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The Existence and Uniqueness of Solution of the Vertical Tensor Complementarity Problem

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  • Dan Wang

    (Xi’an Jiaotong University)

  • Jicheng Li

    (Xi’an Jiaotong University)

Abstract

For the vertical tensor complementarity problems (VTCPs) and generalized order polynomial complementarity problems (GOPCPs), we make contributions to analyzing some properties of solutions. We propose some types of block tensors mainly based on ER-tensor and P-function, respectively, and use these block tensors to investigate existence and uniqueness of solution of the VTCPs. We also propose conditions for the existence of solution to the VTCPs when all involved tensors are nonnegative. Under mild conditions, the boundeness of the solution set and uniqueness of the solution of the GOPCPs are discussed.

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  • Dan Wang & Jicheng Li, 2025. "The Existence and Uniqueness of Solution of the Vertical Tensor Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 206(3), pages 1-23, September.
    • Handle: RePEc:spr:joptap:v:206:y:2025:i:3:d:10.1007_s10957-025-02717-1
    DOI: 10.1007/s10957-025-02717-1
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    References listed on IDEAS

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    1. 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.
    2. 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.
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