A primal-dual simplex method for linear programs

A primal-dual algorithm is developed that optimizes a dual program in concert with improving primal infeasibility. The key distinction from the classic primal-dual simplex method is that the present algorithm uses a much smaller working basis to determine a dual ascent direction quickly. By maintaining partial primal feasilibity while improving the dual objective, the number of infeasible constraints is monotonically reduced to zero. Finite convergence to an optimal primal-dual pair can then be shown in the same manner as the simplex method. Computational experience on large generalized network linear programs demonstrates the algorithm’s promise.