@Article{AAMM-8-3,
author = {Günther, Andreas and Tber, Moulay, Hicham},
title = {A Goal-Oriented Adaptive Moreau-Yosida Algorithm for Control- and State-Constrained Elliptic Control Problems},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2016},
volume = {8},
number = {3},
pages = {426--448},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.2014.m663},
url = {https://global-sci.com/article/73339/a-goal-oriented-adaptive-moreau-yosida-algorithm-for-control-and-state-constrained-elliptic-control-problems}
}