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Multigrid Methods for Control-Constrained Elliptic Optimal Control Problems

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Numerical Mathematics and Advanced Applications 2009

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Abstract

Multigrid schemes that solve control-constrained elliptic optimal control problems discretized by finite differences are presented. A gradient projection method is used to treat the constraints on the control variable. A comparison is made between two multigrid methods, the multigrid for optimization (MGOPT) method and the collective smoothing multigrid (CSMG) method. To illustrate both techniques, we focus on minimization problems governed by elliptic differential equations with constraints on the control variable.

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Author information

Authors and Affiliations

  1. Institute of Mathematics, University of the Philippines, Diliman, Quezon City, Philippines

    Michelle Vallejos

  2. Dipartimento e Facoltà di Ingegneria, Università degli Studi del Sannio, 82100, Benevento, Italia

    Alfio Borzì

Authors
  1. Michelle Vallejos
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  2. Alfio Borzì
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Corresponding author

Correspondence to Michelle Vallejos .

Editor information

Editors and Affiliations

  1. Dept. of Information Technology, Uppsala University, Uppsala, 751 05, Sweden

    Gunilla Kreiss

  2. Dept. of Information Technology, Uppsala University, Uppsala, 751 05, Sweden

    Per Lötstedt

  3. Dept. of Information Technology, Uppsala University, Uppsala, 751 05, Sweden

    Axel Målqvist

  4. Dept. of Information Technology, Uppsala University, Uppsala, 751 05, Sweden

    Maya Neytcheva

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Vallejos, M., Borzì, A. (2010). Multigrid Methods for Control-Constrained Elliptic Optimal Control Problems. In: Kreiss, G., Lötstedt, P., Målqvist, A., Neytcheva, M. (eds) Numerical Mathematics and Advanced Applications 2009. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11795-4_95

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