Primal-dual proximal point algoritm for multicommodity network flow problems

In this paper, the authors consider how to apply a primal-dual proximal point algorithm to the multicommodity network flow problem. A remarkable feature of the algorithm consists in how to find an approximate saddle point of the augmented Lagrangian of the problem. In particular, at each iteration, an approximate solution of the subproblem always satisfies the flow conservation equations for all commodities. This property often turns to be very useful in practical applications. The authors show some results of numerical experiments and examine the effectiveness of the proposed algorithm.