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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 219478, 15 pages
http://dx.doi.org/10.1155/2012/219478
Research Article

The Solution Set Characterization and Error Bound for the Extended Mixed Linear Complementarity Problem

1School of Sciences, Linyi University, Linyi, Shandong 276005, China
2School of Management Science, Qufu Normal University, Rizhao, Shandong 276800, China

Received 19 September 2012; Accepted 8 December 2012

Academic Editor: Jian-Wen Peng

Copyright © 2012 Hongchun Sun and Yiju Wang. 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. R. W. Cottle, J.-S. Pang, and R. E. Stone, The Linear Complementarity Problem, Academic Press, New York, NY, USA, 1992. View at Zentralblatt MATH · View at MathSciNet
  2. F. Facchinei and J. S. Pang, Finite-Dimensional Variational Inequality and Complementarity Problems, Springer, New York, NY, USA, 2003.
  3. M. C. Ferris and J. S. Pang, “Engineering and economic applications of complementarity problems,” Society for Industrial and Applied Mathematics, vol. 39, no. 4, pp. 669–713, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. L. Walras, Elements of Pure Economics, George Allen and Unwin, London, UK, 1954.
  5. S. Karamardian, “Generalized complementarity problem,” Journal of Optimization Theory and Applications, vol. 8, pp. 161–168, 1971. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. G. J. Habetler and A. L. Price, “Existence theory for generalized nonlinear complementarity problems,” Journal of Optimization Theory and Applications, vol. 7, pp. 223–239, 1971. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. O. L. Mangasarian and T. H. Shiau, “Error bounds for monotone linear complementarity problems,” Mathematical Programming, vol. 36, no. 1, pp. 81–89, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. O. L. Mangasarian, “Error bounds for nondegenerate monotone linear complementarity problems,” Mathematical Programming, vol. 48, no. 3, pp. 437–445, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. J.-S. Pang, “Error bounds in mathematical programming,” Mathematical Programming, vol. 79, no. 1–3, pp. 299–332, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. Z.-Q. Luo, O. L. Mangasarian, J. Ren, and M. V. Solodov, “New error bounds for the linear complementarity problem,” Mathematics of Operations Research, vol. 19, no. 4, pp. 880–892, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. O. L. Mangasarian and J. Ren, “New improved error bounds for the linear complementarity problem,” Mathematical Programming, vol. 66, no. 2, pp. 241–255, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. R. Mathias and J.-S. Pang, “Error bounds for the linear complementarity problem with a P-matrix,” Linear Algebra and its Applications, vol. 132, pp. 123–136, 1990. View at Publisher · View at Google Scholar · View at MathSciNet
  13. A. J. Hoffman, “On approximate solutions of systems of linear inequalities,” Journal of Research of the National Bureau of Standards, vol. 49, pp. 263–265, 1952. View at Publisher · View at Google Scholar · View at MathSciNet
  14. J. Zhang and N. Xiu, “Global s-type error bound for the extended linear complementarity problem and applications,” Mathematical Programming B, vol. 88, no. 2, pp. 391–410, 2000. View at Publisher · View at Google Scholar · View at MathSciNet