Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2013, Article ID 497586, 7 pages
http://dx.doi.org/10.1155/2013/497586
Research Article

Properties of Expected Residual Minimization Model for a Class of Stochastic Complementarity Problems

1School of Mathematics, Liaoning University, Liaoning 110036, China
2School of Sciences, Shenyang University, Liaoning 110044, China

Received 31 January 2013; Revised 10 May 2013; Accepted 14 May 2013

Academic Editor: Farhad Hosseinzadeh Lotfi

Copyright © 2013 Mei-Ju Luo and Yuan Lu. 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. F. Facchinei and J. S. Pang, Finite-Dimensional Variational Inequalities and Complementarity Problems, Springer, New York, NY, USA, 2003.
  2. R. W. Cottle, J.-S. Pang, and R. E. Stone, The Linear Complementarity Problem, Computer Science and Scientific Computing, Academic Press, Boston, Mass, USA, 1992. View at Zentralblatt MATH · View at MathSciNet
  3. 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 · View at MathSciNet
  4. G. Gürkan, A. Y. Özge, and S. M. Robinson, “Sample-path solution of stochastic variational inequalities,” Mathematical Programming, vol. 84, no. 2, pp. 313–333, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  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 · View at MathSciNet
  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 · View at MathSciNet
  7. P. Tseng, “Growth behavior of a class of merit functions for the nonlinear complementarity problem,” Journal of Optimization Theory and Applications, vol. 89, no. 1, pp. 17–37, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. H. Fang, X. Chen, and M. Fukushima, “Stochastic R0 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 · View at MathSciNet
  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 · View at MathSciNet
  10. C. Ling, L. Qi, G. Zhou, and L. Caccetta, “The SC1 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 · View at MathSciNet
  11. 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 · View at MathSciNet
  12. C. Zhang and X. Chen, “Smoothing projected gradient method and its application to stochastic linear complementarity problems,” SIAM Journal on Optimization, vol. 20, no. 2, pp. 627–649, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. G. L. Zhou and L. Caccetta, “Feasible semismooth Newton method for a class of stochastic linear complementarity problems,” Journal of Optimization Theory and Applications, vol. 139, no. 2, pp. 379–392, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  14. X. L. Li, H. W. Liu, and Y. K. Huang, “Stochastic P matrix and P0 matrix linear complementarity problem,” Journal of Systems Science and Mathematical Sciences, vol. 31, no. 1, pp. 123–128, 2011. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. K. L. Chung, A Course in Probability Theory, Academic Press, New York, NY, USA, 2nd edition, 1974. View at MathSciNet
  16. B. Chen and P. T. Harker, “Smooth approximations to nonlinear complementarity problems,” SIAM Journal on Optimization, vol. 7, no. 2, pp. 403–420, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet