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Linearized Methods for Tensor Complementarity Problems

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Abstract

In this paper, we first propose a linearized method for solving the tensor complementarity problem. The subproblems of the method can be solved by solving linear complementarity problems with a constant matrix. We show that if the initial point is appropriately chosen, then the generated sequence of iterates converges to a solution of the problem monotonically. We then propose a lower-dimensional equation method and establish its monotone convergence. The subproblems of the method are lower-dimensional systems of linear equations. At last, we do numerical experiments to test the proposed methods. The results show the efficiency of the proposed methods.

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Acknowledgements

The authors would like to thank two anonymous referees for their valuable comments. This paper was supported by the Chinese NSF Grant 11771157 and Hunan Provincial Education Department of China Grant 15C0359.

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Authors and Affiliations

  1. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, Guangdong, China

    Hong-Bo Guan & Dong-Hui Li

  2. School of Mathematics, Physics and Energy Engineering, Hunan Institute of Technology, Hengyang, 421002, Hunan, China

    Hong-Bo Guan

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  1. Hong-Bo Guan
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  2. Dong-Hui Li
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Correspondence to Dong-Hui Li.

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Communicated by Communicated by Liqun Qi.

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Guan, HB., Li, DH. Linearized Methods for Tensor Complementarity Problems. J Optim Theory Appl 184, 972–987 (2020). https://doi.org/10.1007/s10957-019-01627-3

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