  In this paper, we propose Nesterov Accelerated Shuffling Gradient (NASG), a
new algorithm for the convex finite-sum minimization problems. Our method
integrates the traditional Nesterov's acceleration momentum with different
shuffling sampling schemes. We show that our algorithm has an improved rate of
$\mathcal{O}(1/T)$ using unified shuffling schemes, where $T$ is the number of
epochs. This rate is better than that of any other shuffling gradient methods
in convex regime. Our convergence analysis does not require an assumption on
bounded domain or a bounded gradient condition. For randomized shuffling
schemes, we improve the convergence bound further. When employing some initial
condition, we show that our method converges faster near the small neighborhood
of the solution. Numerical simulations demonstrate the efficiency of our
algorithm.
