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Strict feasibility for the polynomial complementarity problem

Author

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  • Xue-liu Li

    (Guangxi Minzu University)

  • Guo-ji Tang

    (Guangxi Minzu University)

Abstract

In the present paper, the strict feasibility of the polynomial complementarity problem (PCP) is investigated. To this end, as a generalization of the concept of S-tensor, a concept of S-tensor tuple is introduced. Some properties of S-tensor tuples are investigated. In particular, several conditions are proposed to judge whether a tensor tuple is an S-tensor tuple or not. Then, based on the S-tensor tuple, the strict feasibility of PCP is investigated.

Suggested Citation

  • Xue-liu Li & Guo-ji Tang, 2024. "Strict feasibility for the polynomial complementarity problem," Journal of Global Optimization, Springer, vol. 89(1), pages 57-71, May.
    • Handle: RePEc:spr:jglopt:v:89:y:2024:i:1:d:10.1007_s10898-023-01339-z
    DOI: 10.1007/s10898-023-01339-z
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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. Yisheng Song & Wei Mei, 2018. "Structural Properties of Tensors and Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 176(2), pages 289-305, February.
    3. 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.
    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. Ge Li & Jicheng Li, 2023. "Improved Fixed Point Iterative Methods for Tensor Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 199(2), pages 787-804, November.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
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