Convergence results of the ERM method for nonlinear stochastic variational inequality problems. (English) Zbl 1187.90295

Luo, M. J.; Lin, G. H.

J. Optim. Theory Appl. 142, No. 3, 569-581 (2009).

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.

Reviewer: Samir Kumar Neogy (New Delhi)

MSC:

90C33

Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)

Keywords:

residual functions; quasi-Monte Carlo methods; compact approximations

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