Skip to main content
SpringerLink
Log in

Stability of the linear complementarity problem at a solution point

  • Published:
Mathematical Programming Submit manuscript

Abstract

In this paper we study the behavior of a solution of the linear complementarity problem when data are perturbed. We give characterizations of strong stability of the linear complementarity problem at a solution. In the case of stability we give sufficient and necessary conditions.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. Aganagic and R.W. Cottle, “A note onQ-matrices”,Mathematical Programming 16 (1979) 374–377.

    Article  MATH  MathSciNet  Google Scholar 

  2. R.D. Doverspike, “Some perturbation results for the linear complementarity problem”,Mathematical Programming 23 (1982) 181–192.

    Article  MATH  MathSciNet  Google Scholar 

  3. R.D. Doverspike and C.E. Lemke, “A partial characterization of a class of matrices defined by solutions to the linear complementarity problem”,Mathematics of Operations Research 7 (1982) 272–294.

    MATH  MathSciNet  Google Scholar 

  4. B.C. Eaves, “The linear complementarity problem”,Management Science 17 (1971) 612–634.

    MathSciNet  MATH  Google Scholar 

  5. C.B. Garcia, “Some classes of matrices in linear complementarity theory”,Mathematical Programming 5 (1974) 299–310.

    Article  Google Scholar 

  6. L.M. Kelly and L.T. Watson, “Erratum: Some perturbation theorems forQ-matrices”,SIAM Journal on Applied Mathematics 34 (1978) 320–321.

    Article  MATH  MathSciNet  Google Scholar 

  7. L.M. Kelly and L.T. Watson, “Q-matrices and spherical geometry”,Linear Algebra and its Applications 25 (1979) 175–190.

    Article  MATH  MathSciNet  Google Scholar 

  8. C.E. Lemke, “Bimatrix equilibrium points and mathematical programming”,Management Science 11 (1965) 681–689.

    MathSciNet  Google Scholar 

  9. O.L. Mangasarian, “Locally unique solutions of quadratic programs, linear and nonlinear complementarity problems”,Mathematical Programming 19 (1980) 200–212.

    Article  MATH  MathSciNet  Google Scholar 

  10. O.L. Mangasarian, “Characterizations of bounded solutions of linear complementarity problems”,Mathematical Programming Study 19 (1982) 153–166.

    MathSciNet  Google Scholar 

  11. K.G. Murty, “On the number of solutions to the complementarity problem and spanning properties of complementarity cones”,Linear Algebra and its Applications 5 (1972) 65–108.

    Article  MATH  MathSciNet  Google Scholar 

  12. J.S. Pang, “OnQ-matrices”,Mathematical Programming 17 (1979) 243–247.

    Article  MATH  MathSciNet  Google Scholar 

  13. S.M. Robinson, “Generalized equations and their solutions, Part I: basic theory”,Mathematical Programming Study 10 (1979) 128–141.

    MATH  Google Scholar 

  14. S.M. Robinson, “Strongly regular generalized equations”,Mathematics of Operations Research 5 (1980) 43–62.

    Article  MATH  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  16. A. Tamir, “The complementarity problem of mathematical programming”, Doctoral dissertation, Case Western Reserve University (Cleveland, OH, 1973).

    Google Scholar 

  17. L.T. Watson, “A variational approach to the linear complementarity problem”, Doctoral thesis, Department of Mathematics, University of Michigan (Ann Arbor, MI, 1974).

    Google Scholar 

  18. L.T. Watson, “Some perturbation theorems forQ-matrices”,SIAM Journal on Applied Mathematics 31 (1976) 379–384.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Virginia Commonwealth University, 23284, Richmond, VA, USA

    Cu Duong HA

Authors
  1. Cu Duong HA
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cu Duong, H. Stability of the linear complementarity problem at a solution point. Mathematical Programming 31, 327–338 (1985). https://doi.org/10.1007/BF02591954

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02591954

Key words

Search

Navigation