Voici le résumé de sa présentation :

We address the solving of nonsmooth convex optimization problems with complex structures, by solving the corresponding system of optimality conditions that involves sums of linear compositions of parallel sums of maximally monotone operators. We formulate first an iterative scheme of Douglas-Rachford type, which processes the set-valued maximally monotone operators via backward steps and the linear continuous operators via explicit forward steps, and analyze its convergence behaviour. Further, we briefly discuss other primal-dual algorithms relying on iterative methods of type forward-backward and forward-backward-forward. The performances of the numerical methods discussed in this talk are illustrated by numerical experiments in image processing, clustering, support vector machines and video processing.