Rates of superlinear convergence for classical quasi-Newton methods

We study the local convergence of classical quasi-Newton methods for nonlinear optimization. Although it was well established a long time ago that asymptotically these converge superlinearly, corresponding rates still remain unknown. In this paper, we address problem. obtain first explicit non-asymptotic superlinear standard methods, which are based on updating formulas from convex Broyden class. particular, well-known DFP and BFGS form $(\frac{n L^2}{\mu^2 k})^{k/2}$ L}{\mu respectively, where $k$ is iteration counter, $n$ dimension problem, $\mu$ strong convexity parameter, $L$ Lipschitz constant gradient.