Abstract
A method of convex combined expectations of the least absolute deviation and least squares about the so-called regularized gap function is proposed for solving nonlinear stochastic variational inequality problems (for short, NSVIP). The NSVIP is formulated as a weighted expected residual minimization problem (in short, WERM) in this way. Moreover, we present a discrete approximation of WERM problem by applying the quasi-Monte Carlo method when the sample space is compact, and a compact approximation approach for the case that the sample space is noncompact. The limiting behaviors of optimal solutions of the discrete approximation problem and the compact approximation are also analyzed, respectively.
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Acknowledgments
The authors would like to thank the Associate Editor and anonymous referees for their helpful comments which greatly improved the paper. This research was supported by the National Natural Science Foundation of China (Grant Numbers: 11171362, 11301567 and 11401058), Doctor of Ministry of Education (Doctoral Category) Foundation (Grant Number: 20120191110031) and Basic and Advanced Research Project of CQ CSTC (Grant Number: cstc2014jcyjA00044).
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Lu, F., Li, S. & Yang, J. Convergence analysis of weighted expected residual method for nonlinear stochastic variational inequality problems. Math Meth Oper Res 82, 229–242 (2015). https://doi.org/10.1007/s00186-015-0512-2
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DOI: https://doi.org/10.1007/s00186-015-0512-2