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Asymptotic Analysis for One-Stage Stochastic Linear Complementarity Problems and Applications

Author

Listed:
  • Shuang Lin

    (Department of Basic Courses Teaching, Dalian Polytechnic University, Dalian 116034, China)

  • Jie Zhang

    (School of Mathematics, Liaoning Normal University, Dalian 116029, China)

  • Chen Qiu

    (School of Mathematics, Liaoning Normal University, Dalian 116029, China)

Abstract

One-stage stochastic linear complementarity problem (SLCP) is a special case of a multi-stage stochastic linear complementarity problem, which has important applications in economic engineering and operations management. In this paper, we establish asymptotic analysis results of a sample-average approximation (SAA) estimator for the SLCP. The asymptotic normality analysis results for the stochastic-constrained optimization problem are extended to the SLCP model and then the conditions, which ensure the convergence in distribution of the sample-average approximation estimator for the SLCP to multivariate normal with zero mean vector and a covariance matrix, are obtained. The results obtained are finally applied for estimating the confidence region of a solution for the SLCP.

Suggested Citation

  • Shuang Lin & Jie Zhang & Chen Qiu, 2023. "Asymptotic Analysis for One-Stage Stochastic Linear Complementarity Problems and Applications," Mathematics, MDPI, vol. 11(2), pages 1-14, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:482-:d:1037560
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    References listed on IDEAS

    as
    1. Alan J. King & R. Tyrrell Rockafellar, 1993. "Asymptotic Theory for Solutions in Statistical Estimation and Stochastic Programming," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 148-162, February.
    2. Xiaojun Chen & Masao Fukushima, 2005. "Expected Residual Minimization Method for Stochastic Linear Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 30(4), pages 1022-1038, November.
    3. Huifu Xu, 2010. "Sample Average Approximation Methods For A Class Of Stochastic Variational Inequality Problems," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 27(01), pages 103-119.
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