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Preprint 13-2004

Analysis of the SQP-method for optimal control problems governed by the instationary Navier-Stokes equations based on Lp-theory

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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

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