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We consider minimizing the composite function that consists of a stronglyconvex 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 FDPGmethod that guarantees an $O(1/k^{1.5})$ rate for the dual proximal gradientnorm decrease. By relating this to the primal function decrease, the proposedapproach decreases the primal function with the improved $O(1/k^{1.5})$ rate.

Fast dual proximal gradient algorithms with rate $O(1/k^{1.5})$ for convex minimization