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Linearized Methods for Tensor Complementarity Problems

Author

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  • Hong-Bo Guan

    (South China Normal University
    Hunan Institute of Technology)

  • Dong-Hui Li

    (South China Normal University)

Abstract

In this paper, we first propose a linearized method for solving the tensor complementarity problem. The subproblems of the method can be solved by solving linear complementarity problems with a constant matrix. We show that if the initial point is appropriately chosen, then the generated sequence of iterates converges to a solution of the problem monotonically. We then propose a lower-dimensional equation method and establish its monotone convergence. The subproblems of the method are lower-dimensional systems of linear equations. At last, we do numerical experiments to test the proposed methods. The results show the efficiency of the proposed methods.

Suggested Citation

  • Hong-Bo Guan & Dong-Hui Li, 2020. "Linearized Methods for Tensor Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 972-987, March.
    • Handle: RePEc:spr:joptap:v:184:y:2020:i:3:d:10.1007_s10957-019-01627-3
    DOI: 10.1007/s10957-019-01627-3
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    References listed on IDEAS

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    1. Shui-Lian Xie & Dong-Hui Li & Hong-Ru Xu, 2017. "An Iterative Method for Finding the Least Solution to the Tensor Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 175(1), pages 119-136, October.
    2. Zheng-Hai Huang & Liqun Qi, 2017. "Formulating an n-person noncooperative game as a tensor complementarity problem," Computational Optimization and Applications, Springer, vol. 66(3), pages 557-576, April.
    3. Yisheng Song & Liqun Qi, 2016. "Tensor Complementarity Problem and Semi-positive Tensors," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 1069-1078, June.
    4. Xue-Li Bai & Zheng-Hai Huang & Yong Wang, 2016. "Global Uniqueness and Solvability for Tensor Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 72-84, July.
    5. Maolin Che & Liqun Qi & Yimin Wei, 2016. "Positive-Definite Tensors to Nonlinear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 475-487, February.
    6. 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.
    7. Shouqiang Du & Liping Zhang, 2019. "A mixed integer programming approach to the tensor complementarity problem," Journal of Global Optimization, Springer, vol. 73(4), pages 789-800, April.
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    Cited by:

    1. 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.
    2. Zheng-Hai Huang & Yu-Fan Li & Yong Wang, 2023. "A fixed point iterative method for tensor complementarity problems with the implicit Z-tensors," Journal of Global Optimization, Springer, vol. 86(2), pages 495-520, June.
    3. Xuezhong Wang & Maolin Che & Yimin Wei, 2022. "Randomized Kaczmarz methods for tensor complementarity problems," Computational Optimization and Applications, Springer, vol. 82(3), pages 595-615, July.

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