[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

Further Discussion on the Error Bound for Generalized Linear Complementarity Problem over a Polyhedral Cone

  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

In this paper, we consider the global error bound for the generalized linear complementarity problem over a polyhedral cone (GLCP). Based on the new transformation of the problem, we establish its global error bound under milder conditions, which improves the result obtained by Sun and Wang (2009) for GLCP by weakening the assumption.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Andreani, R., Friedlander, A., Santos, S.A.: On the resolution of the generalized nonlinear complementarity problem. SIAM J. Optim. 12, 303–321 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  2. Wang, Y.J., Ma, F.M., Zhang, J.Z.: A nonsmooth L–M method for solving the generalized nonlinear complementarity problem over a polyhedral cone. Appl. Math. Optim. 52(1), 73–92 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  3. Zhang, X.Z., Ma, F.M., Wang, Y.J.: A Newton-type algorithm for generalized linear complementarity problem over a polyhedral cone. Appl. Math. Comput. 169, 388–401 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  4. Facchinei, F., Pang, J.S.: Finite-Dimensional Variational Inequality and Complementarity Problems. Springer, New York (2003)

    Google Scholar 

  5. Pang, J.S.: Error bounds in mathematical programming. Math. Program. 79, 299–332 (1997)

    MATH  Google Scholar 

  6. Sun, H.C., Wang, Y.J., Qi, L.Q.: Global error bound for the generalized linear complementarity problem over a polyhedral cone. J. Optim. Theory Appl. 142, 417–429 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. Mangasarian, O.L.: Error bounds for nondegenerate monotone linear complementarity problems. Math. Program. 48, 437–445 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  8. Horn, R.A., Johnson, C.R.: Topics in Matrix Analysis. Cambridge University Press, Cambridge (1991)

    Book  MATH  Google Scholar 

  9. Xiu, N.H., Zhang, J.Z.: Global projection-type error bound for general variational inequalities. J. Optim. Theory Appl. 112(1), 213–228 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  10. Hoffman, A.J.: On the approximate solutions of linear inequalities. J. Res. Natl. Bur. Stand. 49(4), 263–265 (1952)

    Article  Google Scholar 

  11. Yamashita, N., Fukushima, M.: On the rate of convergence of the Levenberg–Marquardt method. Computing, Suppl. 15, 237–249 (2001)

    MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors wish to express their sincere thanks to the associated editor and two anonymous referees for their valuable suggestions and helpful comments which improve the presentation of the paper.

This work was supported by the Natural Science Foundation of China (Grant Nos. 11171180, 11101303), and Specialized Research Fund for the doctoral Program of Chinese Higher Education (20113705110002), and Shandong Provincial Natural Science Foundation (ZR2010AL005, ZR2011FL017).

Author information

Authors and Affiliations

  1. School of Sciences, Linyi University, Linyi, 276005, Shandong, China

    Hongchun Sun

  2. School of Management Science, Qufu Normal University, Rizhao, 276800, Shandong, China

    Yiju Wang

Authors
  1. Hongchun Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yiju Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yiju Wang.

Additional information

Communicated by Nobuo Yamashita.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sun, H., Wang, Y. Further Discussion on the Error Bound for Generalized Linear Complementarity Problem over a Polyhedral Cone. J Optim Theory Appl 159, 93–107 (2013). https://doi.org/10.1007/s10957-013-0290-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10957-013-0290-z

Keywords

Search

Navigation