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On the R0-Tensors and the Solution Map of Tensor Complementarity Problems

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  • Vu Trung Hieu

    (Phuong Dong University)

Abstract

Our purpose is to investigate several properties of the solution map of tensor complementarity problems. To do this, we focus on the R0-tensors and show some results on the local boundedness and the upper semicontinuity. Furthermore, by using a technique from semi-algebraic geometry, we obtain results on the finite-valuedness, the lower semicontinuity, and the local upper-Hölder stability of the map.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:181:y:2019:i:1:d:10.1007_s10957-018-1441-z
    DOI: 10.1007/s10957-018-1441-z
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    References listed on IDEAS

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    1. Shui-Lian Xie & Dong-Hui Li & Hong-Ru Xu, 2017. "An Iterative Method for Finding the Least Solution to the Tensor Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 175(1), pages 119-136, October.
    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. 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. 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.
    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. 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.
    7. 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.
    8. 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.
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    Cited by:

    1. Vu Trung Hieu, 2020. "Solution maps of polynomial variational inequalities," Journal of Global Optimization, Springer, vol. 77(4), pages 807-824, August.
    2. Zheng-Hai Huang & Liqun Qi, 2019. "Tensor Complementarity Problems—Part I: Basic Theory," Journal of Optimization Theory and Applications, Springer, vol. 183(1), pages 1-23, October.
    3. 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.
    4. 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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