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An interior point algorithm with inexact step computation in function space for state constrained optimal control

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Abstract

We consider an interior point method in function space for PDE constrained optimal control problems with state constraints. Our emphasis is on the construction and analysis of an algorithm that integrates a Newton path-following method with adaptive grid refinement. This is done in the framework of inexact Newton methods in function space, where the discretization error of each Newton step is controlled by adaptive grid refinement in the innermost loop. This allows to perform most of the required Newton steps on coarse grids, such that the overall computational time is dominated by the last few steps. For this purpose we propose an a-posteriori error estimator for a problem suited norm.

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

    Anton Schiela & Andreas Günther

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  1. Anton Schiela
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  2. Andreas Günther
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Correspondence to Anton Schiela.

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Schiela, A., Günther, A. An interior point algorithm with inexact step computation in function space for state constrained optimal control. Numer. Math. 119, 373–407 (2011). https://doi.org/10.1007/s00211-011-0381-4

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  • DOI: https://doi.org/10.1007/s00211-011-0381-4

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