  We consider minimizing the composite function that consists of a strongly
convex function and a convex function. The fast dual proximal gradient (FDPG)
method decreases the dual function with a rate $O(1/k^2)$, leading to a rate
$O(1/k)$ for decreasing the primal function. We propose a generalized FDPG
method that guarantees an $O(1/k^{1.5})$ rate for the dual proximal gradient
norm decrease. By relating this to the primal function decrease, the proposed
approach decreases the primal function with the improved $O(1/k^{1.5})$ rate.
