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Formulation and analysis of a sequential quadratic programming method for the optimal Dirichlet boundary control of Navier-Stokes flow. (English) Zbl 0924.76021

Hager, William H. (ed.) et al., Optimal control: theory, algorithms, and applications. Proceedings of a conference, University of Florida, Gainesville, FL, USA, February 27–March 1, 1997. Dordrecht: Kluwer Academic Publishers. Appl. Optim. 15, 178-203 (1998).
Summary: 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.
For the entire collection see [Zbl 0890.00045].

MSC:

76D05 Navier-Stokes equations for incompressible viscous fluids
49J20 Existence theories for optimal control problems involving partial differential equations
90C20 Quadratic programming

Software:

TRICE; L-BFGS
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