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
Primal-Dual Strategy for State-Constrained Optimal Control Problems
Computational Optimization and Applications
A variational discretization concept in control constrained optimization: the linear-quadratic case
Computational Optimization and Applications
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
Feasible and Noninterior Path-Following in Constrained Minimization with Low Multiplier Regularity
SIAM Journal on Control and Optimization
Convergence of a Finite Element Approximation to a State-Constrained Elliptic Control Problem
SIAM Journal on Numerical Analysis
Computational Optimization and Applications
On two numerical methods for state-constrained elliptic control problems
Optimization Methods & Software
Computational Optimization and Applications
SIAM Journal on Control and Optimization
Computational Optimization and Applications
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In the present work, we apply a variational discretization proposed by the first author in (Comput. Optim. Appl. 30:45---61, 2005) to Lavrentiev-regularized state constrained elliptic control problems. We extend the results of (Comput. Optim. Appl. 33:187---208, 2006) and prove weak convergence of the adjoint states and multipliers of the regularized problems to their counterparts of the original problem. Further, we prove error estimates for finite element discretizations of the regularized problem and investigate the overall error imposed by the finite element discretization of the regularized problem compared to the continuous solution of the original problem. Finally we present numerical results which confirm our analytical findings.