Properties of an augmented Lagrangian for design optimization

We consider the task of design optimization, where the constraint is a state equation that can only be solved by a typically rather slowly converging fixed point solver. This process can be augmented by a corresponding adjoint solver, and based on the resulting approximate reduced derivatives, also an optimization iteration, which actually changes the design. To coordinate the three iterative processes, we consider an augmented Lagrangian function that should be consistently reduced whatever combination of sequence of primal, dual and optimization steps one chooses. We present some numerical results for a one-shot strategy where all variables are changed simultaneously.