Landweber-type method with uniformly convex constraints under conditional stability assumptions

The Landweber-type iteration method is one of the most prominent regularization methods for solving ill-posed problems when the data is corrupted by noise. By extending the previous results proposed by de Hoop et al. (2012), the current work systematically investigates the convergence rate of Landweber-type iteration in Banach spaces for nonlinear ill-posed problems. Two types of stopping rules including the discrepancy principle and the heuristic Hanke–Raus rule are provided which are novel in view of existing research work.