Progress in Linear Programming

There is little doubt that barrier methods are now indispensable tools in the solution of large-scale linear programming problems. However, it is our opinion that the results of Lustig, Marsten and Shanno (hereafter LMS) somewhat overstate the performance of these methods relative to the simplex method. We will present a sightly different view of progress in linear programming, one in which barrier methods do not dominate in the solution of large-scale problems