Volume 8, Issue 3
A Goal-Oriented Adaptive Moreau-Yosida Algorithm for Control- and State-Constrained Elliptic Control Problems

Andreas Günther & Moulay Hicham Tber

Adv. Appl. Math. Mech., 8 (2016), pp. 426-448.

Published online: 2018-05

Preview Purchase PDF 2 1208
Export citation
  • Abstract

In this work, we develop an adaptive algorithm for solving elliptic optimal control problems with simultaneously appearing state and control constraints. The algorithm combines a Moreau-Yosida technique for handling state constraints with a semi-smooth Newton method for solving the optimality systems of the regularized sub-problems. The state and adjoint variables are discretized using continuous piecewise linear finite elements while a variational discretization concept is applied for the control. To perform the adaptive mesh refinements cycle we derive local error estimators which extend the goal-oriented error approach to our setting. The performance of the overall adaptive solver is assessed by numerical examples.

  • Keywords

Elliptic optimal control problem, control and state constraints, Moreau-Yosida regularization, semi-smooth Newton method, variational discretization, goal-oriented adaptivity.

  • AMS Subject Headings

49J20, 49K20, 65K10, 65N50

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{AAMM-8-426, author = {}, title = {A Goal-Oriented Adaptive Moreau-Yosida Algorithm for Control- and State-Constrained Elliptic Control Problems}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {8}, number = {3}, pages = {426--448}, abstract = {

In this work, we develop an adaptive algorithm for solving elliptic optimal control problems with simultaneously appearing state and control constraints. The algorithm combines a Moreau-Yosida technique for handling state constraints with a semi-smooth Newton method for solving the optimality systems of the regularized sub-problems. The state and adjoint variables are discretized using continuous piecewise linear finite elements while a variational discretization concept is applied for the control. To perform the adaptive mesh refinements cycle we derive local error estimators which extend the goal-oriented error approach to our setting. The performance of the overall adaptive solver is assessed by numerical examples.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2014.m663}, url = {http://global-sci.org/intro/article_detail/aamm/12096.html} }
TY - JOUR T1 - A Goal-Oriented Adaptive Moreau-Yosida Algorithm for Control- and State-Constrained Elliptic Control Problems JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 426 EP - 448 PY - 2018 DA - 2018/05 SN - 8 DO - http://doi.org/10.4208/aamm.2014.m663 UR - https://global-sci.org/intro/article_detail/aamm/12096.html KW - Elliptic optimal control problem, control and state constraints, Moreau-Yosida regularization, semi-smooth Newton method, variational discretization, goal-oriented adaptivity. AB -

In this work, we develop an adaptive algorithm for solving elliptic optimal control problems with simultaneously appearing state and control constraints. The algorithm combines a Moreau-Yosida technique for handling state constraints with a semi-smooth Newton method for solving the optimality systems of the regularized sub-problems. The state and adjoint variables are discretized using continuous piecewise linear finite elements while a variational discretization concept is applied for the control. To perform the adaptive mesh refinements cycle we derive local error estimators which extend the goal-oriented error approach to our setting. The performance of the overall adaptive solver is assessed by numerical examples.

Andreas Günther & Moulay Hicham Tber. (2020). A Goal-Oriented Adaptive Moreau-Yosida Algorithm for Control- and State-Constrained Elliptic Control Problems. Advances in Applied Mathematics and Mechanics. 8 (3). 426-448. doi:10.4208/aamm.2014.m663
Copy to clipboard
The citation has been copied to your clipboard