Backtracking strategies for accelerated descent methods with smooth composite objectives

We present and analyse a backtracking strategy for a general Fast Iterative Shrinkage/Thresholding Algorithm which has been recently proposed in (Chambolle, Pock, 2016) for strongly convex objective functions. Differently from classical Armijo-type line searching, our backtracking rule allows for local increasing and decreasing of the descent step size (i.e. proximal parameter) along the iterations. For such strategy accelerated convergence rates are proved and numerical results are shown for some exemplar imaging problems.