Stability of elliptic optimal control problems

Optimal Control of Semilinear Elliptic Obstacle Problems

Multigrid Methods for Elliptic Optimal Control Problems

Multigrid methods for elliptic optimal control problems

Shape-Measure Method for Solving Elliptic Optimal Shape Problems (Fixed Control Case)

Lipschitz Stability of Solutions to some State-Constrained Elliptic Optimal Control Problems

In this paper, optimal control problems with pointwise state constraints for linear and semilinear elliptic partial differential equations are studied. The problems are subject to perturbations in the problem data. Lipschitz stability with respect to perturbations of the optimal control and the state and adjoint variables is established initially for linear–quadratic problems. Both the distribu...

Second-Order and Stability Analysis for State-Constrained Elliptic Optimal Control Problems with Sparse Controls

An optimal control problem for a semilinear elliptic partial differential equation is discussed subject to pointwise control constraints on the control and the state. The main novelty of the paper is the presence of the L1-norm of the control as part of the objective functional that eventually leads to sparsity of the optimal control functions. Second-order sufficient optimality conditions are ...