Mathematical Programming

, Volume 46, Issue 1–3, pp 79–84 | Cite as

An exponential example for Terlaky's pivoting rule for the criss-cross simplex method

Article

Abstract

Recently T. Terlaky has proposed a new pivoting rule for the criss-cross simplex method for linear programming and he proved that his rule is convergent. In this note we show that the required number of iterations may be exponential in the number of variables and constraints of the problem.

Key words

Linear programming pivoting rule Gray code 

References

  1. [1]
    D. Avis and V. Chvátal, “Notes on Bland's pivoting rule,”Mathematical Programming Study 8 (1978) 24–34.Google Scholar
  2. [2]
    J.R. Bitner, G. Ehrlich and E.M. Reingold, “Efficient generation of the binary reflected Gray code and its applications,”Communications of the ACM 19 (1976) 517–521.Google Scholar
  3. [3]
    R.G. Bland, “A new pivoting rule for the simplex method,”Mathematics of Operations Research 2 (1977) 103–107.Google Scholar
  4. [4]
    D. Goldfarb and W.Y. Sit, “Worst case behaviour of the steepest edge simplex method,”Discrete Applied Mathematics 1 (1979) 277–285.Google Scholar
  5. [5]
    D.L. Jensen and R.G. Bland, “Combinatorial pivot rules for oriented matroid programming,” paper presented on the 12th International Symposium on Mathematical Programming (Boston, 1985).Google Scholar
  6. [6]
    V. Klee and G.J. Minty, “How good is the Simplex algorithm?“ in: O. Shisha, ed.,Inequalities III (Academic Press, New York, 1972) pp. 158–172.Google Scholar
  7. [7]
    J.K. Lenstra and A.H.G. Rinnooy Kan, “A recursive approach to the generation of combinatorial configurations,” Report No. BW 50/75, Mathematisch Centrum (Amsterdam, 1975).Google Scholar
  8. [8]
    C. Roos, “An exponential example for Terlaky's pivoting rule for the criss-cross simplex method,” Working paper, Delft University of Technology (Delft, 1987).Google Scholar
  9. [9]
    T. Terlaky, “A new, finite criss-cross method,”Optimization 16 (1985) 683–690.Google Scholar
  10. [10]
    S. Zionts, “The criss-cross method for solving linear programming problems,”Management Science 15 (1979) 426–445.Google Scholar

Copyright information

© North-Holland 1990

Authors and Affiliations

  • C. Roos
    • 1
  1. 1.Department of Mathematics and InformaticsDelft University of TechnologyDelftThe Netherlands

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