Skip to main content
Log in

Feasible smooth method based on Barzilai–Borwein method for stochastic linear complementarity problem

  • Original Paper
  • Published:
Numerical Algorithms Aims and scope Submit manuscript

Abstract

In this paper, we propose a feasible smooth method based on Barzilai–Borwein (BB) for stochastic linear complementarity problem. It is based on the expected residual minimization (ERM) formulation for the stochastic linear complementarity problem. Numerical experiments show that the method is efficient.

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.

Similar content being viewed by others

References

  1. Chen, X., Fukushima, M.: Expected residual minimization method for stochastic linear complementarity problems. Math. Oper. Res. 30, 1022–1038 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  2. Chen, X., Zhang, C.: Robust solution of monotone stochastic linear complementarity problems. Math. Program. 117, 51–80 (2008)

    Article  Google Scholar 

  3. Fang, H., Cheng, X., Fukushima, M.: Stochastic R0 matrix linear complementarity problems. SIAM J. Optim. 18, 482–506 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  4. Zhou, G.L., Caccetta, L.: Feasible semismooth Newton method for a class of stochastic linear complementarity. J. Optim. Theory Appl. 139, 379–392 (2008)

    Article  MathSciNet  Google Scholar 

  5. Chen, B., Chen, X., Kanzow, C.: A penalized Fischer–Burmeister NCP-function. Math. Program. 88, 211–216 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  6. Facchinei, F., Pang, J.-S.: Finite-dimensional variational inequalities and complementarity problems (2003)

  7. Fischer, A.: Solution of monotone complementarity problems with locally lipschitzian functions. Math. Program. 76, 513–532 (1997)

    MATH  Google Scholar 

  8. Facchinei, F., Kanzow, C.: A nonsmooth inexact Newton method for the solution of large-scale nonlinear complementarity problems. Math. Program. 76, 493–512 (1997)

    MathSciNet  MATH  Google Scholar 

  9. Sun, D.: A regularization newton method for solving nonlinear complementarity problems. Appl. Math. Optim. 40, 315–339 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  10. Sun, D., Womersley, R.S., Qi, H.: A feasible semismooth asymptotically Newton method for mixed complementarity problems. Math. Program. 94, 167–187 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  11. Ferris, M.C., Pang, J.S.S.: Engineering and economic applications of complementarity problems. SIAM Rev. 39, 669–713 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  12. Gürkan, G., Özge, A.Y., Robinson, S.M.: Sample-path solution of stochastic variational inequalities. Math. Program. 84, 313–333 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  13. Lin, G.-H., Fukushima, M.: New reformulations for stochastic nonlinear complementarity problems. Optim. Methods Softw. 21, 551–564 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  14. Lin, G.-H., Chen, X., Fukushima, M.: New restricted NCP functions and their applications to stochastic NCP and stochastic MPEC. Optimization 56, 641–653 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  15. Kleywegt, A.J., Shapiro, A., de Mello, T.H.: The sample average approximation method for stochastic discrete optimization. SIAM J. Optim. 12, 479–502 (2002)

    Article  Google Scholar 

  16. Zhang, C., Chen, X.: Smoothing projected gradient method and its application to stochastic linear complementarity problems. SIAM J. Optim. 20, 627–649 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  17. Barzilai, J., Borwein, J.M.: Two-point step size gradient methods. IMA J. Numer. Anal. 8, 141–148 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  18. Hager, W., Mair, B.A., Zhang, H.: An affine-scaling interior-point CBB method for box-constrained optimization. Math. Program. 119, 1–32 (2009)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xiangli Li.

Additional information

This work is supported by the Fundamental Research Funds for the Central Universities (JY10000970004) and by the Key Projects of Baoji University of Arts and Sciences (60603098).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, X., Liu, H. & Sun, X. Feasible smooth method based on Barzilai–Borwein method for stochastic linear complementarity problem. Numer Algor 57, 207–215 (2011). https://doi.org/10.1007/s11075-010-9424-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11075-010-9424-7

Keywords

Navigation