Adaptive backtracking and acceleration of a forward-backward algorithm for strongly convex optimisation: convergence results and imaging applications
Luca Calatroni - I3S Laboratory, CNRS, Sophia Antipolis, France
We propose an extension of the Fast Iterative Shrinkage/Thresholding Algorithm (FISTA) algorithm for non-smooth strongly convex composite optimisation problems combined with an adaptive backtracking strategy. Differently from classical monotone line searching rules, the proposed strategy allows for local increasing and decreasing of the descent step size along the iterations and enjoys linear convergence rates defined in terms of quantities averaging both local Lipschitz constant estimates and local condition numbers. We report numerical experiments showing the outperformance of the algorithm compared to standard ones for some imaging problems and we discuss the use of restarting strategies to address situations where the strong convexity parameters are unknown. This is joint work with A. Chambolle
Luca Calatroni completed his Ph.D. in Applied Mathematics in 2015 as part of the Cambridge Image Analysis research group (UK). After that, he carried out his post-doctoral research activity at the University of Genova (Italy) within a Marie Skłowdoska-Curie ITN and later at the École Polytechnique (France) as a Lecteur Hadamard post-doctoral research fellow funded by the FMJH. From October 2019, he is a full-time CNRS researcher at the I3S laboratory in Sophia Antipolis, France. His research focuses on variational methods and non-smooth optimisation algorithms for imaging with applications to biology, cultural heritage and computational neurosciences.
2019-10-29 at 3:30 pm (subject to variability)