The convergence of an interior point method for an elliptic control problem with mixed control-state constraints

The paper addresses a primal interior point method for state-constrained PDE optimal control problems in function space. By a Lavrentiev regularization, the state constraint is transformed to a mixed control-state constraint with bounded Lagrange multiplier. Existence and convergence of the central path are established, and linear convergence of a short-step pathfollowing method is shown. The behaviour of the method is demonstrated by numerical examples. Research supported by the DFG Research Center “Mathematics for key technologies” (Matheon) in Berlin.