  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.
