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On two numerical methods for state-constrained elliptic control problems

Meyer, Christian; Pruefert, Uwe; Tröltzsch, Fredi

Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin

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 known that the Lagrange multipliers associated with the regularized state-constraints are functions in L^2. Moreover, the convergence of the optimal control of the regularized problem 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 tested in function space.