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Convergence of discrete approximation for differential linear stochastic complementarity systems

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Abstract

In this paper, we investigate a class of differential linear stochastic complementarity system consisting of an ordinary differential equation and a stochastic complementarity problem. The existence of solutions for such system is obtained under two cases of the coefficient matrix of the linear stochastic complementarity problem: P-matrix and positive semi-definite matrix. As for the first case, the sample average approximate method and time-stepping method are adopted to get the numerical solutions. Furthermore, a regularization approximation is introduced to the second case to ensure the uniqueness of solutions. The corresponding convergence analysis is conducted, and numerical examples are presented to illustrate the convergence results we derived. Finally, we provide numerical results which come from applications involving dynamic traffic flow problems to support our theorems.

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Acknowledgments

We would like to thank two referees for providing valuable comments and constructive suggestions. J. Luo thanks to the Joint PhD Programmes Leading to Dual Awards between Harbin Institute of Technology and The Hong Kong Polytechnic University. The authors J. Luo and X. Wang appreciate the financial support and research guidance of Professor Xiaojun Chen in the Department of Applied Mathematics of The Hong Kong Polytechnic University.

Funding

This work was supported by the National Natural Science Foundation of China under Grant No. 61573119, and an Innovative Research Project of Shenzhen under Grant No. KQJSCX20180328165509766.

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Authors and Affiliations

  1. School of Science, Harbin Institute of Technology (Shenzhen), Shenzhen, 518055, China

    Jianfeng Luo & Yi Zhao

  2. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China

    Jianfeng Luo & Xiaozhou Wang

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  1. Jianfeng Luo
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  2. Xiaozhou Wang
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  3. Yi Zhao
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Correspondence to Yi Zhao.

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Luo, J., Wang, X. & Zhao, Y. Convergence of discrete approximation for differential linear stochastic complementarity systems. Numer Algor 87, 223–262 (2021). https://doi.org/10.1007/s11075-020-00965-y

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