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The Bounds of Solutions to Polynomial Complementarity Problems

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  • Xue-liu Li

    (Guangxi Minzu University)

  • Guo-ji Tang

    (Guangxi Minzu University)

Abstract

The polynomial complementarity problem (PCP) is an important extension of the tensor complementarity problem (TCP). The main purpose of the present paper is to extend the results on the bounds of solutions of TCP due to Xu–Gu–Huang from TCP to PCP. To that end, the concepts of (generalized) row strictly diagonally dominant tensor to tensor tuple are extended and the properties about them are discussed. By using the introduced structured tensor tuples, the upper and lower bounds on the norm of solutions to PCP are derived. Comparisons between the results presented in the present paper and the existing bounds are made.

Suggested Citation

  • Xue-liu Li & Guo-ji Tang, 2024. "The Bounds of Solutions to Polynomial Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 203(3), pages 2560-2591, December.
    • Handle: RePEc:spr:joptap:v:203:y:2024:i:3:d:10.1007_s10957-024-02511-5
    DOI: 10.1007/s10957-024-02511-5
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    References listed on IDEAS

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    1. Lu-Bin Cui & Yu-Dong Fan & Yi-Sheng Song & Shi-Liang Wu, 2022. "The Existence and Uniqueness of Solution for Tensor Complementarity Problem and Related Systems," Journal of Optimization Theory and Applications, Springer, vol. 192(1), pages 321-334, January.
    2. K. Palpandi & Sonali Sharma, 2021. "Tensor Complementarity Problems with Finite Solution Sets," Journal of Optimization Theory and Applications, Springer, vol. 190(3), pages 951-965, September.
    3. 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.
    4. Vu Trung Hieu, 2020. "Solution maps of polynomial variational inequalities," Journal of Global Optimization, Springer, vol. 77(4), pages 807-824, August.
    5. 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.
    6. 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.
    7. Vu Trung Hieu, 2019. "On the R0-Tensors and the Solution Map of Tensor Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 181(1), pages 163-183, April.
    8. Meng-Meng Zheng & Zheng-Hai Huang & Xiao-Xiao Ma, 2020. "Nonemptiness and Compactness of Solution Sets to Generalized Polynomial Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 185(1), pages 80-98, April.
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