CONVERGENCE OF A PROXIMAL POINT METHOD IN THE PRESENCE OF COMPUTATIONAL ERRORS IN HILBERT SPACES

We study the convergence of a proximal point method in a Hilbert space under the presence of computational errors. Most results known in the literature establish the convergence of proximal point methods when computational errors are summable. In the present paper the convergence of the method is established for nonsummable computational errors. We show that the proximal point method generates a good approximate solution if the sequence of computational errors is bounded from above by some constant.