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Tensor Complementarity Problem and Semi-positive Tensors

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Abstract

In this paper, we prove that a real tensor is strictly semi-positive if and only if the corresponding tensor complementarity problem has a unique solution for any nonnegative vector and that a real tensor is semi-positive if and only if the corresponding tensor complementarity problem has a unique solution for any positive vector. It is shown that a real symmetric tensor is a (strictly) semi-positive tensor if and only if it is (strictly) copositive.

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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 partially supported by the National Natural Science Foundation of P.R. China (Grant Nos. 11571905, 11271112, 61262026), NCET Programm of the Ministry of Education (NCET 13-0738), Program for Innovative Research Team (in Science and Technology) in University of Henan Province(14IRTSTHN023), science and technology programm of Jiangxi Education Committee (LDJH12088). The second author’s work was supported by the Hong Kong Research Grant Council (Grant Nos. PolyU 502111, 501212, 501913 and 15302114).

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Authors and Affiliations

  1. School of Mathematics and Information Science, 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. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

    Liqun Qi

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  1. Yisheng Song
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  2. Liqun Qi
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Correspondence to Liqun Qi.

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Song, Y., Qi, L. Tensor Complementarity Problem and Semi-positive Tensors. J Optim Theory Appl 169, 1069–1078 (2016). https://doi.org/10.1007/s10957-015-0800-2

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  • DOI: https://doi.org/10.1007/s10957-015-0800-2

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