The central path visits all the vertices of the Klee-Minty cube

Optimization Methods and Software

Volumn 21, Issue 5, 2006, Pages 851-865

  Deza, Antoine ^a   Nematollahi, Eissa ^a   Peyghami, Reza ^a   Terlaky, Tamás ^a  

^a MCMASTER UNIVERSITY   (Canada)

Author keywords

Central path; Klee Minty cube; Linear programming

Indexed keywords

GEOMETRY;

CENTRAL PATH; EXPONENTIAL NUMBERS; INTERIOR-POINT METHOD; KLEE-MINTY CUBE; N-DIMENSIONAL CUBES; NEIGHBOURHOOD; SIMPLEX METHODS;

LINEAR PROGRAMMING;

EID: 38349116631     PISSN: 10556788     EISSN: 10294937     Source Type: Journal    
DOI: 10.1080/10556780500407725     Document Type: Article

References (13)

1. Dantzig, G.B., 1951 Maximization of a linear function of variables subject to linear inequalities. In: T.C. Koopmans (Ed.) Activity Analysis of Production and Allocation (New York: John Wiley), pp. 339-347.
2. Klee, V. and Minty, G.J., 1972, How good is the simplex algorithm? In: O. Shisha (Ed.) Inequalities III, (Boston: Academic Press), pp. 159-175.
3. Terlaky, T. and Zhang, S. 1993, Pivot rules for linear programming - a survey. Annals of Operations Research, 46, 203-233.
4. Khachiyan, L.G., 1979, A polynomial algorithm in linear programming. Soviet Mathematics Doklady, 20, 191-194.
5. Karmarkar, N.K., 1984, A new polynomial-time algorithm for linear programming. Combinatorica 4, 373-395.
6. Roos, C., Terlaky, T. and Vial, J-Ph., 1997, Theory and Algorithms for Linear Optimization: An Interior Point Approach. Wiley-Interscience Series in Discrete Mathematics and Optimization (New York: John Wiley).
7. Ye, Y., 1979, Interior-Point Algorithms: Theory and Analysis. Wiley-Interscience Series in Discrete Mathematics and Optimization (New York: John Wiley).
8. Wright, S.J., 1997, Primal-Dual Interior-Point Methods (Philadelphia: SIAM Publications).
9. Todd, M. and Ye, Y., 1996, A lower bound on the number of iterations of long-step and polynomial interior-point linear programming algorithms. Annals of Operations Research, 62, 233-252.
10. Deza, A. Nematollahi, E. and Terlaky, T., 2004, How good are interior point methods? Klee-Minty cubes tighten iteration-complexity bounds. AdvOL-Report 2004/20, McMaster University.
11. Megiddo, N., 1986, Pathways to the optimal set in linear programming. In: N. Megiddo (Ed.) Progress in Mathematical Programming: Interior-Point and Related Methods (New York: Springer-Verlag), pp. 131-158;
12. th Mathematical Programming Symposium of Japan, 1986, Nagoya, Japan, pp. 1-35.
13. th IFIP-Conference, Budapest 1985. Also Lecture Notes in Control and Information Sciences 84, 1986 (New York: Springer), pp. 866-876.