Towards parameter-free (strongly convex) FISTA via adaptive backtracking and restart
Speaker: Luca Calatroni (CNRS researcher in the Morpheme team at the I3S laboratory in Sophia-Antipolis, France.)
Title: Towards parameter-free (strongly convex) FISTA via adaptive backtracking and restart
Abstract: In the first part of this seminar, I will present some extensions of the Fast Iterative Soft-Thresholding Algorithm (FISTA) recently proposed to solve structured non-smooth optimisation problems with strongly convex objectives. I will focus in particular on adaptive (i.e., non-monotone) backtracking strategies possibly endowed with variable-metric updates and inexact evaluation of proximal points, showing both linear convergence results for the objective values and several results to exemplar imaging problems. Next, I will present more recent work where a weaker (Łojasiewicz) condition with unknown parameter is assumed for the objective functional. By defining a suitable algorithmic restarting strategy combined with adaptive backtracking, linear convergence rates depending on local estimates of the problem conditioning can be obtained for FISTA in this case too. By construction, the resulting algorithm is parameter-free and can be thus be applied to several signal/imaging problems where the Lipschitz smoothness and the growth parameter are unknown/poorly estimated.
More information: https://sites.google.com/view/lucacalatroni/
Talk in room M7 101 (Campus Monod, ENS de Lyon)