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Generalized Polynomial Complementarity Problems over a Polyhedral Cone

Author

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  • Tong-tong Shang

    (Guangxi University for Nationalities)

  • Jing Yang

    (Guangxi University for Nationalities)

  • Guo-ji Tang

    (Guangxi University for Nationalities
    Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis)

Abstract

The goal of this paper is to investigate a new model, called generalized polynomial complementarity problems over a polyhedral cone and denoted by GPCPs, which is a natural extension of the polynomial complementarity problems and generalized tensor complementarity problems. Firstly, the properties of the set of all $$R^{K}_{{\varvec{0}}}$$ R 0 K -tensors are investigated. Then, the nonemptiness and compactness of the solution set of GPCPs are proved, when the involved tensor in the leading term of the polynomial is an $$ER^{K}$$ E R K -tensor. Subsequently, under fairly mild assumptions, lower bounds of solution set via an equivalent form are obtained. Finally, a local error bound of the considered problem is derived. The results presented in this paper generalize and improve the corresponding those in the recent literature.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:192:y:2022:i:2:d:10.1007_s10957-021-01969-x
    DOI: 10.1007/s10957-021-01969-x
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    References listed on IDEAS

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    1. Vyacheslav Kalashnikov & George Isac, 2002. "Solvability of Implicit Complementarity Problems," Annals of Operations Research, Springer, vol. 116(1), pages 199-221, October.
    2. 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.
    3. 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.
    4. 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.
    5. Liyun Ling & Chen Ling & Hongjin He, 2020. "Generalized Tensor Complementarity Problems Over a Polyhedral Cone," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 37(04), pages 1-23, August.
    6. 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.
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    8. 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.
    9. Hongchun Sun & Yiju Wang, 2013. "Further Discussion on the Error Bound for Generalized Linear Complementarity Problem over a Polyhedral Cone," Journal of Optimization Theory and Applications, Springer, vol. 159(1), pages 93-107, October.
    10. Xue-Li Bai & Zheng-Hai Huang & Xia Li, 2019. "Stability of Solutions and Continuity of Solution Maps of Tensor Complementarity Problems," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(02), pages 1-19, April.
    11. Yang Xu & Weizhe Gu & He Huang, 2019. "Solvability of Two Classes of Tensor Complementarity Problems," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-8, March.
    12. 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.
    13. Vu Trung Hieu, 2020. "Solution maps of polynomial variational inequalities," Journal of Global Optimization, Springer, vol. 77(4), pages 807-824, August.
    14. 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.
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    Cited by:

    1. Tong-tong Shang & Guo-ji Tang, 2023. "Mixed polynomial variational inequalities," Journal of Global Optimization, Springer, vol. 86(4), pages 953-988, August.
    2. 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.

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