Skip to main content
Log in

On the Convergence Regions of Generalized Accelerated Overrelaxation Method for Linear Complementarity Problems

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

Abstract

In this paper, we use a generalized Accelerated Overrelaxation (GAOR) method and analyze the convergence of this method for solving linear complementarity problems. Furthermore, we improve on the convergence region of this method with acknowledgement of the maximum norm. A numerical example is also given, to illustrate the efficiency of our results.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1

Similar content being viewed by others

References

  1. Murty, K.G.: Linear Complementarity, Linear and Nonlinear Programming. Heldermann, Berlin (1988)

    MATH  Google Scholar 

  2. Cottle, R.W., Pang, J.S., Stone, R.E.: The Linear Complementarity Problem. Academic Press, London (1992)

    MATH  Google Scholar 

  3. Xu, M.H., Luan, G.F.: A rapid algorithm for a class of linear complementarity problems. Appl. Math. Comput. 188, 1647–1655 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  4. Chakraborty, B., Biswal, M.P., Nanda, S.: Solution of parametric vertical block linear complementarity problems. Int. J. Comput. Math. 84, 325–332 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  5. Li, D.H., Nie, Y.Y., Zeng, J.P., Li, Q.N.: Conjugate gradient method for the linear complementarity problem with S-matrix. Math. Comput. Model. 48, 918–928 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Dehghan, M., Hajarian, M.: Convergence of SSOR methods for linear complementarity problems. Oper. Res. Lett. 37, 219–223 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. Bai, Z.Z.: Modulus-based matrix splitting iteration methods for linear complementarity problems. Numer. Linear Algebra Appl. 17, 917–933 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  8. Amri, A., Seeger, A.: Spectral analysis of coupled linear complementarity problems. Linear Algebra Appl. 432, 2507–2523 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  9. Lesaja, G., Roos, C.: Kernel-based interior-point methods for monotone linear complementarity problems over symmetric cones. J. Optim. Theory Appl. 150, 444–474 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  10. Saberi Najafi, H., Edalatpanah, S.A.: On the two SAOR iterative formats for solving linear complementarity problems. I. J. Inf. Technol. Comput. Sci. 5, 19–24 (2011)

    Google Scholar 

  11. Li, Y., Dai, P.: Generalized AOR methods for linear complementarity problem. Appl. Math. Comput. 188, 7–18 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  12. Bai, Z.Z., Evans, D.J.: Matrix multisplitting relaxation methods for linear complementarity problems. Int. J. Comput. Math. 63, 309–326 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  13. James, K.R.: Convergence of matrix iterations subject to diagonal dominance. SIAM J. Numer. Anal. 12, 478–484 (1973)

    Article  Google Scholar 

  14. Herceg, D., Cvetković, L.: On an iterative method for a system of equations. Zb. Rad. Prir.- Mat. Fak., Ser. Mat. 20, 11–15 (1990)

    MATH  Google Scholar 

  15. Song, Y.Z.: On the convergence of the generalized AOR method. Linear Algebra Appl. 256, 199–218 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  16. Varga, R.S.: Matrix Iterative Analysis, 2nd edn. Springer, Berlin (2000)

    Book  MATH  Google Scholar 

  17. Berman, A., Plemmons, R.J.: Nonnegative Matrices in the Mathematical Sciences, 3rd edn. SIAM, Philadelphia (1994)

    Book  MATH  Google Scholar 

  18. Xinmin, W.: Convergence for the MSOR iterative method applied to H-matrices. Appl. Numer. Math. 21, 469–479 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  19. Cvetković, Lj., Rapajić, S.: How to improve MAOR method convergence area for linear complementarity problems. Appl. Math. Comput. 162, 577–584 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  20. Cvetković, Lj., Kostić, V., Varga, R.: A new Geršgorin-type eigenvalue inclusion area. Electron. Trans. Numer. Anal. 18, 73–80 (2004)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to S. A. Edalatpanah.

Additional information

Communicated by Fabian Flores-Bazan.

Dedicated to the memory of Parviz Shahriari.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Saberi Najafi, H., Edalatpanah, S.A. On the Convergence Regions of Generalized Accelerated Overrelaxation Method for Linear Complementarity Problems. J Optim Theory Appl 156, 859–866 (2013). https://doi.org/10.1007/s10957-012-0135-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10957-012-0135-1

Keywords

Navigation