[Dottorcomp] Seminari di Matematica Applicata. Martedì 9 Maggio. Luca Calatroni.

[Stefano Lisini]

Seminari di Matematica Applicata, Dipartimento di Matematica "F. Casorati"
e Istituto del CNR IMATI "E. Magenes" di Pavia.

Martedì 9 maggio 2023, alle ore 15 precise, presso la sala conferenze
dell'IMATI-CNR di Pavia,

Luca Calatroni (CNRS, Laboratoire d’Informatique, Signaux et Systèmes de
Sophia-Antipolis (I3S), France)

terrà un seminario dal titolo:

Parameter-free accelerated algorithms for composite non-smooth optimisation.

Abstract.
A standard approach for the solution of several ill-posed signal and image
processing problems consists in the minimisation of a composite (smooth +
non-smooth) energy functional encoding prior information on the desired
solution as well as on the degradation/noise model. In convex scenarios, a
reference algorithm dealing with this type of problems is the popular
proximal gradient algorithm which deals *explicitly* (i.e. by a gradient
step) with the differentiable part and implicitly (i.e. by a proximal step)
with the non-smooth component typically favouring sparsity w.r.t. to some
representation. To overcome the slow the convergence properties of such
algorithm, inertial techniques enforce accelerated convergence by minimal
changes in the iteration steps. However, from a practical viewpoint, these
algorithms are effective only whenever precise quantitative estimates of
the function regularity are known.
In this talk, I will review some recent contributions on the automation of
the well-known Fast Iterative Soft-Thresholding Algorithm (FISTA) under a
quadratic growth condition of the composite cost functional including (but
not limited to) strongly convex objectives. I will show, in particular, how
linear convergence results can be obtained by using adaptive (i.e.,
non-monotone) backtracking strategies and restarting approaches providing
as a byproduct quantitative estimations of regularity parameters along the
iterations.

Some exemplar imaging problems will be be considered as for numerical
verifications showing improved convergence w.r.t. iterations and CPU times,
thus justifying the use of such algorithms in the context of large-scale
optimisation.

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