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Multigrid Optimization Methods for the Optimal Control of Convection–Diffusion Problems with Bilinear Control

Author

Listed:
  • A. Borzì

    (Universität Würzburg, Emil-Fischer-Straße 30)

  • E.-J. Park

    (Yonsei University)

  • M. Vallejos Lass

    (University of the Philippines
    Technische Universität Darmstadt)

Abstract

Optimal control problems, governed by convection–diffusion equations with bilinear control, are studied. For the realization of the numerical solution, the multigrid for optimization method together with finite difference discretization is utilized and investigated. In addition, the extension to constrained optimal control problems with bilinear control is considered. Results of numerical experiments show the computational performance of the proposed multigrid scheme in solving optimal control problems subject to a convection–diffusion equation with bilinear control. We obtain that the proposed multigrid strategy accelerates classical one-grid optimization schemes and inherits the order of convergence of the finite difference discretization. Moreover, the mesh independence principle is obtained, which is a typical characterization of a multigrid strategy.

Suggested Citation

  • A. Borzì & E.-J. Park & M. Vallejos Lass, 2016. "Multigrid Optimization Methods for the Optimal Control of Convection–Diffusion Problems with Bilinear Control," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 510-533, February.
    • Handle: RePEc:spr:joptap:v:168:y:2016:i:2:d:10.1007_s10957-015-0791-z
    DOI: 10.1007/s10957-015-0791-z
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    Cited by:

    1. Butt, Muhammad Munir, 2022. "On a multigrid solver for stationary Navier–Stokes velocity–pressure tracking-type control problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 246-264.

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