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Properties of Some Classes of Structured Tensors

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Abstract

In this paper, we extend some classes of structured matrices to higher-order tensors. We discuss their relationships with positive semi-definite tensors and some other structured tensors. We show that every principal sub-tensor of such a structured tensor is still a structured tensor in the same class, with a lower dimension. The potential links of such structured tensors with optimization, nonlinear equations, nonlinear complementarity problems, variational inequalities and the non-negative tensor theory are also discussed.

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Acknowledgments

The authors would like to thank the anonymous referees for their valuable suggestions which helped us to improve this manuscript.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, Henan, People’s Republic of China

    Yisheng Song

  2. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

    Liqun Qi

Authors
  1. Yisheng Song
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  2. Liqun Qi
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Corresponding author

Correspondence to Yisheng Song.

Additional information

Yisheng Song’s work was supported by the National Natural Science Foundation of P.R. China (Grant No. 11171094, 11271112). His work was partially done when he was visiting The Hong Kong Polytechnic University. Liqun Qi’s work was supported by the Hong Kong Research Grant Council (Grant No. PolyU 502510, 502111, 501212 and 501913).

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Song, Y., Qi, L. Properties of Some Classes of Structured Tensors. J Optim Theory Appl 165, 854–873 (2015). https://doi.org/10.1007/s10957-014-0616-5

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  • DOI: https://doi.org/10.1007/s10957-014-0616-5

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