Journal of Optimization Theory and Applications

, Volume 137, Issue 2, pp 277-295

First online:

Stochastic Nonlinear Complementarity Problem and Applications to Traffic Equilibrium under Uncertainty

  • C. ZhangAffiliated withDepartment of Applied Mathematics, Beijing Jiaotong University
  • , X. ChenAffiliated withDepartment of Applied Mathematics, The Hong Kong Polytechnic University Email author 

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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.


Stochastic nonlinear complementarity problem Expected residual minimization Traffic equilibrium problem under uncertainty Stochastic R 0 function