  We investigate the convergence properties of exact and inexact
forward-backward algorithms to minimise the sum of two weakly convex functions
defined on a Hilbert space, where one has a Lipschitz-continuous gradient. We
show that the exact forward-backward algorithm converges strongly to a global
solution, provided that the objective function satisfies a sharpness condition.
For the inexact forward-backward algorithm, the same condition ensures that the
distance from the iterates to the solution set approaches a positive threshold
depending on the accuracy level of the proximal computations. As an application
of the considered setting, we provide numerical experiments related to discrete
tomography.
