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Tensor Complementarity Problems with Finite Solution Sets

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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.

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Acknowledgements

The authors are very thankful to the anonymous referees for their useful comments and valuable suggestions which helped us to improve this manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Malaviya National Institute of Technology Jaipur, Jaipur, Rajasthan, 302017, India

    K. Palpandi & Sonali Sharma

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  1. K. Palpandi
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  2. Sonali Sharma
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Correspondence to K. Palpandi.

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Communicated by Liqun Qi.

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Palpandi, K., Sharma, S. Tensor Complementarity Problems with Finite Solution Sets. J Optim Theory Appl 190, 951–965 (2021). https://doi.org/10.1007/s10957-021-01917-9

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  • DOI: https://doi.org/10.1007/s10957-021-01917-9

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