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
SIAM Journal on Control and Optimization
Primal-Dual Active Set Strategy for a General Class of Constrained Optimal Control Problems
SIAM Journal on Optimization
SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
Path-following Methods for a Class of Constrained Minimization Problems in Function Space
SIAM Journal on Optimization
SIAM Journal on Control and Optimization
Convergence of a Finite Element Approximation to a State-Constrained Elliptic Control Problem
SIAM Journal on Numerical Analysis
SIAM Journal on Control and Optimization
Numerical approximation of elliptic control problems with finitely many pointwise constraints
Computational Optimization and Applications
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A family of elliptic optimal control problems with pointwise constraints on control and state is considered. We are interested in approximation of the optimal solution by a finite element discretization of the involved partial differential equations. The discretization error for a problem with mixed state constraints is estimated in the semidiscrete case and in the fully discrete scheme with the convergence of order h|ln驴h| and h 1/2, respectively. However, considering the unregularized continuous problem and the discrete regularized version, and choosing suitable relation between the regularization parameter and the mesh size, i.e., 驴~h 2, a convergence order arbitrary close to 1, i.e., h 1驴β is obtained. Therefore, we benefit from tuning the involved parameters.