Convergence of the gradient method for ill-posed problems
Numerical Analysis
2016-06-02 v1
Abstract
We study the convergence of the gradient descent method for solving ill-posed problems where the solution is characterized as a global minimum of a differentiable functional in a Hilbert space. The classical least-squares functional for nonlinear operator equations is a special instance of this framework and the gradient method then reduces to Landweber iteration. The main result of this article is a proof of weak and strong convergence under new nonlinearity conditions that generalize the classical tangential cone conditions.
Cite
@article{arxiv.1606.00274,
title = {Convergence of the gradient method for ill-posed problems},
author = {Stefan Kindermann},
journal= {arXiv preprint arXiv:1606.00274},
year = {2016}
}