Nonlinear Optimization and Inverse Problems

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

Diffractive optical elements employ the controlled use of light propagation on microstructered interfaces. They perform functions unattainable with traditional elements and can be applied in diffractive measurement technique, spectroscopy, astronomy, optical communication techniques, and information processing. For the design of such elements, Maxwell`s equations have to be solved and special optimization algorithms are to be adapted. [>> 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]

In the area of procuction, there is a huge demand for planning and optimization tools that allow for an accelerated re-planning and reconfiguration of complex production facilities. In this context, the key words are "digital factory" or "Industry 4.0", which represents the transition to a connected, widely self-organized industrial production. This interconnectivity allows not only for the optimization of individual production steps, but also of the entire value chain. [>> more]