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In this paper, we propose Nesterov Accelerated Shuffling Gradient (NASG), anew algorithm for the convex finite-sum minimization problems. Our methodintegrates the traditional Nesterov's acceleration momentum with differentshuffling 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 ofepochs. This rate is better than that of any other shuffling gradient methodsin convex regime. Our convergence analysis does not require an assumption onbounded domain or a bounded gradient condition. For randomized shufflingschemes, we improve the convergence bound further. When employing some initialcondition, we show that our method converges faster near the small neighborhoodof the solution. Numerical simulations demonstrate the efficiency of ouralgorithm.

Nesterov Accelerated Shuffling Gradient Method for Convex Optimization