Stochastic Nonlinear Complementarity Problem and Applications to Traffic Equilibrium under Uncertainty

Abstract

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 R0 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 R0 function. Numerical experiments show that the ERM-SNCP model for TEP under uncertainty has various desirable properties.