  In this paper we analyze several inexact fast augmented Lagrangian methods
for solving linearly constrained convex optimization problems. Mainly, our
methods rely on the combination of excessive-gap-like smoothing technique
developed in [15] and the newly introduced inexact oracle framework from [4].
We analyze several algorithmic instances with constant and adaptive smoothing
parameters and derive total computational complexity results in terms of
projections onto a simple primal set. For the basic inexact fast augmented
Lagrangian algorithm we obtain the overall computational complexity of order
$\mathcal{O}\left(\frac{1}{\epsilon^{5/4}}\right)$, while for the adaptive
variant we get $\mathcal{O}\left(\frac{1}{\epsilon}\right)$, projections onto a
primal set in order to obtain an $\epsilon-$optimal solution for our original
problem.
