  In this paper, we consider large-scale linearly constrained composite convex
optimization problem, whose objective is a sum of a smooth function and a
possibly nonsmooth function. We propose a scalable
\textbf{F}rank-\textbf{W}olfe based \textbf{A}ugmented \textbf{L}agrangian
(FW-AL) method for solving this problem. At each iteration, the proposed FW-AL
method employs the FW method (or its variants) to approximately solve the AL
subproblem {(with fixed Lagrange multiplier)} within a preselected tolerance
and then updates the Lagrange multiplier. The proposed FW-AL method is well
suitable for solving large-scale problems, because its computational cost per
step scales (essentially) linearly with the size of the input. We analyze the
non-ergodic convergence rate of the proposed FW-AL method.
