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Global uniqueness and solvability of tensor complementarity problems for \(\mathcal {H}_{+}\)-tensors

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Abstract

Inthis paper, we study the global uniqueness and solvability of tensor complementarity problems for \(\mathcal {H}_{+}\)-tensors. We obtain a sufficient condition of the global uniqueness and solvability of tensor complementarity problems for \(\mathcal {H}_{+}\)-tensors. We present nonlinear dynamical system models for solving the tensor complementarity problem (TCP). We prove that the presented dynamical system models are stable in the sense of Lyapunov stability theory for considering three classes of structured tensors. The computer simulation results further substantiate that the considered dynamical system can be used to solve the TCP.

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Acknowledgments

We thank the editor and two anonymous reviewers for their detailed and helpful comments.

Funding

Xuezhong Wang is supported by the National Natural Science Foundation of China under grant no. 11771099 and the Natural Science Foundation of Gansu Province and Innovative Ability Promotion Project in Colleges and Universities of Gansu Province. Yimin Wei is also supported by the National Natural Science Foundation of China under grant no. 11771099 and the Innovation Program of Shanghai Municipal Education Commission.

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  1. School of Mathematics and Statistics, Hexi University, Zhangye, 734000, People’s Republic of China

    Xuezhong Wang

  2. School of Economic Mathematics, Southwest University of Finance and Economics, Chengdu, 611130, People’s Republic of China

    Maolin Che

  3. School of Mathematical Sciences and Shanghai Key Laboratory of Contemporary Applied Mathematics, Fudan University, Shanghai, 200433, People’s Republic of China

    Yimin Wei

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  1. Xuezhong Wang
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  2. Maolin Che
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Correspondence to Maolin Che.

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Wang, X., Che, M. & Wei, Y. Global uniqueness and solvability of tensor complementarity problems for \(\mathcal {H}_{+}\)-tensors. Numer Algor 84, 567–590 (2020). https://doi.org/10.1007/s11075-019-00769-9

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