Local convergence of the steepest descent method in Hilbert spaces

[摘要] The aim of this paper is to establish the local convergence of the steepest descent method for C-1- 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 delf. Our approach is based on the solutions of the ordinary differential equation x (t) = -del f (x(t)). (C) 2004 Elsevier Inc. All rights reserved.

[发布日期] 2004-12-15

[关键词] steepest descent method;Palais-Smale condition;locally Lipschitz continuous operator;Picard-Lindelof theorem;Sobolev embedding theorem