  This paper studies the convergence time of dual gradient methods for general
(possibly non-differentiable) strongly convex programs. For general convex
programs, the convergence time of dual subgradient/gradient methods with simple
running averages (running averages started from iteration $0$) is known to be
$O(\frac{1}{\epsilon^{2}})$. This paper shows that the convergence time for
general strongly convex programs is $O(\frac{1}{\epsilon})$. This paper also
considers a variation of the average scheme, called the sliding running
averages, and shows that if the dual function of the strongly convex program is
locally quadratic (Note that the locally quadratic property is implied by the
locally strongly concave property.) then the convergence time of the dual
gradient method with sliding running averages is $O(\log(\frac{1}{\epsilon}))$.
The convergence time analysis is further verified by numerical experiments.
