A dual simplex implementation of a constraint selection algorithm for linear programming

The constraint selection approach to linear programming begins by solving a relaxed version of the problem using only a few of the original constraints. If the solution obtained to this relaxation satisfies the remaining constraints it is optimal for the original LP. Otherwise, additional constraints must be incorporated in a large relaxation. The procedure successively generates larger subproblems until an optimal solution is obtained which satisfies all of the original constraints. Computational results for a dual simplex implementation of this technique indicate that solving several small subproblems in this manner is more computationally efficient than solving the original LP using the revised simplex method.