  In this paper, we develop a unified convergence analysis framework for the
Accelerated Smoothed GAp ReDuction algorithm (ASGARD) introduced in [20,
Tran-Dinh et al, 2015] Unlike[20], the new analysis covers three settings in a
single algorithm: general convexity, strong convexity, and strong convexity and
smoothness. Moreover, we establish the convergence guarantees on three
criteria: (i) gap function, (ii) primal objective residual, and (iii) dual
objective residual. Our convergence rates are optimal (up to a constant factor)
in all cases. While the convergence rate on the primal objective residual for
the general convex case has been established in [20], we prove additional
convergence rates on the gap function and the dual objective residual. The
analysis for the last two cases is completely new. Our results provide a
complete picture on the convergence guarantees of ASGARD. Finally, we present
four different numerical experiments on a representative optimization model to
verify our algorithm and compare it with Nesterov's smoothing technique.
