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Expected Residual Minimization Method for Stochastic Variational Inequality Problems

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  • M. J. Luo

    (Dalian University of Technology)

  • G. H. Lin

    (Dalian University of Technology)

Abstract

This paper considers a stochastic variational inequality problem (SVIP). We first formulate SVIP as an optimization problem (ERM problem) that minimizes the expected residual of the so-called regularized gap function. Then, we focus on a SVIP subclass in which the function involved is assumed to be affine. We study the properties of the ERM problem and propose a quasi-Monte Carlo method for solving the problem. Comprehensive convergence analysis is included as well.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:140:y:2009:i:1:d:10.1007_s10957-008-9439-6
    DOI: 10.1007/s10957-008-9439-6
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    References listed on IDEAS

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    1. Daniel De Wolf & Yves Smeers, 1997. "A Stochastic Version of a Stackelberg-Nash-Cournot Equilibrium Model," Management Science, INFORMS, vol. 43(2), pages 190-197, 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. De Wolf, D. & Smeers, Y., 1997. "A stochastic version of a Stackelberg-Nash-Cournot equilibrium model," LIDAM Reprints CORE 1257, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. 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.
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    Cited by:

    1. Xiao-Juan Zhang & Xue-Wu Du & Zhen-Ping Yang & Gui-Hua Lin, 2019. "An Infeasible Stochastic Approximation and Projection Algorithm for Stochastic Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 1053-1076, December.
    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. Min Li & Chao Zhang, 2020. "Two-Stage Stochastic Variational Inequality Arising from Stochastic Programming," Journal of Optimization Theory and Applications, Springer, vol. 186(1), pages 324-343, July.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Yanfang Zhang & Xiaojun Chen, 2014. "Regularizations for Stochastic Linear Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 163(2), pages 460-481, November.
    9. Yan Gu & Jianlin Jiang & Shun Zhang, 2023. "Distributionally robust Weber problem with uncertain demand," Computational Optimization and Applications, Springer, vol. 85(3), pages 705-752, July.

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