Gradient projection method for stable approximation of quasisolutions to irregular nonlinear operator equations

An iterative process of the gradient projection type is constructed and examined as a tool for approximating quasisolutions to irregular nonlinear operator equations in a Hilbert space. One step of this process combines a gradient descent step in a finite-dimensional affine subspace and the Fejrér operator with respect to the convex closed set to which the quasisolution belongs. It is proved that the approximations generated by the proposed method stabilize in a small neighborhood of the desired quasisolution, and the diameter of this neighborhood is estimated.