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A Matching-Strategy-Inspired Preconditioning for Elliptic Optimal Control Problems

Author

Listed:
  • Chaojie Wang

    (School of Mathematics and Statistics, Beijing Technology and Business University, Beijing 100048, China)

  • Jie Chen

    (School of Mathematics and Statistics, Beijing Technology and Business University, Beijing 100048, China)

  • Shuen Sun

    (School of Mathematics and Statistics, Beijing Technology and Business University, Beijing 100048, China)

Abstract

In this paper, a new preconditioning method is proposed for the linear system arising from the elliptic optimal control problem. It is based on row permutations of the linear system and approximations of the corresponding Schur complement inspired by the matching strategy. The eigenvalue bounds of the preconditioned matrices are shown to be independent of mesh size and regularization parameter. Numerical results illustrate the efficiency of the proposed preconditioning methods.

Suggested Citation

  • Chaojie Wang & Jie Chen & Shuen Sun, 2023. "A Matching-Strategy-Inspired Preconditioning for Elliptic Optimal Control Problems," Mathematics, MDPI, vol. 11(12), pages 1-8, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2599-:d:1165305
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    References listed on IDEAS

    as
    1. Ole Løseth Elvetun & Bjørn Fredrik Nielsen, 2016. "The split Bregman algorithm applied to PDE-constrained optimization problems with total variation regularization," Computational Optimization and Applications, Springer, vol. 64(3), pages 699-724, July.
    2. Wang, Chaojie & Li, Hongyi & Zhao, Di, 2019. "Improved block preconditioners for linear systems arising from half-quadratic image restoration," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
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