An incremental primal-dual method for generalized networks

The primal simplex method has been computationally superior to primal-dual simplex and out-of-kilter methods for solving large-scale generalized network linear programs. In this paper, a new primal-dual simplex method is proposed that is well suited for capitalizing on the network structure. The algorithm employs a dynamically sized subbasis matrix to monotonically decrease the number of infeasible node constraints while simultaneously optimizing a dual program. Computational results indicate an implementation of this algorithm is efficient and faster than a state-of-the-art generalized network primal simplex code on many randomly generated benchmark problems.