A new preconditioner for elliptic PDE-constrained optimization problems

  • Hamid Mirchi
  • Davod Khojasteh SalkuyehEmail author
Original Paper


We propose a preconditioner to accelerate the convergence of the GMRES iterative method for solving the system of linear equations obtained from discretize-then-optimize approach applied to optimal control problems constrained by a partial differential equation. Eigenvalue distribution of the preconditioned matrix as well as its eigenvectors are discussed. Numerical results of the proposed preconditioner are compared with several existing preconditioners to show its efficiency.


Preconditioner GMRES Finite element PDE-constrained Optimization 


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The authors would like to thank the anonymous referees for their valuable comments and constructive suggestions. The work of Davod Khojasteh Salkuyeh is partially supported by University of Guilan.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of Mathematical SciencesUniversity of GuilanRashtIran

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