On the cone eigenvalue complementarity problem for higher-order tensors

Chen Ling, Hongjin He, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

43 Citations (Scopus)


In this paper, we consider the tensor generalized eigenvalue complementarity problem (TGEiCP), which is an interesting generalization of matrix eigenvalue complementarity problem (EiCP). First, we give an affirmative result showing that TGEiCP is solvable and has at least one solution under some reasonable assumptions. Then, we introduce two optimization reformulations of TGEiCP, thereby beneficially establishing an upper bound on cone eigenvalues of tensors. Moreover, some new results concerning the bounds on the number of eigenvalues of TGEiCP further enrich the theory of TGEiCP. Last but not least, an implementable projection algorithm for solving TGEiCP is also developed for the problem under consideration. As an illustration of our theoretical results, preliminary computational results are reported.
Original languageEnglish
Pages (from-to)143-168
Number of pages26
JournalComputational Optimization and Applications
Issue number1
Publication statusPublished - 1 Jan 2016


  • Cone eigenvalue
  • Eigenvalue complementarity problem
  • Higher order tensor
  • Optimization reformulation
  • Projection algorithm

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Control and Optimization


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