization of the space TCLP. Then an approximation method, by using a sequence of semidefinite programming problems, is proposed to solve the TCLP. In particular, we reformulate the extreme Z-eigenvalue problem as a special TCLP. It gives a numerical algorithm to compute the extreme Z-eigenvalue of an even order tensor with dimension larger than three, which improves the literature. Numerical experiments show the efficiency of the proposed method.
Original languageEnglish
Pages (from-to)972-984
Number of pages13
JournalNumerical Linear Algebra with Applications
Issue number6
Publication statusPublished - 1 Dec 2013


  • Semidefinite programming
  • Tensor conic linear programming
  • Z-eigenvalue

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics

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