  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.
