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A Fixed Point Iterative Method for Tensor Complementarity Problems

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Abstract

Tensor complementarity problem (TCP) has attracted many attentions in recent years. In this paper, we equivalently reformulate tensor complementarity problem as a fixed point equation. Based on the fixed point equation, projected fixed point iterative methods are proposed and corresponding convergence proofs on the fixed point iterative methods for the tensor complementarity problem associated with a power Lipschitz tensor are investigated. Furthermore, the monotone convergence analysis of the fixed point iteration method for the tensor complementarity problem involving an \({\mathcal {L}}\) tensor is given. Numerical examples are tested to illustrate the given approach.

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Acknowledgements

The author would like to thank the editor and two anonymous referees for their valuable comments and suggestions, which greatly improve the original manuscript. He also thanks Dr. Jianchao Bai for the discussion of numerical examples and Prof. Jicheng Li for the advice in Xi’an Jiaotong University.

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  1. School of Information Engineering, Sanming University, Sanming, 365004, Fujian, People’s Republic of China

    Ping-Fan Dai

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  1. Ping-Fan Dai
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Correspondence to Ping-Fan Dai.

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This work was supported by the National Natural Science Foundation of China (11671318) and the Natural Science Foundations of Fujian Province of China (2016J01028, 2017N0029).

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Dai, PF. A Fixed Point Iterative Method for Tensor Complementarity Problems. J Sci Comput 84, 49 (2020). https://doi.org/10.1007/s10915-020-01299-6

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  • DOI: https://doi.org/10.1007/s10915-020-01299-6

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