Formulation and Analysis of a
Sequential Quadratic Programming Method
for the Optimal Dirichlet Boundary Control
of Navier-Stokes Flow
Matthias Heinkenschloss
Department of Computational and Applied Mathematics
Rice University
In: W. W. Hager and P. M. Pardalos (eds.).
Optimal Control: Theory, Algorithms, and Applications.
Kluwer Academic Publishers B.V.,
1998, pp. 178-203.
Abstract
The optimal boundary control of Navier-Stokes flow
is formulated as a constrained optimization problem
and a sequential quadratic programming (SQP) approach is
studied for its solution.
Since SQP methods treat states and controls as
independent variables and do not insist on
satisfying the constraints during the iterations,
care must be taken to avoid a possible incompatibility
of Dirichlet boundary conditions and incompressibility constraint.
In this paper, compatibility is enforced by choosing
appropriate function spaces. The resulting optimization
problem is analyzed. Differentiability of the constraints
and surjectivity of linearized constraints are verified
and adjoints are computed. An SQP method is applied to
the optimization problem and compared with other approaches.
Keywords
Optimal flow control, Navier-Stokes equations,
sequential quadratic programming.
1991 Mathematics Subject Classification
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