NEW METHOD FOR NONSMOOTH CONVEX-OPTIMIZATION

A new method for minimizing a proper closed convex function fis propos ed and its convergence properties are studied. The convergence rate de pends on both the growth speed off at minimizers and the choice of pro ximal parameters. An application of the method extends the correspondi ng results given by Kort and Bertsekas for proximal minimization algor ithms to the case in which the iteration points are calculated approxi mately. In particular, it relaxes the convergence conditions of Rockaf ellar's results for the proximal point algorithm.