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Convergence Results of the ERM Method for Nonlinear Stochastic Variational Inequality Problems

Author

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  • M. J. Luo

    (Dalian University of Technology)

  • G. H. Lin

    (Dalian University of Technology)

Abstract

This paper considers the expected residual minimization (ERM) method proposed by Luo and Lin (J. Optim. Theory Appl. 140:103–116, 2009) for a class of stochastic variational inequality problems. Different from the work mentioned above, the function involved is assumed to be nonlinear in this paper. We first consider a quasi-Monte Carlo method for the case where the underlying sample space is compact and show that the ERM method is convergent under very mild conditions. Then, we suggest a compact approximation approach for the case where the sample space is noncompact.

Suggested Citation

  • M. J. Luo & G. H. Lin, 2009. "Convergence Results of the ERM Method for Nonlinear Stochastic Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 142(3), pages 569-581, September.
    • Handle: RePEc:spr:joptap:v:142:y:2009:i:3:d:10.1007_s10957-009-9534-3
    DOI: 10.1007/s10957-009-9534-3
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    References listed on IDEAS

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    1. 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.
    2. C. Zhang & X. Chen, 2008. "Stochastic Nonlinear Complementarity Problem and Applications to Traffic Equilibrium under Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 137(2), pages 277-295, May.
    3. M. J. Luo & G. H. Lin, 2009. "Expected Residual Minimization Method for Stochastic Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 140(1), pages 103-116, January.
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    Cited by:

    1. Lu, Fang & Li, Sheng-jie, 2015. "Method of weighted expected residual for solving stochastic variational inequality problems," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 651-663.
    2. Meiju Luo & Menghan Du & Yue Zhang, 2023. "Deterministic Bi-Criteria Model for Solving Stochastic Mixed Vector Variational Inequality Problems," Mathematics, MDPI, vol. 11(15), pages 1-19, August.
    3. Fang Lu & Shengjie Li & Jing Yang, 2015. "Convergence analysis of weighted expected residual method for nonlinear stochastic variational inequality problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 82(2), pages 229-242, October.
    4. Yong Zhao & Jin Zhang & Xinmin Yang & Gui-Hua Lin, 2017. "Expected Residual Minimization Formulation for a Class of Stochastic Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 175(2), pages 545-566, November.

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