New Results on Superlinear Convergence of Classical Quasi-Newton Methods

Abstract We present a new theoretical analysis of local superlinear convergence classical quasi-Newton methods from the convex Broyden class. As result, we obtain significant improvement in currently known estimates rates for these methods. In particular, show that corresponding rate Broyden–Fletcher–Goldfarb–Shanno method depends only on product dimensionality problem and logarithm its condition number.