In this talk we present and backtracking strategy for a variant of the Beck and Teboulle’s Fast Iterative Shrinkage/Thresholding Algorithm (FISTA) which has been recently proposed by Chambolle and Pock (2016) for strongly convex objective functions. Differently from standard Armijo-type line searching, our backtracking rule allows for local increase and decrease of the Lipschitz constant estimate along the iterations, i.e. decrease/increase of the gradient step size. For such adaptive strategy we prove accelerated convergence rates showing in particular linear convergence in smooth cases. We validate the resulting algorithm on some exemplar image denoising problems where strong convexity appears typically after smoothing of the regularisation term.
This is joint work with A. Chambolle (CMAP, École Poltechnique).