Topological degree for maximal monotone operators and application to parametric optimization problems.
Two conditions are given each of which is both necessary and sufficient for a point to be a global Pareto minimum. The first one is obtained by studying programs where each criterion appears as a single objective function, while the second one is given in terms of a "restricted Lagrangian". The conditions are compared with the familiar characterizations of properly efficient and weakly efficient points of Karlin and Geoffrion.
A general framework for calculating shape derivatives for optimization problems with partial differential equations as constraints is presented. The proposed technique allows to obtain the shape derivative of the cost without the necessity to involve the shape derivative of the state variable. In fact, the state variable is only required to be Lipschitz continuous with respect to the geometry perturbations. Applications to inverse interface problems, and shape optimization for elliptic systems...
In der vorliegenden Arbeit leiten wir ein hinreichendes Kriterium für lokale Optimalität bei allgemeinen quadratischen Optimierungsproblemen her. Wir verwenden dabei in Anlehnung an die lineare parametrische Optimierung gewisse Stabilitätsmengen, wie sie erstmals K. Lommatzsch verwendet hat.