On continuous deformations of semi-infinite optimization problems

We consider differentiable semi-infinite optimization problems depending on a real parameter. For generic one-parametric families we roughly classify the corresponding set of generalized critical points into eight types. Five of these types also occur in problems with a finite number of inequality constraints. The other three types are typical for the semi-infinite case. We discuss Type 6 in detail. This singularity is due to the fact that in the associated lower level problem a Lagrange parameter corresponding to an active inequality constraint vanishes. The set of generalized critical points is not smooth at such a point. In addition it will be shown that the (quadratic) index either remains constant or changes by at most one when passing along a point of Type 6. An explicit example will be provided. The points of Type 1 - 6 generically occur if the index set of inequality constraints is constant and is described by means of finitely many smooth constraints for which the gradients of active constraints are linearly independent throughout. The other types (Type 7 and Type 8) are related to the violation of the latter linear independence. (orig.)Available from TIB Hannover: RR 1843(94-02) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Regularized penalty methods for optimal control of ill-posed elliptic systems

Application of prox-regularization to ill-posed stationary control problems is investigated. Stable variants of penalty methods with one-step and multi-step regularizations in the auxiliary problems are developed and their convergence is proved for distributed as well as boundary control problems with state constraints and Dirichlet or Neumann conditions. (orig.)SIGLEAvailable from TIB Hannover: RO 7722(522) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman