On two numerical methods for state-constrained elliptic control problems

A linear-quadratic elliptic control problem with pointwise box constraints on the state is considered. The state constraints are treated by a Lavrentiev type regularization. It is shown that the Lagrange multipliers associated with the regularized state constraints are functions in L 2. Moreover, the convergence of the regularized controls is proven for regularization parameter tending to zero. To solve the problem numerically, an interior point method and a primal–dual active set strategy are implemented and treated in function space.