Iteration methods for convexly constrained ill-posed problems in hilbert space

Abstract Minimization problems in Hilbert space with quadratic objective function and closed convex constraint set C are considered. In case the minimum is not unique we are looking for the solution of minimal norm. If a problem is ill-posed, i.e. if the solution does not depend continuously on the data, and if the data are subject to errors then it has to be solved by means of regularization methods. The regularizing properties of some gradient projection methods—i.e. convergence for exact data, order of convergence under additional assumptions on the solution and stability for perturbed data—are the main issues of this paper.