Combining projected Jacobi method with dual projected pseudo quasi Newton method for multicommodity network flow problems

In this paper, we present a projected Jacobi method combined with a novel dual projected pseudo quasi Newton method for solving general multicommodity network flow problems (MNFPs), which often arise in transportation systems and data communication networks. The quadratic problems induced from the projected Jacobi method in solving the MNFP are difficult due to their large dimensionality; however, they can be solved very efficiently by the proposed dual projected pseudo quasi Newton method, which takes advantage of the network sparsity. We show the convergence of our method and demonstrate its efficiency by several numerical examples