Stochastic Nonlinear Complementarity Problem and?Applications to?Traffic Equilibrium under?Uncertainty

The expected residual minimization (ERM) formulation for the stochastic nonlinear complementarity problem (SNCP) is studied in this paper. We show that the involved function is a stochastic R ₀ function if and only if the objective function in the ERM formulation is coercive under a mild assumption. Moreover, we model the traffic equilibrium problem (TEP) under uncertainty as SNCP and show that the objective function in the ERM formulation is a stochastic R ₀ function. Numerical experiments show that the ERM-SNCP model for TEP under uncertainty has various desirable properties. This work was partially supported by a Grant-in-Aid from the Japan Society for the Promotion of Science. The authors thank Professor Guihua Lin for pointing out an error in Proposition 2.1 on an earlier version of this paper. The authors are also grateful to the referees for their insightful comments.