Control of an elliptic problem with pointwise state constraints
SIAM Journal on Control and Optimization
Augemented Lagrangian Techniques for Elliptic State Constrained Optimal Control Problems
SIAM Journal on Control and Optimization
Adaptive Finite Element Methods for Optimal Control of Partial Differential Equations: Basic Concept
SIAM Journal on Control and Optimization
A Posteriori Error Estimates for Control Problems Governed by Stokes 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
Positivity preserving finite element approximation
Mathematics of Computation
A level set approach for the solution of a state-constrained optimal control problem
Numerische Mathematik
Convergence of a Finite Element Approximation to a State-Constrained Elliptic Control Problem
SIAM Journal on Numerical Analysis
Goal-Oriented Adaptivity in Control Constrained Optimal Control of Partial Differential Equations
SIAM Journal on Control and Optimization
Error estimates for parabolic optimal control problems with control and state constraints
Computational Optimization and Applications
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In this paper, we propose a mixed variational scheme for optimal control problems with point-wise state constraints, the main idea is to reformulate the optimal control problems to a constrained minimization problem involving only the state, which is characterized by a fourth order variational inequality. Then mixed form based on this fourth order variational inequality is formulated and a direct numerical algorithm is proposed without the optimality conditions of underlying optimal control problems. The a priori and a posteriori error estimates are proved for the mixed finite element scheme. Numerical experiments confirm the efficiency of the new strategy.