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

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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.

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Authors and Affiliations

  1. Institut für Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, 10623, Berlin, Germany

    Uwe Prüfert & Fredi Tröltzsch

  2. Konrad-Zuse-Zentrum für Informationstechnik Berlin, Takustraße 7, 14195, Berlin-Dahlem, Germany

    Martin Weiser

Authors
  1. Uwe Prüfert
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  2. Fredi Tröltzsch
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  3. Martin Weiser
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Corresponding author

Correspondence to Fredi Tröltzsch.

Additional information

Research supported by the DFG Research Center “Mathematics for key technologies” (Matheon) in Berlin.

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Prüfert, U., Tröltzsch, F. & Weiser, M. The convergence of an interior point method for an elliptic control problem with mixed control-state constraints. Comput Optim Appl 39, 183–218 (2008). https://doi.org/10.1007/s10589-007-9063-7

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  • DOI: https://doi.org/10.1007/s10589-007-9063-7

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