  We propose two numerical algorithms in the fully nonconvex setting for the
minimization of the sum of a smooth function and the composition of a nonsmooth
function with a linear operator. The iterative schemes are formulated in the
spirit of the proximal alternating direction method of multipliers and its
linearized variant, respectively. The proximal terms are introduced via
variable metrics, a fact which allows us to derive new proximal splitting
algorithms for nonconvex structured optimization problems, as particular
instances of the general schemes. Under mild conditions on the sequence of
variable metrics and by assuming that a regularization of the associated
augmented Lagrangian has the Kurdyka-Lojasiewicz property, we prove that the
iterates converge to a KKT point of the objective function. By assuming that
the augmented Lagrangian has the Lojasiewicz property, we also derive
convergence rates for both the augmented Lagrangian and the iterates.
