Boundary control of semilinear elliptic equations with pointwise state constraints
SIAM Journal on Control and Optimization
Optimal Control Problems with Mixed Control-State Constraints
SIAM Journal on Control and Optimization
Semismooth Newton Methods for Operator Equations in Function Spaces
SIAM Journal on Optimization
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
Path-following Methods for a Class of Constrained Minimization Problems in Function Space
SIAM Journal on Optimization
On two numerical methods for state-constrained elliptic control problems
Optimization Methods & Software
Computational Optimization and Applications
Computational Optimization and Applications
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A linear elliptic control problem with pointwise state constraints is considered. These constraints are given in the domain. In contrast to this, the control acts only at the boundary. We propose a general concept using virtual control in this paper. The virtual control is introduced in objective, state equation, and constraints. Moreover, additional control constraints for the virtual control are investigated. An error estimate for the regularization error is derived as main result of the paper. The theory is illustrated by numerical tests.