An exponential example for Terlaky's pivoting rule for the criss-cross simplex method Authors
Received: 20 April 1987 Revised: 01 April 1988 DOI:
Cite this article as: Roos, C. Mathematical Programming (1990) 46: 79. doi:10.1007/BF01585729
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.
D. Avis and V. Chvátal, “Notes on Bland's pivoting rule,”
Mathematical Programming Study 8 (1978) 24–34.
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.
R.G. Bland, “A new pivoting rule for the simplex method,”
Mathematics of Operations Research 2 (1977) 103–107.
D. Goldfarb and W.Y. Sit, “Worst case behaviour of the steepest edge simplex method,”
Discrete Applied Mathematics 1 (1979) 277–285.
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).
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.
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).
C. Roos, “An exponential example for Terlaky's pivoting rule for the criss-cross simplex method,” Working paper, Delft University of Technology (Delft, 1987).
T. Terlaky, “A new, finite criss-cross method,”
Optimization 16 (1985) 683–690.
S. Zionts, “The criss-cross method for solving linear programming problems,”
Management Science 15 (1979) 426–445.