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A Semi-smooth Newton Method for Regularized State-constrained Optimal Control of the Navier-Stokes Equations

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Abstract

In this paper, we study semi-smooth Newton methods for the numerical solution of regularized pointwise state-constrained optimal control problems governed by the Navier-Stokes equations. After deriving an appropriate optimality system for the original problem, a class of Moreau-Yosida regularized problems is introduced and the convergence of their solutions to the original optimal one is proved. For each regularized problem a semi-smooth Newton method is applied and its local superlinear convergence verified. Finally, selected numerical results illustrate the behavior of the method and a comparison between the max-min and the Fischer-Burmeister as complementarity functionals is carried out.

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Authors and Affiliations

  1. Department of Mathematics, EPN Quito, Ecuador and Institute for Mathematics, TU, Berlin, Germany

    J. C. de los Reyes

  2. Institute for Mathematics and Scientific Computing, Karl-Franzens-University of Graz, Austria

    K. Kunisch

Authors
  1. J. C. de los Reyes
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  2. K. Kunisch
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Correspondence to J. C. de los Reyes.

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de los Reyes, J.C., Kunisch, K. A Semi-smooth Newton Method for Regularized State-constrained Optimal Control of the Navier-Stokes Equations. Computing 78, 287–309 (2006). https://doi.org/10.1007/s00607-006-0183-1

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  • DOI: https://doi.org/10.1007/s00607-006-0183-1

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