We propose a unifying algorithm for non-smooth non-convex optimization. The algorithm approximates the objective function by a convex model function and finds an approximate Bregman proximal point of the convex model. We prove convergence to a stationary point under weak assumptions on the growth of the model function error. Special instances of the algorithm with Euclidean distance are, e.g., Gradient Descent, Forward--Backward Splitting, ProxDescent. Applications include non-linear inverse problems in image processing and machine learning.

This presentation is part of Minisymposium “MS10 - Advanced optimization methods for image processing (2 parts)”
organized by: Marco Prato (University of Modena and Reggio Emilia) , Ignace Loris (Université Libre de Bruxelles) .

Authors:

Peter Ochs (Saarland University)

Jalal Fadili (Université Caen)

Keywords:

bregman proximal minimization, model functions, non-smooth non-convex optimization