  Motivated by big data applications, first-order methods have been extremely
popular in recent years. However, naive gradient methods generally converge
slowly. Hence, much efforts have been made to accelerate various first-order
methods. This paper proposes two accelerated methods towards solving structured
linearly constrained convex programming, for which we assume composite convex
objective.
  The first method is the accelerated linearized augmented Lagrangian method
(LALM). At each update to the primal variable, it allows linearization to the
differentiable function and also the augmented term, and thus it enables easy
subproblems. Assuming merely weak convexity, we show that LALM owns $O(1/t)$
convergence if parameters are kept fixed during all the iterations and can be
accelerated to $O(1/t^2)$ if the parameters are adapted, where $t$ is the
number of total iterations.
  The second method is the accelerated linearized alternating direction method
of multipliers (LADMM). In addition to the composite convexity, it further
assumes two-block structure on the objective. Different from classic ADMM, our
method allows linearization to the objective and also augmented term to make
the update simple. Assuming strong convexity on one block variable, we show
that LADMM also enjoys $O(1/t^2)$ convergence with adaptive parameters. This
result is a significant improvement over that in [Goldstein et. al, SIIMS'14],
which requires strong convexity on both block variables and no linearization to
the objective or augmented term.
  Numerical experiments are performed on quadratic programming, image
denoising, and support vector machine. The proposed accelerated methods are
compared to nonaccelerated ones and also existing accelerated methods. The
results demonstrate the validness of acceleration and superior performance of
the proposed methods over existing ones.
