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Structured tensor tuples to polynomial complementarity problems

Author

Listed:
  • Tong-tong Shang

    (Guizhou University
    Guangxi Minzu University)

  • Guo-ji Tang

    (Guangxi Minzu University)

Abstract

It is well known that structured tensors play an important role in the investigation of tensor complementarity problems. The polynomial complementarity problem is a natural generalization of the tensor complementarity problem. Similar to the investigation of tensor complementarity problems, it is believed that structured tensor tuples will play an important role in the investigation of polynomial complementarity problems. In the present paper, several classes of structured tensor tuples are introduced and the relationships between them are discussed. By using the structured tensor(s) (tuples), the uniqueness of the solution and the global upper bound of the solution set of the polynomial complementarity problem are investigated. The results presented in the present paper generalize the corresponding those in the recent literature.

Suggested Citation

  • Tong-tong Shang & Guo-ji Tang, 2023. "Structured tensor tuples to polynomial complementarity problems," Journal of Global Optimization, Springer, vol. 86(4), pages 867-883, August.
    • Handle: RePEc:spr:jglopt:v:86:y:2023:i:4:d:10.1007_s10898-023-01302-y
    DOI: 10.1007/s10898-023-01302-y
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    References listed on IDEAS

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    1. Yong Wang & Zheng-Hai Huang & Liqun Qi, 2018. "Global Uniqueness and Solvability of Tensor Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 177(1), pages 137-152, April.
    2. Wei Mei & Qingzhi Yang, 2020. "Properties of Structured Tensors and Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 185(1), pages 99-114, April.
    3. 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.
    4. Tong-tong Shang & Jing Yang & Guo-ji Tang, 2022. "Generalized Polynomial Complementarity Problems over a Polyhedral Cone," Journal of Optimization Theory and Applications, Springer, vol. 192(2), pages 443-483, February.
    5. 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.
    6. Wenjie Mu & Jianghua Fan, 2022. "Existence results for solutions of mixed tensor variational inequalities," Journal of Global Optimization, Springer, vol. 82(2), pages 389-412, February.
    7. Yisheng Song & Liqun Qi, 2016. "Eigenvalue analysis of constrained minimization problem for homogeneous polynomial," Journal of Global Optimization, Springer, vol. 64(3), pages 563-575, March.
    8. Yisheng Song & Liqun Qi, 2016. "Tensor Complementarity Problem and Semi-positive Tensors," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 1069-1078, June.
    9. Shenglong Hu & Jie Wang & Zheng-Hai Huang, 2018. "Error Bounds for the Solution Sets of Quadratic Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 983-1000, December.
    10. Zheng-Hai Huang & Yu-Fan Li & Yong Wang, 2023. "A fixed point iterative method for tensor complementarity problems with the implicit Z-tensors," Journal of Global Optimization, Springer, vol. 86(2), pages 495-520, June.
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    12. 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.
    13. 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.
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