Error Estimates for the Numerical Approximation of a Semilinear Elliptic Control Problem
Computational Optimization and Applications
Error Estimates for the Numerical Approximation of Boundary Semilinear Elliptic Control Problems
Computational Optimization and Applications
Error estimates for the numerical approximation of Neumann control problems
Computational Optimization and Applications - Special issue: Numerical analysis of optimization in partial differential equations
Error estimates for the numerical approximation of Neumann control problems
Computational Optimization and Applications
Computational Optimization and Applications
Computational Optimization and Applications
Approximation of Boundary Control Problems on Curved Domains
SIAM Journal on Control and Optimization
On finite element error estimates for optimal control problems with elliptic PDEs
LSSC'09 Proceedings of the 7th international conference on Large-Scale Scientific Computing
Second Order Analysis for Optimal Control Problems: Improving Results Expected From Abstract Theory
SIAM Journal on Optimization
Computational Optimization and Applications
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This paper deals with necessary and sufficient optimality conditions for control problems governed by semilinear elliptic partial differential equations with finitely many equality and inequality state constraints. Some recent results on this topic for optimal control problems based upon results for abstract optimization problems are compared with some new results using methods adapted to the control problems. Meanwhile, the Lagrangian formulation is followed to provide the optimality conditions in the first case; the Lagrangian and Hamiltonian functions are used in the second statement. Finally, we prove the equivalence of both formulations.