Control of an elliptic problem with pointwise state constraints
SIAM Journal on Control and Optimization
Boundary control of semilinear elliptic equations with pointwise state constraints
SIAM Journal on Control and Optimization
Primal-Dual Strategy for Constrained Optimal Control Problems
SIAM Journal on Control and Optimization
Computational Optimization and Applications
Augmented Lagrangian methods for nonsmooth, convex optimization in Hilbert spaces
Nonlinear Analysis: Theory, Methods & Applications
Smoothing Methods and Semismooth Methods for Nondifferentiable Operator Equations
SIAM Journal on Numerical Analysis
Primal-Dual Strategy for State-Constrained Optimal Control Problems
Computational Optimization and Applications
The Primal-Dual Active Set Strategy as a Semismooth Newton Method
SIAM Journal on Optimization
Optimal Control of PDEs with Regularized Pointwise State Constraints
Computational Optimization and Applications
A virtual control concept for state constrained optimal control problems
Computational Optimization and Applications
Error estimates for parabolic optimal control problem by fully discrete mixed finite element methods
Finite Elements in Analysis and Design
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A Lavrentiev type regularization technique for solving elliptic boundary control problems with pointwise state constraints is considered. The main concept behind this regularization is to look for controls in the range of the adjoint control-to-state mapping. After investigating the analysis of the method, a semismooth Newton method based on the optimality conditions is presented. The theoretical results are confirmed by numerical tests. Moreover, they are validated by comparing the regularization technique with standard numerical codes based on the discretize-then-optimize concept.