  This paper proposes and establishes the iteration-complexity of an inexact
proximal accelerated augmented Lagrangian (IPAAL) method for solving linearly
constrained smooth nonconvex composite optimization problems. Each IPAAL
iteration consists of inexactly solving a proximal augmented Lagrangian
subproblem by an accelerated composite gradient (ACG) method followed by a
suitable Lagrange multiplier update. It is shown that IPAAL generates an
approximate stationary solution in at most ${\cal O}(\log(1/\rho)/\rho^{3})$
ACG iterations, where $\rho>0$ is the given tolerance. It is also shown that
the previous complexity bound can be sharpened to ${\cal
O}(\log(1/\rho)/\rho^{2.5})$ under additional mildly stronger assumptions. The
above bounds are derived assuming that the initial point is neither feasible
nor the domain of the composite term of the objective function is bounded. Some
preliminary numerical results are presented to illustrate the performance of
the IPAAL method.
