Inhalt des Dokuments
Preprint 13-2004
Analysis of the SQP-method for optimal control problems governed by the instationary Navier-Stokes equations based on Lp-theory
Author(s) :
Daniel Wachsmuth
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 13-2004
MSC 2000
- 49M37 Methods of nonlinear programming type
-
49N60 Regularity of solutions
Abstract :
The aim of this article is to present a convergence theory of the SQP-method applied
to optimal control problems for the instationary Navier-Stokes equations.
We will employ a second-order sufficient optimality condition, which requires that
the second derivative of the
Lagrangian is positive definit on a subspace of inactive constraints. Therefore, we have
to use $L^p$-theory of optimal controls of the instationary
Navier-Stokes equations rather than Hilbert space methods.
We prove local convergence of the SQP-method. This behaviour
is confirmed by numerical tests.
Keywords :
Optimal control, Navier-Stokes equations, control constraints, Lipschitz stability,
SQP-method