On two numerical methods for state-constrained elliptic control problems

Authors:
Chr. Meyer;U. Prüfert;F. Tröltzsch
Affiliations:
Weierstrass Institute for Applied Analysis and Stochastics, Germany;Institut für Mathematik, Technische Universität, Berlin, Germany;Institut für Mathematik, Technische Universität, Berlin, Germany
Venue:
Optimization Methods & Software
Year:
2007

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Abstract

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 L2. 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.