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Volume 19, Issue 2-3
A Comparison of Regularization Methods for Boundary Optimal Control Problems

Giorgio Bornia, Andrea Chierici & Saikanth Ratnavale

Int. J. Numer. Anal. Mod., 19 (2022), pp. 329-346.

Published online: 2022-04

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  • Abstract

In this work we propose and compare multiple approaches for the formulation of boundary optimal control problems constrained by PDEs. In particular, we define a property of balanced regularity that is not satisfied by traditional approaches. In order to instead guarantee this property, we consider the use of other regularization terms, one involving fractional Sobolev norms and the other one based on the introduction of lifting functions. As required by the fractional norm approach, we present a semi-analytical numerical implementation of the fractional Laplacian operator. All the proposed formulations are also considered in conjunction with constraints of inequality type on the control variable. Numerical results are reported to compare all the presented regularization techniques.

  • Keywords

Boundary optimal control, regularization methods, inequality constraints

  • AMS Subject Headings

49N60, 49M25, 35R11

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{IJNAM-19-329, author = {Bornia , GiorgioChierici , Andrea and Ratnavale , Saikanth}, title = {A Comparison of Regularization Methods for Boundary Optimal Control Problems }, journal = {International Journal of Numerical Analysis and Modeling}, year = {2022}, volume = {19}, number = {2-3}, pages = {329--346}, abstract = {

In this work we propose and compare multiple approaches for the formulation of boundary optimal control problems constrained by PDEs. In particular, we define a property of balanced regularity that is not satisfied by traditional approaches. In order to instead guarantee this property, we consider the use of other regularization terms, one involving fractional Sobolev norms and the other one based on the introduction of lifting functions. As required by the fractional norm approach, we present a semi-analytical numerical implementation of the fractional Laplacian operator. All the proposed formulations are also considered in conjunction with constraints of inequality type on the control variable. Numerical results are reported to compare all the presented regularization techniques.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/20484.html} }
TY - JOUR T1 - A Comparison of Regularization Methods for Boundary Optimal Control Problems AU - Bornia , Giorgio AU - Chierici , Andrea AU - Ratnavale , Saikanth JO - International Journal of Numerical Analysis and Modeling VL - 2-3 SP - 329 EP - 346 PY - 2022 DA - 2022/04 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/20484.html KW - Boundary optimal control, regularization methods, inequality constraints AB -

In this work we propose and compare multiple approaches for the formulation of boundary optimal control problems constrained by PDEs. In particular, we define a property of balanced regularity that is not satisfied by traditional approaches. In order to instead guarantee this property, we consider the use of other regularization terms, one involving fractional Sobolev norms and the other one based on the introduction of lifting functions. As required by the fractional norm approach, we present a semi-analytical numerical implementation of the fractional Laplacian operator. All the proposed formulations are also considered in conjunction with constraints of inequality type on the control variable. Numerical results are reported to compare all the presented regularization techniques.

Bornia , GiorgioChierici , Andrea and Ratnavale , Saikanth. (2022). A Comparison of Regularization Methods for Boundary Optimal Control Problems . International Journal of Numerical Analysis and Modeling. 19 (2-3). 329-346. doi:
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