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An Iterative Method for Horizontal Tensor Complementarity Problems

Author

Listed:
  • Chen Sun

    (Tianjin University)

  • Yong Wang

    (Tianjin University)

  • Zheng-Hai Huang

    (Tianjin University)

Abstract

In this paper, we focus on a class of horizontal tensor complementarity problems (HTCPs). By introducing the block representative tensor, we show that finding a solution of HTCP is equivalent to finding a nonnegative solution of a related tensor equation. We establish the theory of the existence and uniqueness of solution of HTCPs under the proper assumptions. In particular, in the case of the concerned block representative tensor possessing the strong M-property, we propose an algorithm to solve HTCPs by efficiently exploiting the beneficial properties of block representative tensor, and show that the iterative sequence generated by the algorithm is monotone decreasing and converges to a solution of HTCPs. The final numerical experiments verify the correctness of the theory in this paper and show the effectiveness of the proposed algorithm.

Suggested Citation

  • Chen Sun & Yong Wang & Zheng-Hai Huang, 2024. "An Iterative Method for Horizontal Tensor Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 202(2), pages 854-877, August.
    • Handle: RePEc:spr:joptap:v:202:y:2024:i:2:d:10.1007_s10957-024-02450-1
    DOI: 10.1007/s10957-024-02450-1
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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. Francesco Mezzadri & Emanuele Galligani, 2019. "Splitting Methods for a Class of Horizontal Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 180(2), pages 500-517, February.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Xuezhong Wang & Ping Wei & Yimin Wei, 2023. "A Fixed Point Iterative Method for Third-order Tensor Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 197(1), pages 334-357, April.
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