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Global Uniqueness and Solvability for Tensor Complementarity Problems

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Abstract

Recently, the tensor complementarity problem has been investigated in the literature. An important question involving the property of global uniqueness and solvability for a class of tensor complementarity problems was proposed by Song and Qi (J Optim Theory Appl, 165:854–873, 2015). In the present paper, we give an answer to this question by constructing two counterexamples. We also show that the solution set of this class of tensor complementarity problems is nonempty and compact. In particular, we introduce a class of related structured tensors and show that the corresponding tensor complementarity problem has the property of global uniqueness and solvability.

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Acknowledgments

This work is partially supported by the National Natural Science Foundation of China (Grant Nos. 11171252 and 11431002).

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Authors and Affiliations

  1. Department of Mathematics, School of Science, Tianjin University, Tianjin, 300072, People’s Republic of China

    Xue-Li Bai, Zheng-Hai Huang & Yong Wang

  2. Center for Applied Mathematics of Tianjin University, Tianjin, People’s Republic of China

    Zheng-Hai Huang

Authors
  1. Xue-Li Bai
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  2. Zheng-Hai Huang
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  3. Yong Wang
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Correspondence to Zheng-Hai Huang.

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Communicated by Liqun Qi.

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Bai, XL., Huang, ZH. & Wang, Y. Global Uniqueness and Solvability for Tensor Complementarity Problems. J Optim Theory Appl 170, 72–84 (2016). https://doi.org/10.1007/s10957-016-0903-4

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