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

Authors:
Uwe Prüfert;Fredi Tröltzsch;Martin Weiser
Affiliations:
Institut für Mathematik, Technische Universität Berlin, Berlin, Germany 10623;Institut für Mathematik, Technische Universität Berlin, Berlin, Germany 10623;Konrad-Zuse-Zentrum für Informationstechnik Berlin, Berlin-Dahlem, Germany 14195
Venue:
Computational Optimization and Applications
Year:
2008

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Abstract

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.