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Mesh-independence of semismooth Newton methods for Lavrentiev-regularized state constrained nonlinear optimal control problems

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Abstract

A class of nonlinear elliptic optimal control problems with mixed control-state constraints arising, e.g., in Lavrentiev-type regularized state constrained optimal control is considered. Based on its first order necessary optimality conditions, a semismooth Newton method is proposed and its fast local convergence in function space as well as a mesh-independence principle for appropriate discretizations are proved. The paper ends by a numerical verification of the theoretical results including a study of the algorithm in the case of vanishing Lavrentiev-parameter. The latter process is realized numerically by a combination of a nested iteration concept and an extrapolation technique for the state with respect to the Lavrentiev-parameter.

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Authors and Affiliations

  1. Institute of Mathematics and Scientific Computing, University of Graz, 8010, Graz, Austria

    M. Hintermüller

  2. Institut für Mathematik, Technische Universität Berlin, Str. des 17. Juni 136, 10623, Berlin, Germany

    F. Tröltzsch & I. Yousept

Authors
  1. M. Hintermüller
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  2. F. Tröltzsch
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  3. I. Yousept
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Correspondence to M. Hintermüller.

Additional information

M. Hintermüller acknowledges support by the Austrian Science Fund FWF under START-program Y305 “Interfaces and Free Boundaries”.

F. Tröltzsch and I. Yousept acknowledge support through DFG Research Center “Mathematics for Key Technologies” (FZT 86) in Berlin.

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Hintermüller, M., Tröltzsch, F. & Yousept, I. Mesh-independence of semismooth Newton methods for Lavrentiev-regularized state constrained nonlinear optimal control problems. Numer. Math. 108, 571–603 (2008). https://doi.org/10.1007/s00211-007-0134-6

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  • DOI: https://doi.org/10.1007/s00211-007-0134-6

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