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