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Numerical Analysis for PDE-Constrained Optimal Control Problems

Organizers:
Ira Neitzel (Technische Universitat Munchen, Germany) and Johannes Pfefferer (Universitat der Bundeswehr Munchen, Germany)

Abstract:
Mathematical models of many optimization problems appearing in science, industry, economics, or medicine involve constraints in form of partial dierential equations (PDEs). Due to these PDE-constraints, the corresponding optimization problems can in general not be tackled directly, but are solved numerically either after discretization of the whole problem or by solving discretized optimality conditions that were obtained in functions spaces. In either case, an important step of the discretization process is the discretization of the PDE by e.g. finite elements. Among others, important research topics arising in this context involve the development of a priori and a posteriori error estimates for a given quantity of interest such as the optimal control. In recent years, PDE-constrained optimal control problems with a wide range of additional mathematical dfficulties either due to regularity issues of the PDE, the computational domain, or additional constraints such as state- or gradient-state constraints have been investigated. The proposed mini-symposium intends to bring together scientist working in the field of numerical analysis for PDE-constrained optimal control problems to provide a platform for an exchange of new results and different viewpoints.