TY - JOUR
T1 - An upper bound for the number of different solutions generated by the primal simplex method with any selection rule of entering variables
AU - Kitahara, Tomonari
AU - Mizuno, Shinji
N1 - Funding Information:
The authors are grateful to anonymous reviewers for their helpful comments on the original version of this manuscript. This research is supported in part by Grant-in Aid for Young Scientists (B) 23710164 and Grant-in-Aid for Science Research (A) 20241038 of Japan Society for the Promotion of Science.
PY - 2013/6
Y1 - 2013/6
N2 - Recently, Kitahara, and Mizuno derived an upper bound for the number of different solutions generated by the primal simplex method with Dantzig's (the most negative) pivoting rule. In this paper, we obtain an upper bound with any pivoting rule which chooses an entering variable whose reduced cost is negative at each iteration. The upper bound is applied to a linear programming problem with a totally unimodular matrix. We also obtain a similar upper bound for the dual simplex method.
AB - Recently, Kitahara, and Mizuno derived an upper bound for the number of different solutions generated by the primal simplex method with Dantzig's (the most negative) pivoting rule. In this paper, we obtain an upper bound with any pivoting rule which chooses an entering variable whose reduced cost is negative at each iteration. The upper bound is applied to a linear programming problem with a totally unimodular matrix. We also obtain a similar upper bound for the dual simplex method.
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U2 - 10.1142/S0217595913400125
DO - 10.1142/S0217595913400125
M3 - Article
AN - SCOPUS:84879611311
SN - 0217-5959
VL - 30
JO - Asia-Pacific Journal of Operational Research
JF - Asia-Pacific Journal of Operational Research
IS - 3
M1 - 1340012
ER -