In this paper, we derive the explicit finite time local convergence of Nesterov accelerated the Broyden-Fletcher-Goldfarb-Shanno (NA-BFGS) under the assumption that the objective function is strongly convex, its gradient is Lipschitz continuous, and its Hessian is Lipschitz continuous at the optimal point. We have shown that the rate of convergence of the NA-BFGS method is $(\frac{1}{k})^{\frac{k}{2}}$. Further, we show that Nesterov accelerated BFGS gives a faster convergence rate than the classical Broyden-Fletcher-Goldfarb-Shanno (BFGS). This is the first work that theoretically guarantees the superlinear convergence of NA-BFGS non-asymptotically.

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View Non-asymptotic superlinear convergence of Nesterov accelerated BFGS