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Method of weighted expected residual for solving stochastic variational inequality problems

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  • Lu, Fang
  • Li, Sheng-jie

Abstract

This paper is concerned in constructing a deterministic model for the stochastic affine variational inequality problems with nonlinear perturbation (for short, SVIPP) based on the convex combined expectations of the least absolute deviation and least squares about the so-called regularized gap function. We formulate SVIPP as a weighted expected residual minimization problem (in short, WERM). Some properties of the WERM problem are derived under suitable conditions. Moreover, we obtain a discrete approximation of WERM problem by applying the quasi-Monte Carlo method. The limiting behavior of optimal solutions and stationary points of the approximation problem are analyzed as well.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:269:y:2015:i:c:p:651-663
    DOI: 10.1016/j.amc.2015.07.115
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    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. 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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