Department of Mathematics

Dr. Ira Neitzel (TU München): "Nunmerical analysis of nonconvex optimal control problems with semilinear PDEs".

Jul 20, 2015 from 04:00 PM to 05:00 PM

WR 383 - Raum 306/307

Abstract:

In this talk we will give an overview about finite element discretization error estimates for optimal control problems with semilinear elliptic and parabolic PDE. We will discuss problems with additional pointwise control constraints and - regularized or unregularized - pointwise state constraints. The discretization approach we will use for the underlying PDEs consists of piecewise linear finite elements in space, and, in case of parabolic problems, piecewise constant finite elements in time. At the beginning of the talk, special attention will be placed on second order sufficient optimality conditions, that result in a quadratic growth condition which guarantees that a stationary point is a strict local minimum. The spaces in which these growth conditions are obtained clearly influence the numerical analysis, since convergence results in the corresponding norms become necessary.

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