First-order methods for optimization in data analytics

The course gives an introduction to first-order primal-dual methods for nonsmooth optimization problems arising in data science, in particular in image processing, inverse problems and machine learning. First-order primal-dual methods belong to the most successful optimization methods to solve these problems. The methods are based on a saddle point formulation of the problem and alternate between primal and dual update steps. The lecture covers in particular the following methods: - Primal-dual proximal splitting method (PDPS, Chambolle-Pock method) and generalizations - Alternating direction method of multipliers (ADMM) und preconditioned variants - Preconditioned proximal point methods - Relation between these methods Applications include image denoising, image deblurring, inverse problems related to medical imaging and others.