Stability in Affine Optimal Control Problems Constrained by Semilinear Elliptic Partial Differential Equations

Optimal control of partial differential equations with affine control constraints

Numerical solution of PDE optimal control problems involving affine pointwise control constraints is investigated. Optimality conditions are derived and a semi-smooth Newton method is presented. Global and local superlinear convergence of the method are obtained for linear problems. Differently from box constraints, in the case of general affine constraints a proper weighting of the control cos...

Analysis and Finite Element Approximations of Stochastic Optimal Control Problems Constrained by Stochastic Elliptic Partial Differential Equations

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Optimal Control of Semilinear Elliptic Obstacle Problems

Finite element methods for semilinear elliptic stochastic partial differential equations

We study finite element methods for semilinear stochastic partial differential equations. Error estimates are established. Numerical examples are also presented to examine our theoretical results. Mathematics Subject Classification (2000) 65N30 · 65N15 · 65C30 · 60H15

Differential Stability of Control Constrained Optimal Control Problems for the Navier-Stokes Equations

Distributed optimal control problems for the time-dependent and the stationary Navier-Stokes equations subject to pointwise control constraints are considered. Under a coercivity condition on the Hessian of the Lagrange function, optimal solutions are shown to be directionally differentiable functions of perturbation parameters such as the Reynolds number, the desired trajectory, or the initial...