The optimal decay for the solution of the Monotone Inclusion associated to FISTA for b<=3 is 2b/3

Jf Aujol (1) , Charles H Dossal (1)

1 IMB - Institut de Mathématiques de Bordeaux

It was recently proved that the decay of the solution of the ODE associated to the Nesterov Fast Gradient Algorithm with a parameter b 3 was 0(1 t 2b 3). In this note we prove that this decay is achieved for the solution of the associated monotone inclusion for a specific function.

Mots clés: Monotone Inclusion; FISTA; convergence rate; Nesterov; acceleration

Domaines: Optimisation et contrôle [math.OC]

Jf Aujol, Charles H Dossal. The optimal decay for the solution of the Monotone Inclusion associated to FISTA for b<=3 is 2b/3. 2017. ⟨hal-01565933⟩