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Stochastic nonlinear complementarity problem and applications to traffic equilibrium under uncertainty. (English) Zbl 1163.90034
This paper deals with the expected residual minimization (ERM) formulation for the stochastic nonlinear complementarity problem (SNCP). The solution set of ERM formulation for the SNCP is studied in this paper. The authors define stochastic ${R}_{0}$ function and 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. Finally, the traffic equilibrium problem (TEP) under uncertainty is modeled as SNCP and it is shown that the objective function in the ERM formulation is a stochastic ${R}_{0}$ function. See also [X. Chen and M. Fukushima, Math. Oper. Res. 30, No. 4, 1022–1038 (2005; Zbl 1162.90527)] and [G. Gürkan, A. Y. Özge and S. M. Robinson, Math. Program. 84, No. 2 (A), 313–333 (1999; Zbl 0972.90079)]. Numerical experimental results of the ERM formulation and the Expected Value (EV) formulation for TEP under uncertainty are also reported.
##### MSC:
 90C33 Complementarity and equilibrium problems; variational inequalities (finite dimensions) 90C15 Stochastic programming 90B20 Traffic problems
##### References:
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