ABSTRACT
The dual simplex method, introduced by Carlton Lemke does the dual of this procedure. It starts with a basic feasible solution in the dual, whose complementary basis in the primal is infeasible, and works its way towards primal feasibility. In one sense, the self-dual parametric algorithm is a variation of the primal and dual simplex algorithms. The former selects entering and leaving basic variables in reverse order, because it begins with dual feasibility and works towards primal feasibility. The reasoning behind the simplex algorithm remains the same: Change the value of a nonbasic variable by if the net effect is good for the objective function. Make as large as possible without violating feasibility, at which point some basic variable reaches its bound, and becomes nonbasic. The simplex method variant for lower and upper bounds was first developed when computer memory was severely limited.
