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Anders Forsgren (andersfkth.se) Abstract: Pivoting methods are of vital importance for linear programming, the simplex method being the by far most wellknown. In this paper, a primaldual pair of linear programs in canonical form is considered. We show that there exists a sequence of pivots, whose length is bounded by the minimum dimension of the constraint matrix, such that the pivot creates a nonsingular submatrix of the constraint matrix which increases by one row and one column at each iteration. Solving a pair of linear equations for each of these submatrices generates a sequence of optimal solutions of a primaldual pair of linear programs of increasing dimensions, originating at the origin. The optimal solutions to the original primaldual pair of linear programs are obtained in the final step. It is only an existence result, we have not been able to generate any rules based on properties of the problem to generate the sequence. The result is obtained by a decomposition of the final basis matrix. Keywords: linear programming, pivoting, primaldual pair, shortest path Category 1: Linear, Cone and Semidefinite Programming (Linear Programming ) Citation: arXiv:1908.09735 [math.OC], 2019. Download: [PDF] Entry Submitted: 08/28/2019 Modify/Update this entry  
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