On the Stability of Second Order Sufficient Optimality Conditions for State Constrained Elliptic Control Problems with Respect to Discretization

Ira Neitzel*, Johannes Pfefferer and Arnd Rösch

We discuss the finite element discretization of optimal control problems governed by a semilinear elliptic state equation and subject to pointwise state constraints. The problem under consideration is nonconvex due to the nonlinearity of the state equation, hence second order sufficient conditions (SSC) play a role in the numerical analysis. We prove that the SSC transfer from the continuous to the discrete problem formulation. In addition, we show a rate of convergence of discrete local solutions to continuous local solutions.

Mathematics Subject Classification: 49M25

Keywords: second order sufficient optimality condition; finite element discretization; convergence rates, optimal control

Minisymposion: Stability, Sensitivity and Error Analysis for Optimal Control Problems