Smoothing technique for nonsmooth composite minimization with linear operator

Understand

We introduce and analyze an algorithm for the minimization of convex functions that are the sum of differentiable terms and proximable terms composed with linear operators.

• The method builds upon the recently developed smoothed gap technique.
• In addition to a precise convergence rate result, valid even in the presence of linear inclusion constraints, this new method allows an explicit treatment of the gradient of differentiable functions and can be enhanced with line-search.
• We also study the consequences of restarting the acceleration of the algorithm at a given frequency.