A sparse-block-matrix technique based method for nonlinear multicommodity network flow problems with large number of commodities

We present a sparse-block-matrix technique based method for solving nonlinear multicommodity network flow problems with large number of commodities. Our method combines a well-known projected quasi-Newton (PQN) method and a dual projected pseudo quasi-Newton (DPPQN) method, which solves the method, there is a sparse block-two-element matrix property residing in the dual quadratic subproblem, and the dual function can be formulated as a scaled projection problem. To exploit these two characteristics, we propose a sparse-block-matrix technique and an n-iteration scaled projection technique to further enhance the computational efficiency of DPPQN method, especially in the case of large number of commodities. We demonstrate the efficiency of the DPPQN method embedded with the two new techniques by comparing with a previously developed efficient algorithm. Test results show that the proposed method outperforms the previously developed method in the case of large number of commodities.