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We present and analyse a backtracking strategy for a general Fast IterativeShrinkage/Thresholding Algorithm which has been recently proposed in(Chambolle, Pock, 2016) for strongly convex objective functions. Differentlyfrom classical Armijo-type line searching, our backtracking rule allows forlocal increasing and decreasing of the descent step size (i.e. proximalparameter) along the iterations. For such strategy accelerated convergencerates are proved and numerical results are shown for some exemplar imagingproblems.

Backtracking strategies for accelerated descent methods with smooth composite objectives