Accelerated Quasi-Newton Proximal Extragradient: Faster Rate for Smooth Convex Optimization

In this paper, we propose an accelerated quasi-Newton proximal extragradient method for solving unconstrained smooth convex optimization problems. With access only to the gradients of the objective, we prove that our method can achieve a convergence rate of $\mathcal{O}\bigl(\min\\{\frac{1}{k^2}, \frac{\sqrt{d\log k}}{k^{2.5}}\\}\bigr)$,