Abstract
It is shown that in Hilbert spaces the gradient maps of convex functionals with uniformly bounded continuous second Frechét derivatives satisfy monotonicity conditions that insure that some convex combination of the identity, I, and I − ▽ f is either strictly contractive or at worst nonexpansive. This result leads to a complete resolution of the convergence question for a large class of associated gradient processes. In particular, weak convergence of the successive approximation sequence is established even in the singular case where f″ is not strictly positive at critical points of f.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.