LOWER BOUNDS FOR THE MAXIMUM NUMBER OF SOLUTIONS GENERATED BY THE SIMPLEX METHOD(<Special Issue>SCOPE (Seminar on Computation and OPtimization for new Extensions))

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  • LOWER BOUNDS FOR THE MAXIMUM NUMBER OF SOLUTIONS GENERATED BY THE SIMPLEX METHOD

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Kitahara and Mizuno [3] get upper bounds for the maximum number of different basic feasible solutions generated by the simplex method with the most negative pivoting rule. In this paper, we obtain lower bounds of the maximum number to show how tight the upper bounds are. Part of the results in this paper are shown in Kitahara and Mizuno [4] as a quick report without proof. They present a simple variant of Klee-Minty's LP and get a lower bound. In this paper, we explain and prove the properties of the variant more precisely. We also show a new lower bound by using a simple example of LP.

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