On the use of state constraints in optimal control of singular PDEs

We consider optimal control of nonlinear partial di erential equations involving potentially singular solution-dependent terms. Singularity can be prevented by either restricting controls to a closed admissible set for which well-posedness of the equation can be guaranteed, or by explicitly enforcing pointwise bounds on the state. Bymeans of an elliptic model problem, we contrast the requirements for deriving existence of solutions and rst order optimality conditions for both the control-constrained and the state-constrained formulation. Our analysis as well as numerical tests illustrate that control constraints lead to severe restrictions on the attainable states, which is not the case for state constraints.