Interior point methods for multicommodity network flows

This article studies the linear multicommodity network flow problem. This kind of problem arises in a wide variety of contexts. A numerical implementation of the primal-dual interior-point method is designed to solve the problem. In the interior-point method, at each iteration, the corresponding linear system, expressed as a normal equations system, is solved by using the AINV algorithm combined with a preconditioned conjugate gradient algorithm or by the AINV algorithm for the whole normal equations. Numerical experiments are conducted for networks of different dimensions and numbers of products for the distribution problem. The computational results show the effectiveness of the interior-point method for this class of network problems.