Operations Research Transactions ›› 2015, Vol. 19 ›› Issue (3): 34-41.doi: 10.15960/j.cnki.issn.1007-6093.2015.03.005

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Some properties on Pareto-eigenvalues of higher-order tensors

XU Feng1, LING Chen1,*   

  1. 1. Department of Mathematics, Hangzhou Dianzi University, Hangzhou, 310018, China
  • Received:2015-04-18 Online:2015-09-15 Published:2015-09-15

Abstract:

We consider the higher-order tensor eigenvalue complementarity problem (TEiCP). Since finding the largest Pareto-eigenvalue of tensor is NP-hard in general, in this paper we focus on studying the estimation of the Pareto-eigenvalue. We also present some properties for Pareto-eigenvalues of Z-tensors and M-tensors.

Key words: higher order tensor, eigenvalue complementarity, Pareto-eigenvalue, nonnegative tensor, M-tensor