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Randomized Kaczmarz methods for tensor complementarity problems

Author

Listed:
  • Xuezhong Wang

    (Hexi University)

  • Maolin Che

    (Southwestern University of Finance and Economics)

  • Yimin Wei

    (Fudan University)

Abstract

In this paper, we equivalently reformulate the tensor complementarity problem as a system of fixed point equations. Based on this system, we propose the (extend) randomized Kaczmarz methods for solving the tensor complementarity problem associated with nonnegative $$\mathcal {P}$$ P -tensors and nonsingular $$\mathcal {M}$$ M -tensors. We also analyze the upper bounds of the mean squared error and the estimate of the convergence rate for these two iterative methods. The computer simulation results further substantiate that the presented two randomized Kaczmarz type methods can be used to solve TCP with these two cases of tensors.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:82:y:2022:i:3:d:10.1007_s10589-022-00382-y
    DOI: 10.1007/s10589-022-00382-y
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    References listed on IDEAS

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    Cited by:

    1. 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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