| Abstract: | The present paper deals with a special scheme of iterative prox-regularization applied to approximation of ill-posed convex variational problems. In distinction to the standard iterative regularization, here for each approximate problem the number of steps of the prox-method is determined within the iteration method by means of a distance criterion between two succeeding iterates. Convergence is proved under conditions which do not contradict the usual organization of discretization methods. Apriori bounds for the distance between the current solutions of the approximate problems and a solution of the original problem are described. That permits to control the number of steps of the pro x-method with the goal to use rough approximations more effectively.Rate of convergence of the minimizing sequence is estimated under the condition that the choice of controlling parameters is suitably regulated during the iteration method. For special classes of ill-posed variational problems a linear rate of convergence W.r.t. the objective functional values and the arguments is established. |
