Gradient-projection method for finding quasisolutions of nonlinear irregular operator equations

We propose and study an iterative method for finding quasisolutions of nonlinear ill-posed operator equations on closed convex subsets of a Hilbert space in the presence of errors. The process under consideration combines the gradient-projection method and the projections of iterations obtained onto suitably constructed finite-dimensional subspaces. We establish that the iterations generated by our method are stabilized in a small neighborhood of the quasisolution as the iteration number increases.