Skip to main content
SpringerLink
Log in

New improved error bounds for the linear complementarity problem

  • Published:
Mathematical Programming Submit manuscript

Abstract

New local and global error bounds are given for both nonmonotone and monotone linear complementarity problems. Comparisons of various residuals used in these error bounds are given. A possible candidate for a “best” error bound emerges from our comparisons as the sum of two natural residuals.

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

Access this article

Log in via an institution

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. R.W. Cottle, J.-S. Pang and R.E. Stone,The Linear Complementarity Problem (Academic Press, New York, 1992).

    Google Scholar 

  2. Z.-Q. Luo, O.L. Mangasarian, J. Ren and M.V. Solodov, “New error bounds for the linear complementarity problem,”Mathematics of Operations Research, 19(3) (1994).

  3. Z.-Q. Luo and P. Tseng, “Error bound and the convergence analysis of matrix splitting algorithms for the affine variational inequality problem,”SIAM Journal in Optimization 2 (1992) 43–54.

    Google Scholar 

  4. O.L. Mangasarian and T.-H. Shiau, “Error bounds for monotone linear complementarity problems,”Mathematical Programming 36 (1986) 81–89.

    Google Scholar 

  5. O.L. Mangasarian, “Error bounds for nondegenerate monotone linear complementarity problems,”Mathematical Programming 48 (1990) 437–445.

    Google Scholar 

  6. O.L. Mangasarian, “Global error bounds for monotone affine variational inequality problems,”Linear Algebra and Its Applications 174 (1992) 153–163.

    Google Scholar 

  7. R. Mathias and J.-S. Pang, “Error bounds for the linear complementarity problem with aP-matrix,”Linear Algebra and Applications 132 (1990) 123–136.

    Google Scholar 

  8. K.G. Murty,Linear Complementarity, Linear and Nonlinear Programming (Heldermann Verlag, Berlin, 1988).

    Google Scholar 

  9. J.-S. Pang, “Inexact newton methods for the nonlinear complementarity problem,”Mathematical Programming 36 (1986) 54–71.

    Google Scholar 

  10. S.M. Robinson, “Some continuity properties of polyhedral multifunctions,”Mathematical Programming Study 14 (1981) 206–214.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer Sciences Department, University of Wisconsin, 1210 West Dayton Street, 53706, Madison, WI, USA

    O. L. Mangasarian & J. Ren

Authors
  1. O. L. Mangasarian
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Ren
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This material is based on research supported by Air Force Office of Scientific Research Grant AFOSR-89-0410 and National Science Foundation Grant CCR-9101801.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mangasarian, O.L., Ren, J. New improved error bounds for the linear complementarity problem. Mathematical Programming 66, 241–255 (1994). https://doi.org/10.1007/BF01581148

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01581148

Keywords

Search

Navigation