BFGS convergence to nonsmooth minimizers of convex functions

Abstract

The popular BFGS quasi-Newton minimization algorithm under reasonable conditions converges globally on smooth convex functions. This result was proved by Powell in 1976: we consider its implications for functions that are not smooth. In particular, an analogous convergence result holds for functions, like the Euclidean norm, that are nonsmooth at the minimizer.

Cited by in corpus (1)

• On the convergence of BFGS on a class of piecewise linear non-smooth functions