Standard computer implementations of Dantzig's simplex method for linear programming are based upon forming the inverse of the basic matrix and updating the inverse after every step of the method.

Abstract: The goal is to give some theoretical explanation for the efficiency of the simplex method of George Dantzig. Fixing the number of constraints and using Dantzig's self-dual parametric ...

It is proved that this method gives the same sequence of iterations as formulation of the simplex method for quadratic programming given earlier by Dantzing and the authors, which may be called the ...

Linear programming(LP) is the term used for defining a wide range of optimization problems in which the objective function to be minimized or maximized is linear in the unknown variables and the ...

This book offers a theoretical and computational presentation of a variety of linear programming algorithms and methods with an emphasis on the revised simplex method and its components. A theoretical ...

The researchers showed that the simplex method using Tardos' basic algorithm is strongly polynomial for totally unimodular linear programming problems, if the problems are nondegenerate. These ...

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The former method is not applicable when a primal basic feasible solution is not easily at hand and the later method needs to an initial dual basic feasible solution. In this paper, we develop a novel ...