Journal of Optimization Theory and Applications

, Volume 177, Issue 1, pp 127–136

# On a Class of Semi-Positive Tensors in Tensor Complementarity Problem

Article

## Abstract

Recently, the tensor complementarity problem has been investigated in the literature. In this paper, we extend a class of structured matrices to higher-order tensors; the corresponding tensor complementarity problem has a unique solution for any nonzero nonnegative vector. We discuss their relationships with semi-positive tensors and strictly semi-positive tensors. We also study the property of such a structured tensor. 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. We also give two equivalent formulations of such a structured tensor.

## Keywords

Tensor complementarity problem E-tensor Strictly semi-positive tensor Principal sub-tensor

## Mathematics Subject Classification

15A18 15A69 90C33

## Notes

### Acknowledgements

The authors would like to thank the editors and anonymous referees 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. 11371276).

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