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Randomized Kaczmarz methods for tensor complementarity problems

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Abstract

In this paper, we equivalently reformulate the tensor complementarity problem as a system of fixed point equations. Based on this system, we propose the (extend) randomized Kaczmarz methods for solving the tensor complementarity problem associated with nonnegative \(\mathcal {P}\)-tensors and nonsingular \(\mathcal {M}\)-tensors. We also analyze the upper bounds of the mean squared error and the estimate of the convergence rate for these two iterative methods. The computer simulation results further substantiate that the presented two randomized Kaczmarz type methods can be used to solve TCP with these two cases of tensors.

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Acknowledgements

We thank the editor and two anonymous reviewers for their detailed and helpful comments.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Hexi University, Zhangye, 734000, People’s Republic of China

    Xuezhong Wang

  2. School of Mathematics, Southwestern University of Finance and Economics, Chengdu, 611130, People’s Republic of China

    Maolin Che

  3. School of Mathematical Sciences and Shanghai Key Laboratory of Contemporary Applied Mathematics, Fudan University, Shanghai, 200433, People’s Republic of China

    Yimin Wei

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  1. Xuezhong Wang
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Correspondence to Maolin Che.

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Xuezhong Wang: This author is supported by the National Natural Science Foundation of China under Grant 12061032; Start-Up Fund of Doctoral Research, Hexi University. Partial work was finished when this author visited Key Laboratory of Mathematics for Nonlinear Sciences at Fudan University.

Maolin Che: This author is supported by the National Natural Science Foundation of China under Grants 12061032 and 11901471.

Yimin Wei: This author is supported by the National Natural Science Foundation of China under Grant 11771099, Innovation Program of Shanghai Municipal Education Commission and Shanghai Municipal Science and Technology Commission under Grant 22WZ2501900.

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Wang, X., Che, M. & Wei, Y. Randomized Kaczmarz methods for tensor complementarity problems. Comput Optim Appl 82, 595–615 (2022). https://doi.org/10.1007/s10589-022-00382-y

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