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 ...

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 ...

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 ...

Introducing the Pivot Adaptive Method (PAM) - a faster variant of Gabasov's Adaptive Method (AM) for minimizing computation time. Explore the resolution of problems through successive tables and ...

Gabasov and Kirillova have generalized the Simplex method in 1995 [15] [16] [17] , and developed the Adaptive Method (AM), a primal-dual method, for linear programming with bounded variables.

It is known that the simplex method requires an exponential number of iterations for some special linear programming instances. Hence the method is neither polynomial nor a strongly-polynomial ...

A global convergent algorithm is proposed to solve bilevel linear fractional-linear programming, which is a special class of bilevel programming. In our algorithm, replacing the lower level problem by ...