A Goal-Oriented Adaptive Moreau-Yosida Algorithm for Control- and State-Constrained Elliptic Control Problems (Advances in Applied Mathematics and Mechanics, 2018)
In this work, we develop an adaptive algorithm for solving elliptic optimalcontrol problems with simultaneously appearing state and control constraints. Thealgorithm combines a Moreau-Yosida technique for handling state constraints with asemi-smooth Newton method for solving the optimality systems of the regularizedsub-problems. The state and adjoint variables are discretized using continuous piecewiselinear finite elements while a variational discretization concept is applied for thecontrol. To perform the adaptive mesh refinements cycle we derive local error estimatorswhich extend the goal-oriented error approach to our setting. The performance ofthe overall adaptive solver is assessed by numerical examples.