Superlinear convergence of the control reduced interior point method for PDE constrained optimization

A thorough convergence analysis of the Control Reduced Interior Point Method in function space is performed. This recently proposed method is a primal interior point pathfollowing scheme with the special feature, that the control variable is eliminated from the optimality system. Apart from global linear convergence we show, that this method converges locally almost quadrat-ically, if the optimal solution satisfies a certain non-degeneracy condition. In numerical experiments we observe, that a prototype implementation of our method behaves as predicted by our theoretical results.