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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 816528, 15 pages
Expected Residual Minimization Method for a Class of Stochastic Quasivariational Inequality Problems
Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China
Received 22 August 2012; Accepted 15 October 2012
Academic Editor: Xue-Xiang Huang
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.
- P. T. Harker, “Generalized Nash games and quasi-variational inequalities,” European Journal of Operational Research, vol. 54, pp. 81–94, 1991.
- 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.
- 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.
- 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.
- 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.
- 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.
- H. Fang, X. Chen, and M. Fukushima, “Stochastic matrix linear complementarity problems,” SIAM Journal on Optimization, vol. 18, no. 2, pp. 482–506, 2007.
- 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.
- 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.
- G. H. Lin and M. Fukushima, “New reformulations for stochastic nonlinear complementarity problems,” Optimization Methods & Software, vol. 21, no. 4, pp. 551–564, 2006.
- C. Ling, L. Qi, G. Zhou, and L. Caccetta, “The property of an expected residual function arising from stochastic complementarity problems,” Operations Research Letters, vol. 36, no. 4, pp. 456–460, 2008.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- K. Taji, “On gap functions for quasi-variational inequalities,” Abstract and Applied Analysis, vol. 2008, Article ID 531361, 7 pages, 2008.
- A. Auslender, Optimisation: Méthodes Numériques, Masson, Paris, France, 1976.
- M. Fukushima, “Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems,” Mathematical Programming, vol. 53, no. 1, pp. 99–110, 1992.
- P. Billingsley, Probability and Measure, John Wiley & Sons, New York, NY, USA, 1995.