The Pivot Adaptive Method for Solving Linear Programming Problems

A new variant of the Adaptive Method (AM) of Gabasov is presented, to minimize the computation time. Unlike the original method and its some variants, we need not to compute the inverse of the basic matrix at each iteration, or to solve the linear systems with the basic matrix. In fact, to compute the new support feasible solution, the simplex pivoting rule is used by introducing a matrix that we will define. This variant is called “the Pivot Adaptive Method” (PAM); it allows presenting the resolution of a given problem under the shape of successive tables as we will see in example. The proofs that are not given by Gabasov will also be presented here, namely the proofs for the theorem of the optimality criterion and for the theorem of existence of an optimal support, and at the end, a brief comparison between our method and the Simplex Method will be given.