A semi-smooth Newton method for regularized state-constrained optimal control of the Navier-Stokes equations

Revised version of the preprint first published 01. September 2005 under the title "A semi-smooth Newton method for state-constrained optimal control of the Navier-Stokes equations"In this paper we study semi-smooth Newton methods for the numerical solution of pointwise state-constrained optimal control problems governed by the Navier-Stokes equations. After deriving an appropriate optimality system, a class of 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 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