Local convergence of the steepest descent method in Hilbert spaces

The aim of this paper is to establish the local convergence of the steepest descent method for C1- functionals f :H→R defined on an infinite-dimensional Hilbert space H, under a Palais–Smaletype condition. The functionals f under consideration are also assumed to have a locally Lipschitz continuous gradient operator ∇f . Our approach is based on the solutions of the ordinary differential equation ˙x(t)=−∇f (x(t)).  2004 Elsevier Inc. All rights reserved.