Nonsmooth Variational Problems and Operator Equations

The group contributes to the following application oriented research topics of WIAS:

Image processing tools based on mathematical algorithms from statistics or variational methods enable a bulk of applications in the medical sciences. They range from image enhancement to automatic image analysis. [>> more]

This work is focussed on the modeling of damage and on phase separation in modern solder materials for microelectronic devices. [>> more]

Mathematical models and computational techniques are nowadays utilized in medical sciences for noninvasive diagnostic, diseases characterization, therapy planning, and treatment monitoring. The research at WIAS focuses on efficient and robust models for biological tissues and fluids, on the usage of advanced mathematical models in data assimilation and medical imaging applications, as well as on techniques in optimization, machine learning, and optimal control for decision support in biomedicine. [>> more]

Optimization problems in energy management are concerned with the planning of production and distribution of different energy sources (power, gas), in order to cover a given customer's demand. In this context, the consideration of uncertainties (e.g., loads, meteorological parmeters, prices) in transportation networks represents a major challenge. The aim is to find cost optimal decisions which are robust at the same time with respect to uncertainties. The additional consideration of markets and the physica of energy transport then lead to risk-averse optimal control problems with equilibrium constraints. [>> more]