The talk **Robust preconditioners for PDE-constrained optimal control problems with control constraints, **by Mattia Tani, will be held on Monday March 31, 2014 at 8:30 in room K4. After that, Petr Sýkora will talk about his recent work**. **Finally, PhD students from group A (Tomáš Gergelits, Radim Hošek, Adam Janečka and Martin Řehoř) will do a short progress report of the actual status of their research.

**Abstract of the talk**

Numerical solution of PDE-constrained optimal control problems often leads to large and sparse saddle point linear systems, which require good preconditioners to be efficiently solved using Krylov methods. In particular, when further constraints are imposed on the control and/or on the state variables, the employment of a semismooth Newton method makes necessary to solve one such system at every iteration.

In this talk we will focus on the problem of finding robust preconditioners for sequences of linear systems stemming from a class of optimal control problems in which inequality constraints are imposed on the control. Here, “robust” means that the number of iteration of the chosen Krylov method should not depend on the problem parameters, e.g. the discretization parameter. After a review of the state-of-the-art approaches, we will present a new preconditioner, which is based on a full block-matrix factorization of the Schur complement of the system matrix. Numerical experiments on 3D problems are presented.

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