Higher order methods are often used for the numerical solution of nonlinear constrained optimal control problems. For that reason we have to solve a linear-quadratic optimal control problem in each step of such an algorithm. In this talk we propose a primal-dual strategy to solve constrained linear-quadratic optimal control problems. This strategy based on an Augmented Lagrangian. Using a merit function we prove the strong convergence of control and state under certain assumptions. This result implies finite step convergence for the discretized problems. After the theoretical part we show some numerical examples.
This paper is a joint work with K. Kunisch (Graz).