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On Q-tensors

Author

Listed:
  • Parthasarathy T

    (Chennai Mathematical Institute)

  • Ravindran G

    (Indian Statistical Institute)

  • Sunil Kumar

    (Indian Statistical Institute)

Abstract

A tensor is a multidimensional analog of a matrix. Q-matrices have been extensively studied in the context of the linear complementarity problem due to their solvability for any given vector q. In this article, we extend certain results of Q-matrices to Q-tensors. Characterizing a tensor as a Q-tensor remains a challenging problem in the literature. In this article, we establish sufficient conditions under which a principal subtensor of a Q-tensor is also a Q-tensor. Furthermore, we extend a result due to Huang, Suo and Wang. It is well-known that R-tensors are Q-tensors, although the converse does not always hold. We also provide conditions under which a Q-tensor can be classified as an R-tensor. Additionally, we prove several results pertaining to positive (nonnegative) tensors.

Suggested Citation

  • Parthasarathy T & Ravindran G & Sunil Kumar, 2025. "On Q-tensors," Journal of Optimization Theory and Applications, Springer, vol. 207(2), pages 1-13, November.
    • Handle: RePEc:spr:joptap:v:207:y:2025:i:2:d:10.1007_s10957-025-02796-0
    DOI: 10.1007/s10957-025-02796-0
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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. 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.
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