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Convergence results of the ERM method for nonlinear stochastic variational inequality problems. (English) Zbl 1187.90295
The authors consider the expected residual minimization (ERM) method proposed by M. J. Luo and G. H. Lin [J. Optim. Theory Appl. 140, 103–116 (2009; Zbl 1190.90112)] and continue to study the proposed method for a stochastic variational inequality problem. The function involved is assumed to be nonlinear in this paper. The authors 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, a compact approximation approach is presented for the case where the sample space is noncompact.

MSC:
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
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