Formulation and Analysis of a Sequential Quadratic Programming Method for the Optimal Dirichlet Boundary Control of Navier-Stokes Flow

  • Matthias Heinkenschloss
Part of the Applied Optimization book series (APOP, volume 15)

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. 

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Copyright information

© Springer Science+Business Media Dordrecht 1998

Authors and Affiliations

  • Matthias Heinkenschloss
    • 1
  1. 1.Department of Computational and Applied MathematicsRice UniversityHoustonUSA

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