Modern analysis of local convergence for classical quasi-Newton methods

Abstract

In this talk, we present a modern analysis of local superlinear convergence for the standard BFGS and DFP quasi-Newton methods for unconstrained optimization. Our analysis, in contrast to the classical one, is non-asymptotic and gives explicit complexity estimates. One interesting conclusion is that BFGS is almost insensitive to the condition number: the principal factor in the corresponding complexity bound is the product of the problem dimension and the logarithm of its condition number.