Add to ORKGThe paper deals with regularized penalty-barrier methods for ill-posed convex programming problems. The approach suggested combines a generalized proximal algorithm developed in (5) with an interior-point-strategy, using barrier function. In the spirit of a proximal algorithm we consider interior-point-methods in which on each step a strongly convex function has to be minimized and the prox-term can be scaled by a variable scaling factor (cf. formula (3)). In the first part of the paper convergence of the regularized penalty method is studied for an axiomatically given class of penalty functions (Theorem 1). The technique used here differs essentially from those in other papers, where usually a uniform approximation of the original problem ...