In this paper we devise a new version of primal simplex algorithms in which the classical iteration is decomposed two basic operations: the move and the pivot. The move operation decreases the primal objective value and the pivot operation increases the dual objective. We define the condition number of the pivot operation and present a reduced duality gaps pivot rule, acquire a sufficient condition of the strongly polynomial simplex methods for linear programming problems based on the new simplex version.
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Report on the school of Information and Mathematics, Yangtzeu university
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View A reduced duality gaps simplex algorithm for linear programming