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Tensor Complementarity Problems with Finite Solution Sets

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  • K. Palpandi

    (Malaviya National Institute of Technology Jaipur)

  • Sonali Sharma

    (Malaviya National Institute of Technology Jaipur)

Abstract

In this paper, we first extend the concept of non-degenerate matrices to tensors and we then study the finiteness properties of the solution set of non-degenerate tensor complementarity problems. When the involving tensor in the tensor complementarity problem is a positive linear combination of rank-one symmetric tensors, we show that the solution set of the tensor complementarity problem is convex if the underlying tensor is positive semidefinite, and the tensor complementarity problem has the globally uniqueness solvable property if the underlying tensor is positive definite. Finally, we prove that a symmetric P tensor with an additional condition has the globally uniqueness solvable property.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:190:y:2021:i:3:d:10.1007_s10957-021-01917-9
    DOI: 10.1007/s10957-021-01917-9
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    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. 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.
    6. 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.
    7. 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.
    8. Zheng-Hai Huang & Liqun Qi, 2019. "Tensor Complementarity Problems—Part III: Applications," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 771-791, December.
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    Cited by:

    1. 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.

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