Recent developments in imaging and data analysis techniques came along with an increasing need for fast convex optimization methods for solving large scale problems. A simple optimization strategy to minimize the sum of a Lipschitz differentiable function and a non smooth function is the forward-backward algorithm. In this presentation, several approaches to accelerate convergence speed and to reduce complexity of this algorithm will be proposed. More precisely, in a first part, preconditioning methods adapted to non convex minimization problems will be presented, and in a second part, stochastic optimization techniques will be described in the context of convex optimization. The different proposed methods will be used to solve several inverse problems in signal and image processing.

__ Bio__: Audrey Repetti is a post-doctoral researcher at the Heriot-Watt university, in Scotland. She received her M.Sc. degree from the Université Pierre et Marie Curie (Paris VI) in applied mathematics, and her Ph.D. degree from the Université Paris-Est Marne-la-Vallée in signal and image processing. Her research interests include convex and non convex optimization, and signal and image processing.