On gradient simplex methods for linear programs

A variety of pivot column selection rules based upon the gradient criteria (including the steepest edge) have been explored to improve the efficiency of the primal simplex method. Simplex-like algorithms have been proposed imbedding the gradient direction (GD) which includes all variables whose increase or decrease leads to an improvement in the objective function. Recently a framework has been developed in the simplex method to incorporate the reduced-gradient direction (RGD) consisting of only variables whose increase leads to an improvement in the objective function. In this paper, the results are extended to embed GD in the simplex method based on the concept of combining directions. Also mathematical properties related to combining directions as well as deleting a variable from all basic directions are presented.