The Landweber method for nonlinear inverse problems

Inverse problems deal with recovering the causes for a desired or given effect and are all over science. To address their ill-posedness, regularization is used to solve them, such as the Landweber method. It is simply a gradient method for an equivalent minimization problem, and computationally cheaper than most methods. We discuss obtaining its convergence for nonlinear problems under noisy data with and without assuming smoothness on the problem, as motivated by an example in plasma physics.