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Acceptable Solutions and Backward Errors for Tensor Complementarity Problems

Author

Listed:
  • Shouqiang Du

    (Qingdao University)

  • Weiyang Ding

    (Fudan University)

  • Yimin Wei

    (Fudan University)

Abstract

Backward error analysis reveals the numerical stability of algorithms and provides elaborate stopping criteria for iterative methods. Compared with numerical linear algebra problems, the backward error analysis for optimization problems is more rarely conducted in the literature. This paper is devoted to the backward error analysis for several generalizations of tensor complementarity problems. We first present sufficient and necessary conditions for the acceptable solutions for the extended tensor complementarity problem, the vertical tensor complementarity problem, and an extended form of tensor complementarity problem. Next, the backward errors for tensor complementarity problem are also proposed, which can be used to verify the stability of the tensor complementarity problem algorithms. Finally, some numerical examples are reported to illustrate the proposed backward errors for tensor complementarity problems.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:188:y:2021:i:1:d:10.1007_s10957-020-01774-y
    DOI: 10.1007/s10957-020-01774-y
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    References listed on IDEAS

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    1. Jie Wang & Shenglong Hu & Zheng-Hai Huang, 2018. "Solution Sets of Quadratic Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 176(1), pages 120-136, January.
    2. Shouqiang Du & Maolin Che & Yimin Wei, 2020. "Stochastic structured tensors to stochastic complementarity problems," Computational Optimization and Applications, Springer, vol. 75(3), pages 649-668, April.
    3. Vu Trung Hieu & Yimin Wei & Jen-Chih Yao, 2020. "Notes on the Optimization Problems Corresponding to Polynomial Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 687-695, February.
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    10. Liqun Qi & Zheng-Hai Huang, 2019. "Tensor Complementarity Problems—Part II: Solution Methods," Journal of Optimization Theory and Applications, Springer, vol. 183(2), pages 365-385, November.
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    16. 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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    Cited by:

    1. 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.
    2. 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.
    3. Shouqiang Du & Liyuan Cui & Yuanyuan Chen & Yimin Wei, 2022. "Stochastic Tensor Complementarity Problem with Discrete Distribution," Journal of Optimization Theory and Applications, Springer, vol. 192(3), pages 912-929, March.

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