  In this paper, we develop a unified convergence analysis framework for the
\textit{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.
