### Adam Ouorou (France Télécom)

#### A proximal subgradient projection algorithm for some nonlinear multicommodity flow problems

*Monday 9 February 2004 at 15.30, JCMB 5327*

##### Abstract

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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