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 - <p style="text-align: justify;">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.</p>