In this article, we consider applying a proximal algorithm introduced by Ouorou to some convex multicommodity network flow minimization problems. This algorithm follows the characterization of saddle points introduced earlier but can be derived from Martinet's proximal algorithm. In the primal space, the algorithm can be viewed as a regularized version of the projection algorithm by Rosen. A remarkable feature of the algorithm is that the projection step for multicommodity flow problems reduces to solving independent linear systems (one for each commodity) involving the node-arc incidence matrix of the network. The algorithm is therefore amenable to parallel implementation. We present some numerical results on large-scale routing problems arising in telecommunications and quadratic multicommodity flow problems. A comparison with a specialized code for multicommodity flow problems indicates that this proximal algorithm is specially designed for very large-scale instances. © 2006 Wiley Periodicals, Inc. NETWORKS, Vol. 49(1), 18–27 2007
['Adam Ouorou']
Implementing a proximal algorithm for some nonlinear multicommodity flow problems