Journal of Optimization Theory and Applications

, Volume 142, Issue 3, pp 569–581

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


DOI: 10.1007/s10957-009-9534-3

Cite this article as:
Luo, M.J. & Lin, G.H. J Optim Theory Appl (2009) 142: 569. doi:10.1007/s10957-009-9534-3


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.


Stochastic variational inequalitiesResidual functionsQuasi-Monte Carlo methodsCompact approximations

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of Applied MathematicsDalian University of TechnologyDalianChina