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Estimations on upper and lower bounds of solutions to a class of tensor complementarity problems

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Abstract

We introduce a class of structured tensors, called generalized row strictly diagonally dominant tensors, and discuss some relationships between it and several classes of structured tensors, including nonnegative tensors, B-tensors, and strictly copositive tensors. In particular, we give estimations on upper and lower bounds of solutions to the tensor complementarity problem (TCP) when the involved tensor is a generalized row strictly diagonally dominant tensor with all positive diagonal entries. The main advantage of the results obtained in this paper is that both bounds we obtained depend only on the tensor and constant vector involved in the TCP; and hence, they are very easy to calculate.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11431002, 11871051).

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Authors and Affiliations

  1. School of Mathematics, Tianjin University, Tianjin, 300350, China

    Yang Xu, Weizhe Gu & Zheng-Hai Huang

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  1. Yang Xu
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  2. Weizhe Gu
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  3. Zheng-Hai Huang
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Correspondence to Zheng-Hai Huang.

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Xu, Y., Gu, W. & Huang, ZH. Estimations on upper and lower bounds of solutions to a class of tensor complementarity problems. Front. Math. China 14, 661–671 (2019). https://doi.org/10.1007/s11464-019-0770-z

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  • DOI: https://doi.org/10.1007/s11464-019-0770-z

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