Publications

Berger, Thomas; Gernandt, Hannes; Trunk, Carsten; Winkler, Henrik; Wojtylak, Michał
The gap distance to the set of singular matrix pencils. - Ilmenau : Technische Universität Ilmenau, Institut für Mathematik, 2018. - 1 Online-Ressource (22 Seiten). - (Preprint ; M18,05)

We study matrix pencils sE-A using the associated linear subspace ker[A,-E]. The distance between subspaces is measured in terms of the gap metric. In particular, we investigate the gap distance of a regular matrix pencil to the set of singular pencils and provide upper and lower bounds for it. A relation to the distance to singularity in the Frobenius norm is provided.

http://nbn-resolving.de/urn:nbn:de:gbv:ilm1-2018200051

Niebling, Julia; Eichfelder, Gabriele
A branch-and-bound based algorithm for nonconvex multiobjective optimization. - Ilmenau : Technische Universität Ilmenau, Institut für Mathematik, 2018. - 1 Online-Ressource (29 Seiten). - (Preprint ; M18,03)
http://nbn-resolving.de/urn:nbn:de:gbv:ilm1-2018200024

Hassi, Seppo; Snoo, Hendrik S. V. de; Winkler, Henrik
Limit properties of eigenvalues in spectral gaps. - In: Indefinite Inner Product Spaces, Schur Analysis, and Differential Equations, (2018), S. 335-355

https://doi.org/10.1007/978-3-319-68849-7_13

Braun, Philipp; Faulwasser, Timm; Grüne, Lars; Kellett, Christopher M.; Weller, Steven R.; Worthmann, Karl
Hierarchical distributed ADMM for predictive control with applications in power networks. - In: IFAC journal of systems and control, ISSN 2468-6018, Bd. 3 (2018), S. 10-22

https://doi.org/10.1016/j.ifacsc.2018.01.001

Eichfelder, Gabriele; Gerlach, Tobias
On classes of set optimization problems which are reducible to vector optimization problems and its impact on numerical test instances. - Ilmenau : Technische Universität Ilmenau, Institut für Mathematik, 2018. - 1 Online-Ressource (25 Seiten). - (Preprint ; M18,01)

Set optimization with the set approach has recently gained increasing interest due to its practical relevance. In this problem class one studies optimization problems with a set-valued objective map and defines optimality based on a direct comparison of the images of the objective function, which are sets here. Meanwhile, in the literature a wide range of theoretical tools as scalarization approaches and derivative concepts as well as first numerical algorithms are available. These numerical algorithms require on the one hand test instances where the optimal solution sets are known. On the other hand, in most examples and test instances in the literature only set-valued maps with a very simple structure are used. We study in this paper such special set-valued maps and we show that some of them are such simple that they can equivalently be expressed as a vector optimization problem. Thus we try to start drawing a line between simple set-valued problems and such problems which have no representation as multiobjective problems. Those having a representation can be used for defining test instances for numerical algorithms with easy verifiable optimal solution set.

http://nbn-resolving.de/urn:nbn:de:gbv:ilm1-2017200588