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Error bound for the generalized complementarity problem with analytic functions

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Abstract

In this paper, we consider the global error bound for the generalized complementarity problem (GCP) with analytic functions. Based on the new technique, we establish computable global error bound under milder conditions, which refines the previously known results.

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References

  1. H. C. Sun. Error bound estimation for the generalized complementarity problem in engineering and economic equilibrium modeling. Advances in Wireless Networks and Information Systems, Lecture Notes in Electrical Engineering, vol. 72, pp. 227–233, 2010.

    Article  Google Scholar 

  2. S. C. Chiam, K. C. Tan, A. A. Mamum. Evolutionary multiobjective portfolio optimization in practical context. International Journal of Automation and Computing, vol.5, no. 1, pp. 67–80, 2008.

    Article  Google Scholar 

  3. P. S.V. Nataraj, M. Arounassalame. A new subdivision algorithm for the Bernstein polynomial approach to global optimization. International Journal of Automation and Computing, vol. 4, no. 4, pp. 342–352, 2007.

    Article  Google Scholar 

  4. H. C. Sun, Y. L. Dong. A new type of solution method for the generalized linear complementarity problem over a polyhedral cone. International Journal of Automation and Computing, vol. 6, no. 3, pp. 228–233, 2009.

    Article  MathSciNet  Google Scholar 

  5. F. Facchinei, J. S. Pang. Finite-dimensional Variational Inequality and Complementarity Problems, New York, USA: Springer, 2003.

    Google Scholar 

  6. Z. Q. Luo, O. L. Mangasarian, J. Ren, M. V. Solodov. New error bound for the linear complementarity problem. Mathematics of Operations Research, vol. 19, no. 4, pp. 880–892, 1994.

    Article  MathSciNet  MATH  Google Scholar 

  7. O. L. Mangasarian, J. Ren. New improved error bounds for the linear complementarity problem. Mathematic Programming, vol. 66, no. 1–3, pp. 241–255, 1994.

    Article  MathSciNet  MATH  Google Scholar 

  8. O. L. Mangasarian. Error bounds for nondegenerate monotone linear complementarity problems. Mathematic Programming, vol. 48, no. 1–3, pp. 437–445, 1990.

    Article  MathSciNet  MATH  Google Scholar 

  9. B. Chen. Error bounds for R 0-type and monotone nonlinear complementarity problems. Journal of Optimization Theory and Applications, vol. 108, no. 2, pp. 297–316, 2001.

    Article  MathSciNet  MATH  Google Scholar 

  10. N. H. Xiu, J. Z. Zhang. Global projection-type error bound for general variational inequalities. Journal of Optimization Theory and Applications, vol. 112, no. 1, pp. 213–228, 2002.

    Article  MathSciNet  MATH  Google Scholar 

  11. H. C. Sun, Y. J. Wang, L. Q. Qi. Global error bound for the generalized linear complementarity problem over a polyhedral cone. Journal of Optimization Theory and Applications, vol. 142, no. 2, pp. 417–429, 2009.

    Article  MathSciNet  MATH  Google Scholar 

  12. Z. Q. Luo, J. S. Pang. Error bounds for analytic systems and their applications. Mathematic Programming, vol. 67, no. 1–3, pp. 1–28, 1994.

    Article  MathSciNet  MATH  Google Scholar 

  13. Y. J. Wang, N. H. Xiu. Theory and Algorithms for Nonlinear Programming, Xi’an, PRC: Shanxi Science and Technology Press, pp.170–171, 2004. (in Chinese)

    Google Scholar 

  14. A. J. Hoffman. On the approximate solutions of linear inequalities. Journal of Research of National Bureau of Standards, vol. 49, no. 4, pp. 263–265, 1952.

    Google Scholar 

  15. R. W. Cottle, J. S. Pang, R. E. Stone. The Linear Complementarity Problem, Boston, USA: Academic Press, pp.162–180, 1992.

    MATH  Google Scholar 

  16. Y. J. Wang, F. M. Ma, J. Z. Zhang. A nonsmooth L-M method for solving the generalized nonlinear complementarity problem over a polyhedral cone. Applied Mathematics and Optimization, vol. 52, no. 1, pp. 73–92, 2005.

    Article  MathSciNet  MATH  Google Scholar 

  17. N. Yamashita, M. Fukushima, On the rate of convergence of the Levenberg-Marquardt method. Computing Supplement, vol. 15, pp. 239–249, 2001.

    Article  MathSciNet  Google Scholar 

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Correspondence to Hong-Chun Sun.

Additional information

This work was supported by National Natural Science Foundation of China (Nos. 11171180 and 11101303), Specialized Research Fund for the Doctoral Program of Chinese Higher Education (No. 20113705110002), and Shandong Provincial Natural Science Foundation (Nos. ZR2010AL005 and ZR2011FL017).

Hong-Chun Sun received his B. Sc. degree in mathematics from Qufu Normal University (QNU), PRC in 1990, and received his M. Sc. degree in operations and cybernetics from QNU in 2005. Currently, he is professor in the School of Sciences at Linyi University, PRC.

His research interest includes nonlinear optimization.

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Sun, HC. Error bound for the generalized complementarity problem with analytic functions. Int. J. Autom. Comput. 9, 288–291 (2012). https://doi.org/10.1007/s11633-012-0646-0

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  • DOI: https://doi.org/10.1007/s11633-012-0646-0

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