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

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Author(s) : Juan Carlos de los Reyes , Karl Kunisch

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 23-2005

MSC 2000

76D55 Flow control and optimization
49M29 Methods involving duality

Abstract :
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.

Keywords : Optimal control, Navier-Stokes equations, state constraints, semi-smooth Newton methods