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 primalsimplex method. Simplex-like algorithms have been proposed imbedding the gradientdirection (GD) which includes all variables whose increase or decrease leads to an improvementin the objective function. Recently a frame work has been developed in thesimplex method to incorporate the reduced-gradient direction (RGD) consisting of onlyvariables 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 conceptof combining directions. Also mathematical properties related to combining directionsas well as deleting a variable from all basic directions are presented.
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