Rate of convergence analysis of dual-based variables decomposition methods for strongly convex problems

We consider the problem of minimizing the sum of a strongly convex function and a term comprising the sum of extended real-valued proper closed convex functions. We derive the primal representation of dual-based block descent methods and establish a relation between primal and dual rates of convergence, allowing to compute the efficiency estimates of different methods. We illustrate the effectiveness of the methods by numerical experiments on total variation-based denoising problems.