Optimization problems in fractional Sobolev spaces with applications to sparse control problems

• Applicant: Professor Dr. Daniel Wachsmuth
• Subject Area: Mathematics
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 512301538

The aim of the project is to develop analytical tools and numerical algorithms to tackle nonconvex and nonsmooth optimization problems in fractional Sobolev spaces. The main motivation comes from sparse optimal control problems. Special emphasis will be laid on problems with time-dependent controls that should be sparse with respect to the spatial variable. The resulting optimization problems have a particular structure: the objective functional to be minimized (or parts of it) can be written as a difference of convex functions. This structure will be exploited to devise efficient optimization algorithms.

• DFG Programme: Research Grants