  We propose a forward-backward proximal-type algorithm with inertial/memory
effects for minimizing the sum of a nonsmooth function with a smooth one in the
nonconvex setting. The sequence of iterates generated by the algorithm
converges to a critical point of the objective function provided an appropriate
regularization of the objective satisfies the Kurdyka-\L{}ojasiewicz
inequality, which is for instance fulfilled for semi-algebraic functions. We
illustrate the theoretical results by considering two numerical experiments:
the first one concerns the ability of recovering the local optimal solutions of
nonconvex optimization problems, while the second one refers to the restoration
of a noisy blurred image.
