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A general preconditioner for a class of vertical tensor complementarity problems

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  • Shi-Liang Wu

    (Yunnan Normal University
    Yunnan Normal University)

  • Mei Long

    (Yunnan Normal University)

  • Cui-Xia Li

    (Yunnan Normal University)

Abstract

In this paper, based on the methodology of the preconditioning technique, our objective is devoted to solving a class of vertical tensor complementarity problems (VTCP) by the preconditioned fixed point method based on tensor splitting. We firstly propose a general preconditioner based on the amount of negative components of special vector involved. Secondly, some convergence and comparison theorems of the proposed method are given. Thirdly, we analyze the influence of the parameter on the convergence rate of the proposed method. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.

Suggested Citation

  • Shi-Liang Wu & Mei Long & Cui-Xia Li, 2025. "A general preconditioner for a class of vertical tensor complementarity problems," Computational Optimization and Applications, Springer, vol. 92(1), pages 345-373, September.
    • Handle: RePEc:spr:coopap:v:92:y:2025:i:1:d:10.1007_s10589-025-00700-0
    DOI: 10.1007/s10589-025-00700-0
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    References listed on IDEAS

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    1. Yisheng Song & Gaohang Yu, 2016. "Properties of Solution Set of Tensor Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 85-96, July.
    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. Qingyang Jia & Zheng-Hai Huang & Yong Wang, 2024. "Generalized Multilinear Games and Vertical Tensor Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 200(2), pages 602-633, February.
    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.
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