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Zbl 1163.90034
Zhang, C.; Chen, X.
Stochastic nonlinear complementarity problem and applications to traffic equilibrium under uncertainty. (English)
[J] J. Optim. Theory Appl. 137, No. 2, 277-295 (2008). ISSN 0022-3239; ISSN 1573-2878/e

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 [{\it X. Chen} and {\it M. Fukushima}, Math. Oper. Res. 30, No. 4, 1022--1038 (2005; Zbl 1162.90527)] and [{\it G. Gürkan, A. Y. Özge} and {\it 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.
[Samir Kumar Neogy (New Delhi)]

MSC 2000:: *90C33 Complementarity problems
90C15 Stochastic programming
90B20 Highway traffic

Keywords: stochastic nonlinear complementarity problem; expected residual minimization; traffic equilibrium problem under uncertainty; stochastic $R_{0}$ function; expected value formulation

Citations: Zbl 0972.90079; Zbl 1162.90527

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