Journal of Applied Mathematics and Decision Sciences
Volume 8 (2004), Issue 2, Pages 107-129
On gradient simplex methods for linear programs
Merrick School of Business, University of Baltimore, 21201, MD, USA
Copyright © 2004 R. R. Vemuganti. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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 frame work 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.