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The GUS-Property and Modulus-Based Methods for Tensor Complementarity Problems

Author

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  • Ping-Fan Dai

    (Hanshan Normal University
    Sanming University)

  • Shi-Liang Wu

    (Yunnan Normal University)

Abstract

In this paper, we consider the global uniqueness and solvability (GUS) of tensor complementarity problems for special power Lipschitz tensors (SPL-tensors). It is shown that a SPL-tensor is a P-tensor, but not necessarily an H-tensor. And it is also proved that tensor complementarity problems of SPL-tensors have the GUS-property. In addition, we propose modulus-based tensor splitting methods to solve the tensor complementarity problem. We consider both stand and accelerated tensor splitting methods for solving the reformulated fixed-point equations of tensor complementarity problems. The convergence analysis of two classes of modulus-based iterative methods is discussed when the system tensors are power Lipschitz tensors. Numerical examples are given to illustrate the effectiveness and efficiency of the presented approaches.

Suggested Citation

  • Ping-Fan Dai & Shi-Liang Wu, 2022. "The GUS-Property and Modulus-Based Methods for Tensor Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 195(3), pages 976-1006, December.
    • Handle: RePEc:spr:joptap:v:195:y:2022:i:3:d:10.1007_s10957-022-02089-w
    DOI: 10.1007/s10957-022-02089-w
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    References listed on IDEAS

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    9. Zheng-Hai Huang & Liqun Qi, 2019. "Tensor Complementarity Problems—Part I: Basic Theory," Journal of Optimization Theory and Applications, Springer, vol. 183(1), pages 1-23, October.
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    11. Zheng-Hai Huang & Liqun Qi, 2019. "Tensor Complementarity Problems—Part III: Applications," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 771-791, December.
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