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Volume 5, Issue 1
Multigrid Methods for Elliptic Optimal Control Problems with Pointwise State Constraints

Michelle Vallejos

DOI: 10.4208/nmtma.2011.m12si06

Numer. Math. Theor. Meth. Appl., 5 (2012), pp. 99-109.

Published online: 2012-05

[An open-access article; the PDF is free to any online user.]

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  • Abstract

An elliptic optimal control problem with constraints on the state variable is considered. The Lavrentiev-type regularization is used to treat the constraints on the state variable. To solve the problem numerically, the multigrid for optimization (MGOPT) technique and the collective smoothing multigrid (CSMG) are implemented. Numerical results are reported to illustrate and compare the efficiency of both multigrid strategies.

  • Keywords

Elliptic optimal control problems, Lavrentiev regularization, multigrid methods, pointwise state constraints.

  • AMS Subject Headings

49K20, 65N06, 65N55

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-5-99, author = {}, title = {Multigrid Methods for Elliptic Optimal Control Problems with Pointwise State Constraints}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2012}, volume = {5}, number = {1}, pages = {99--109}, abstract = {

An elliptic optimal control problem with constraints on the state variable is considered. The Lavrentiev-type regularization is used to treat the constraints on the state variable. To solve the problem numerically, the multigrid for optimization (MGOPT) technique and the collective smoothing multigrid (CSMG) are implemented. Numerical results are reported to illustrate and compare the efficiency of both multigrid strategies.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2011.m12si06}, url = {http://global-sci.org/intro/article_detail/nmtma/5930.html} }
TY - JOUR T1 - Multigrid Methods for Elliptic Optimal Control Problems with Pointwise State Constraints JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 99 EP - 109 PY - 2012 DA - 2012/05 SN - 5 DO - http://doi.org/10.4208/nmtma.2011.m12si06 UR - https://global-sci.org/intro/article_detail/nmtma/5930.html KW - Elliptic optimal control problems, Lavrentiev regularization, multigrid methods, pointwise state constraints. AB -

An elliptic optimal control problem with constraints on the state variable is considered. The Lavrentiev-type regularization is used to treat the constraints on the state variable. To solve the problem numerically, the multigrid for optimization (MGOPT) technique and the collective smoothing multigrid (CSMG) are implemented. Numerical results are reported to illustrate and compare the efficiency of both multigrid strategies.

Michelle Vallejos. (2020). Multigrid Methods for Elliptic Optimal Control Problems with Pointwise State Constraints. Numerical Mathematics: Theory, Methods and Applications. 5 (1). 99-109. doi:10.4208/nmtma.2011.m12si06
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