Computational experiments with flow models for multicommmodity using non linear and non-separable cost functions

In this paper we present the study and the numerical implementation of the primal–dual interior-point method for the solution of the convex nonlinear multicommodity network flow problem. At each iteration of the interior-point method, we solve the corresponding linear system, expressed by the augmented-indefinite system, using an indefinite preconditioned conjugate gradient algorithm combined with the AINV algorithm. We conduct some numerical experiments for networks of different dimensions and number of products and for some nonlinear costs. The computational results show the effectiveness of the interior-point method for this class of network problem.