Balancing Neumann-Neumann Methods for Elliptic Optimal Control Problems

  • Matthias Heinkenschloss
  • Hoang Nguyen
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 40)


We present Neumann-Neumann domain decomposition preconditioners for the solution of elliptic linear quadratic optimal control problems. The preconditioner is applied to the optimality system. A Schur complement formulation is derived that reformulates the original optimality system as a system in the state and adjoint variables restricted to the subdomain boundaries. The application of the Schur complement matrix requires the solution of subdomain optimal control problems with Dirichlet boundary conditions on the subdomain interfaces. The application of the inverses of the subdomain Schur complement matrices require the solution of subdomain optimal control problems with Neumann boundary conditions on the subdomain interfaces. Numerical tests show that the dependence of this preconditioner on mesh size and subdomain size is comparable to its counterpart applied to elliptic equations only.


Optimal Control Problem Domain Decomposition Sequential Quadratic Programming Domain Decomposition Method Saddle Point Problem 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Matthias Heinkenschloss
    • 1
  • Hoang Nguyen
    • 1
  1. 1.Department of Computational and Applied MathematicsRice UniversityUSA

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