Skip to main content
Log in

Cycling in linear complementarity problems

  • Short Communication
  • Published:
Mathematical Programming Submit manuscript

Abstract

A bound for the minimum length of a cycle in Lemke's Algorithm is derived. An example illustrates that this bound is sharp, and that the fewest number of variables is seven.

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.

References

  1. E.M.L. Beale, “Cycling in the dual simplex algorithm”,Naval Research Logistics Quarterly 2 (1955) 269–275.

    Google Scholar 

  2. G.B. Dantzig,Linear programming and extensions (Princeton University Press, Princeton, 1963).

    Google Scholar 

  3. A.J. Hoffman, “Cycling in the simplex algorithm”, National Bureau of Standards, Rept. No. 2974 (December 1953).

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

    Google Scholar 

  5. C.M. Lemke, “On complementary pivot theory”, in: G.B. Dantzig and A.F. Veinott, Jr., eds.,Mathematics of the Decision Sciences (Am. Math. Soc., Providence, RI, 1968) pp. 95–114.

    Google Scholar 

  6. A. Ravindran, “Algorithm 431 [H]. A computer routine for quadratic and linear programming problems”,Communications of the ACM 15 (1972) 818–820.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kostreva, M.M. Cycling in linear complementarity problems. Mathematical Programming 16, 127–130 (1979). https://doi.org/10.1007/BF01582098

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01582098

Key words

Navigation