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Properties of Solution Set of Tensor Complementarity Problem

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Abstract

In this paper, a new subclass of tensors is introduced and it is proved that this class of new tensors can be defined by the feasible region of the corresponding tensor complementarity problem. Furthermore, the boundedness of solution set of the tensor complementarity problem is equivalent to the uniqueness of solution for such a problem with zero vector. For the tensor complementarity problem with a strictly semi-positive tensor, we proved the global upper bounds of its solution set. In particular, such upper bounds are closely associated with the smallest Pareto eigenvalue of such a tensor.

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Acknowledgments

The authors would like to thank the editors and anonymous referees for their valuable suggestions which helped us to improve this manuscript. The first author’s work was supported by the National Natural Science Foundation of P. R. China (Grant No. 11571095) and Program for Innovative Research Team (in Science and Technology) in University of Henan Province (14RTSTHN023). The second author’s work was supported by the National Natural Science Foundation of China (No. 61262026) and Programm of the Ministry of Education (NCET 13-0738), JGZX programm of Jiangxi Province (20112BCB23027), Natural Science Foundation of Jiangxi Province (20132BAB201026), science and technology programm of Jiangxi Education Committee (LDJH12088).

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Authors and Affiliations

  1. School of Mathematics and Information Science and Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, Henan Normal University, Xinxiang, 453007, Henan, People’s Republic of China

    Yisheng Song

  2. School of Mathematics and Computer Sciences, Gannan Normal University, Ganzhou, 341000, People’s Republic of China

    Gaohang Yu

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  1. Yisheng Song
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  2. Gaohang Yu
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Correspondence to Yisheng Song.

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Communicated by Liqun Qi.

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Song, Y., Yu, G. Properties of Solution Set of Tensor Complementarity Problem. J Optim Theory Appl 170, 85–96 (2016). https://doi.org/10.1007/s10957-016-0907-0

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  • DOI: https://doi.org/10.1007/s10957-016-0907-0

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