Motivated by some large-scale nonlinear routing problems in telecommunications, we propose a new algortihm for linearly constrained strictly convex problems. This algorithm follows the characterization of saddle points using two different augmented Lagrangian functions defined for the primal problem and its dual. In the primal space, the algorithm appears as a nonsoomth version of the projection algorithm by Rosen with a proximal feature: the direction in which the criteria is improved do not depend on the current iterate but on the next iterate. The dual iterates are generated through an unconstrained subproblem which can be solved efficiently by limited memory BFGS methods. Convergence of the method is established, and to assess the numerical behaviour of the algorithm, we use some multicommodity network flows problems.
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