Abstract
In this paper, we present some new results on a class of tensors, which are defined by the solvability of the corresponding tensor complementarity problem. For such structured tensors, we give a sufficient condition to guarantee the nonzero solution of the corresponding tensor complementarity problem with a vector containing at least two nonzero components and discuss their relationships with some other structured tensors. Furthermore, with respect to the tensor complementarity problem with a nonnegative such structured tensor, we obtain the upper and lower bounds of its solution set, and by the way, we show that the eigenvalues of such a tensor are closely related to this solution set.
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Acknowledgements
The authors would like to thank the anonymous referees/editors for their valuable suggestions which helped us to improve this manuscript. This work was supported by the National Natural Science Foundation of China (Grant No. 11671217).
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Communicated by Liqun Qi.
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Mei, W., Yang, Q. Properties of Structured Tensors and Complementarity Problems. J Optim Theory Appl 185, 99–114 (2020). https://doi.org/10.1007/s10957-020-01631-y
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DOI: https://doi.org/10.1007/s10957-020-01631-y
Keywords
- Structured tensor
- Tensor complementarity problems
- Strictly semi-positive tensor
- Norm
- Upper and lower bounds