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A Fixed Point Iterative Method for Third-order Tensor Linear Complementarity Problems

Author

Listed:
  • Xuezhong Wang

    (Hexi University)

  • Ping Wei

    (Hexi University)

  • Yimin Wei

    (Fudan University)

Abstract

Fixed point iterative approach for solving the third-order tensor linear complementarity problems (TLCP) is presented in this paper. Theoretical analysis shows that the third-order tensor linear complementarity problem is equivalent to a fixed point equation under tensor T-product. Based on the fixed point equation, a fixed point iterative method is proposed and corresponding convergence proof are studied. Moreover, we provide estimations of the convergence rate. The computer-simulation results further substantiate that the proposed fixed point iterative method can solve the TLCP.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:197:y:2023:i:1:d:10.1007_s10957-023-02169-5
    DOI: 10.1007/s10957-023-02169-5
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. M. Seetharama Gowda & Jong-Shi Pang, 1992. "On Solution Stability of the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 77-83, February.
    4. Meng-Meng Zheng & Zheng-Hai Huang & Yong Wang, 2021. "T-positive semidefiniteness of third-order symmetric tensors and T-semidefinite programming," Computational Optimization and Applications, Springer, vol. 78(1), pages 239-272, January.
    5. Xuezhong Wang & Maolin Che & Yimin Wei, 2020. "Tensor neural network models for tensor singular value decompositions," Computational Optimization and Applications, Springer, vol. 75(3), pages 753-777, April.
    6. 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.
    7. Wendi Bao & Feiyu Zhang & Weiguo Li & Qin Wang & Ying Gao, 2022. "Randomized Average Kaczmarz Algorithm for Tensor Linear Systems," Mathematics, MDPI, vol. 10(23), pages 1-24, December.
    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.
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