Proximal Point Algorithm

Abstract

In a Hilbert space, we study the convergence of an iterative proximal point method to a common zero of a finite family of maximal monotone operators 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 this chapter, 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 a constant. Moreover, for a known computational error, we find out what an approximate solution can be obtained and how many iterates one needs for this.