The Constrained Gradient Method of Linear Programming

In this paper ail efficient algorithm is presented for solving the general linear programming problem whereby, from a point on the boundary of the feasible point set, the "steepest" or "constrained gradient" direction from the point is found. Moving as far in this direction as feasibility permits, one gets the next feasible point, etc. The process ends in a finite number of such steps. In a recent report [11], Thurber describes this gradient method. What Thurber's formulation lacks, however, is an "efficient" procedure for finding the "constrained gradient" at a point. The main purpose of this paper is to furnish such a procedure, and to incorporate the procedure into a general method such that optimality is achieved in a finite number of "basis changes. " Following the preliminaries of Part I, the constrained gradient method is described in Part II, with proof of finiteness of the total number of iterations. In Part III, the method is compared with others.