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An Iterative Method for Horizontal Tensor Complementarity Problems

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Abstract

In this paper, we focus on a class of horizontal tensor complementarity problems (HTCPs). By introducing the block representative tensor, we show that finding a solution of HTCP is equivalent to finding a nonnegative solution of a related tensor equation. We establish the theory of the existence and uniqueness of solution of HTCPs under the proper assumptions. In particular, in the case of the concerned block representative tensor possessing the strong M-property, we propose an algorithm to solve HTCPs by efficiently exploiting the beneficial properties of block representative tensor, and show that the iterative sequence generated by the algorithm is monotone decreasing and converges to a solution of HTCPs. The final numerical experiments verify the correctness of the theory in this paper and show the effectiveness of the proposed algorithm.

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Acknowledgements

This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 12171357 and 12371309).

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Correspondence to Yong Wang.

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Communicated by Emanuele Galligani.

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Sun, C., Wang, Y. & Huang, ZH. An Iterative Method for Horizontal Tensor Complementarity Problems. J Optim Theory Appl 202, 854–877 (2024). https://doi.org/10.1007/s10957-024-02450-1

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