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A Modulus-Based Formulation for the Vertical Tensor Complementarity Problem

Author

Listed:
  • Xue-Fan Zhao

    (Yunnan Normal University)

  • Shi-Liang Wu

    (Yunnan Normal University
    Yunnan Normal University)

  • Cui-Xia Li

    (Yunnan Normal University)

Abstract

In this paper, we introduce a modulus-based formulation for solving vertical tensor complementarity problems (VTCP) with an arbitrary number of tensors. This formulation allows us to design the modulus-based tensor splitting iterative method to fit different number of tensors. In this context, we especially analyze the modulus-based tensor splitting iterative methods for solving VTCP with two tensors, and provide sufficient conditions in combination with the properties of the power Lipschitz tensor for their convergence. We then extend the methods to solve VTCP with any number of tensors, and study the convergence analysis under proper conditions. Finally, the proposed methods are evaluated by numerical experiments.

Suggested Citation

  • Xue-Fan Zhao & Shi-Liang Wu & Cui-Xia Li, 2024. "A Modulus-Based Formulation for the Vertical Tensor Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 203(3), pages 2759-2783, December.
    • Handle: RePEc:spr:joptap:v:203:y:2024:i:3:d:10.1007_s10957-024-02544-w
    DOI: 10.1007/s10957-024-02544-w
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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. Lixing Han, 2019. "A Continuation Method for Tensor Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 180(3), pages 949-963, March.
    3. 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.
    4. 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.
    5. Shouqiang Du & Weiyang Ding & Yimin Wei, 2021. "Acceptable Solutions and Backward Errors for Tensor Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 188(1), pages 260-276, January.
    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. Yisheng Song & Liqun Qi, 2015. "Properties of Some Classes of Structured Tensors," Journal of Optimization Theory and Applications, Springer, vol. 165(3), pages 854-873, June.
    8. 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.
    9. 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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