Copyright © 2012 Hui-Qiang Ma and Nan-Jing Huang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

1. P. T. Harker, “Generalized Nash games and quasi-variational inequalities,” European Journal of Operational Research, vol. 54, pp. 81–94, 1991.
2. K. Kubota and M. Fukushima, “Gap function approach to the generalized Nash equilibrium problem,” Journal of Optimization Theory and Applications, vol. 144, no. 3, pp. 511–531, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
3. J. S. Pang and M. Fukushima, “Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games,” Computational Management Science, vol. 2, no. 1, pp. 21–56, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
4. R. P. Agdeppa, N. Yamashita, and M. Fukushima, “Convex expected residual models for stochastic affine variational inequality problems and its application to the traffic equilibrium problem,” Pacific Journal of Optimization, vol. 6, no. 1, pp. 3–19, 2010. View at Zentralblatt MATH
5. X. Chen and M. Fukushima, “Expected residual minimization method for stochastic linear complementarity problems,” Mathematics of Operations Research, vol. 30, no. 4, pp. 1022–1038, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
6. X. Chen, C. Zhang, and M. Fukushima, “Robust solution of monotone stochastic linear complementarity problems,” Mathematical Programming, vol. 117, no. 1-2, pp. 51–80, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
7. H. Fang, X. Chen, and M. Fukushima, “Stochastic $R_0$ matrix linear complementarity problems,” SIAM Journal on Optimization, vol. 18, no. 2, pp. 482–506, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
8. H. Jiang and H. Xu, “Stochastic approximation approaches to the stochastic variational inequality problem,” IEEE Transactions on Automatic Control, vol. 53, no. 6, pp. 1462–1475, 2008. View at Publisher · View at Google Scholar
9. G. H. Lin, X. Chen, and M. Fukushima, “New restricted NCP functions and their applications to stochastic NCP and stochastic MPEC,” Optimization, vol. 56, no. 5-6, pp. 641–953, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
10. G. H. Lin and M. Fukushima, “New reformulations for stochastic nonlinear complementarity problems,” Optimization Methods & Software, vol. 21, no. 4, pp. 551–564, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
11. C. Ling, L. Qi, G. Zhou, and L. Caccetta, “The $S{C}^1$ property of an expected residual function arising from stochastic complementarity problems,” Operations Research Letters, vol. 36, no. 4, pp. 456–460, 2008. View at Publisher · View at Google Scholar
12. M. J. Luo and G. H. Lin, “Expected residual minimization method for stochastic variational inequality problems,” Journal of Optimization Theory and Applications, vol. 140, no. 1, pp. 103–116, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
13. M. J. Luo and G. H. Lin, “Convergence results of the ERM method for nonlinear stochastic variational inequality problems,” Journal of Optimization Theory and Applications, vol. 142, no. 3, pp. 569–581, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
14. M. Z. Wang, M. M. Ali, and G. H. Lin, “Sample average approximation method for stochastic complementarity problems with applications to supply chain supernetworks,” Journal of Industrial and Management Optimization, vol. 7, no. 2, pp. 317–345, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
15. H. Xu, “Sample average approximation methods for a class of stochastic variational inequality problems,” Asia-Pacific Journal of Operational Research, vol. 27, no. 1, pp. 103–119, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
16. C. Zhang and X. Chen, “Stochastic nonlinear complementarity problem and applications to traffic equilibrium under uncertainty,” Journal of Optimization Theory and Applications, vol. 137, no. 2, pp. 277–295, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
17. M. Fukushima, “A class of gap functions for quasi-variational inequality problems,” Journal of Industrial and Management Optimization, vol. 3, no. 2, pp. 165–171, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
18. K. Taji, “On gap functions for quasi-variational inequalities,” Abstract and Applied Analysis, vol. 2008, Article ID 531361, 7 pages, 2008. View at Publisher · View at Google Scholar
19. A. Auslender, Optimisation: Méthodes Numériques, Masson, Paris, France, 1976.
20. M. Fukushima, “Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems,” Mathematical Programming, vol. 53, no. 1, pp. 99–110, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
21. P. Billingsley, Probability and Measure, John Wiley & Sons, New York, NY, USA, 1995.