M 614

The talk is concerned with the optimization of elastoplastic derformation processes. To make the problem analytically capable, we consider the simplified model of static elastoplasticity with linear kinematic hardening for the description of the plastic deformation process. For simplicity we moreover assume the applied loads to be directly controlable. The associated optimal control problem turns out to be an elliptic mathematical problem with equilibrium constraints (MPEC) in function space. MPECs are known to be difficult to handle, in particular since the standard Karush-Kuhn-Tucker (KKT) theory fails, even in the finite dimensional case. Hence various alternative stationarity concepts have been developed to overcome this problem. In the talk we will establish Clarke (C) and strong stationarity for the problem at hand. While the C-stationarity system is derived by applying a regularization approach for the original optimal control problem, we establish the strong stationarity system for an auxiliary model problem involving an ample control. Both optimality systems are the infinite dimensional counterparts of the respective finite dimensional stationarity concepts.

Prof. Dr. Christian Meyer

TU Dortmund, Fakultät für Mathematik, LS X (Wissenschaftliches Rechnen)