A lower dimensional linear equation approach to the M-tensor complementarity problem


We are interested in finding a solution to the tensor complementarity problem with a strong M-tensor, which we call the M-tensor complementarity problem. We propose a lower dimensional linear equation approach to solve that problem. At each iteration, only a lower dimensional system of linear equation needs to be solved. The coefficient matrices of the lower dimensional linear systems are independent of the iteration after finitely many iterations. We show that starting from zero or some nonnegative point, the method generates a sequence of iterates that converges to a solution of the problem monotonically. We then make an improvement to the method and establish its monotone convergence. At last, we do numerical experiments to test the proposed methods. The results positively support the proposed methods.

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Supported by the NSF of China Grant 11771157, 11801184, the NSF of Guangdong Province Grant No. 2020B1515310013, and the Education Department of Hunan Province grant No. 20C0559.

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Correspondence to Hong-Bo Guan.

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Li, DH., Chen, CD. & Guan, HB. A lower dimensional linear equation approach to the M-tensor complementarity problem. Calcolo 58, 5 (2021). https://doi.org/10.1007/s10092-021-00397-7

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  • M-tensor complementarity problem
  • Lower dimensional linear equation approach
  • Monotone convergence

Mathematics Subject Classification

  • 15A69
  • 65K10
  • 90C33