Property $C$ with constraints for PDE

Optimization with PDE Constraints

Property (T) for C*-dynamical systems

In this paper, we introduce a notion of property (T) for a C<span style="font-family: txsy; font-size: 7pt; color: #000000; font-style: norm...

Stochastic Collocation for Optimal Control Problems with Stochastic PDE Constraints

We discuss the use of stochastic collocation for the solution of optimal control problems which are constrained by stochastic partial differential equations (SPDE). Thereby the constraining SPDE depends on data which is not deterministic but random. Assuming a deterministic control, randomness within the states of the input data will propagate to the states of the system. For the solution of SP...

Multigrid Algorithms for Inverse Problems with Linear Parabolic PDE Constraints

We present a multigrid algorithm for the solution of distributed parameter inverse problems constrained by variable-coefficient linear parabolic partial differential equations. We consider problems in which the inversion variable is a function of space only; for stability we use an L2 Tikhonov regularization. The main feature of our algorithm is that its convergence rate is mesh-independent—eve...

Numerical Techniques for Optimization Problems with PDE Constraints

Optimization problems with partial differential equation (PDE) constraints arise in many science and engineering applications. Their robust and efficient solution present many mathematical challenges and requires a tight integration of properties and structures of the underlying problem, of fast numerical PDE solvers, and of numerical nonlinear optimization. This workshop brought together exper...