Application of prox-regularization to ill-posed stationary control problems is investigated. Stable variants of penalty methods with one-step and multi-step regularizations in the auxiliary problems are developed and their convergence is proved for distributed as well as boundary control problems with state constraints and Dirichlet or Neumann conditions. (orig.)SIGLEAvailable from TIB Hannover: RO 7722(522) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman