We propose augmented Lagrangian methods to solve state and control constrained optimal central problems. The approach is based on the Lagrangian formulation of nonsmooth convex optimization in Hilbert spaces developed in [K. Ito and K. Kunisch, Augmented Lagrangian Methods for Nonsmooth Convex Optimization in Hilbert Spaces, preprint, 1994]. We investigate a linear optimal control problem with a boundary control function as in [M. Bergounioux, Numer. Funct. Anal. Optim., 14 (1993), pp. 515-543]. Both the equation and the constraints are augmented. The proposed methods are general and can be adapted to a much wider class of problems.