Block-Activated Algorithms for Multicomponent Fully Nonsmooth Minimization.

We investigate block-activated proximal algorithms for multicomponent minimization problems involving a separable nonsmooth convex function penalizing the components individually, and nonsmooth convex coupling terms penalizing linear mixtures of the components. In the case of smooth coupling functions, several algorithms exist and they are well understood. By contrast, in the fully nonsmooth case, few block-activated methods are available and little effort has been devoted to assessing their merits and numerical performance. The goal of the paper is to address this gap. The numerical experiments concern machine learning and signal recovery problems.