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Prof. Dr. Michael Stiebitz

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Publications at the institute since 1990

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Mnich, Matthias; Rutter, Ignaz; Schmidt, Jens M.;
Linear-time recognition of map graphs with outerplanar witness. - In: Discrete optimization. - New York, NY [u.a.] : Elsevier, Bd. 28 (2018), S. 63-77
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.
Schmidt, Jens M.;
Tight bounds for the vertices of degree k in minimally k-connected graphs. - In: Journal of graph theory. - New York, NY [u.a.] : Wiley, ISSN 1097-0118, Bd. 88 (2018), 1, S. 146-153
Boeck, Thomas; Terzijska, Dzulia; Eichfelder, Gabriele;
Maximum electromagnetic drag configurations for a translating conducting cylinder with distant magnetic dipoles. - In: Journal of engineering mathematics. - Dordrecht [u.a.] : Springer Science + Business Media B.V, ISSN 1573-2703, Bd. 108 (2018), 1, S. 123-141

We report a semianalytic and numerical investigation of the maximal induced Lorentz force on an electrically conducting cylinder in translation along its axis that is caused by the presence of multiple distant magnetic dipoles. The problem is motivated by Lorentz force velocimetry, where induction creates a drag force on a magnet system placed next to a conducting flow. The magnetic field should maximize this drag force, which is usually quite small. Our approach is based on a long-wave theory developed for a single distant magnetic dipole. We determine the optimal orientations of the dipole moments providing the strongest Lorentz force for different dipole configurations using numerical optimization methods. Different constraints are considered for dipoles arranged on a concentric circle in a plane perpendicular to the cylinder axis. In this case, the quadratic form for the force in terms of the dipole moments can be obtained analytically, and it resembles the expression of the energy in a classical spin model. When all dipoles are equal and their positions on the circle are not constrained, the maximal force results when all dipoles are gathered in one point with all dipole moments pointing in radial direction. When the dipoles are equal and have equidistant spacing on the circle, we find that the optimal orientations of the dipole moments approach a limiting distribution. It differs from the so-called Halbach distribution that provides a uniform magnetic field in the cross section of the cylinder. The corresponding force is about 10% larger than that for the Halbach distribution but 60% smaller than for the unconstrained dipole positions. With the so-called spherical constraint for a classical spin model, the maximal force can be found from the eigenvalues of the coefficient matrix. It is typically 10% larger than the maximal force for equal dipoles because the constraint is weaker. We also study equal and evenly spaced dipoles along one or two lines parallel to the cylinder axis. The patterns of optimal magnetic moment orientations are fairly similar for different dipole numbers when the inter-dipole distance is within a certain interval. This behavior can be explained by reference to the magnetic field distribution of a single distant dipole on the cylinder axis.
Hotz, Thomas;
Hilft Honig Husten heilen?. - In: Kinderuni Ilmenau 2017. - Ilmenau, (2017)

Dietrich, Thomas; Krug, Silvia; Hotz, Thomas; Zimmermann, Armin;
Towards energy consumption prediction with safety margins for multicopter systems. - In: Proceedings of the 11th EAI International Conference on Performance Evaluation Methodologies and Tools : VALUETOOLS 2017 : 5-7 December 2017, Venice, Italy.. - New York, NY, USA : ACM, ISBN 978-1-4503-6346-4, (2017), S. 227-228
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Glock, Matthias; Hotz, Thomas;
Constructing universal, non-asymptotic confidence sets for intrinsic means on the circle. - In: Geometric science of information : third International Conference, GSI 2017, Paris, France, November 7-9, 2017 : proceedings.. - Cham : Springer International Publishing, ISBN 978-3-319-68445-1, (2017), S. 477-485
Müller, Matthias A.; Worthmann, Karl;
On quadratic stage costs for mobile robots in model predictive control. - In: Proceedings in applied mathematics and mechanics : PAMM.. - Weinheim [u.a.] : Wiley-VCH, ISSN 1617-7061, Bd. 17 (2017), 1, S. 825-826
Bergmann, Jean Pierre; Bielenin, Martin; Herzog, Roland A.; Hildebrand, Jörg; Riedel, Ilka; Schricker, Klaus; Trunk, Carsten; Worthmann, Karl;
Prevention of solidification cracking during pulsed laser beam welding. - In: Proceedings in applied mathematics and mechanics : PAMM.. - Weinheim [u.a.] : Wiley-VCH, ISSN 1617-7061, Bd. 17 (2017), 1, S. 405-406
Berger, Thomas; Gernandt, Hannes; Trunk, Carsten; Winkler, Henrik; Wojtylak, Michał;
A new bound for the distance to singularity of a regular matrix pencil. - In: Proceedings in applied mathematics and mechanics : PAMM.. - Weinheim [u.a.] : Wiley-VCH, ISSN 1617-7061, Bd. 17 (2017), 1, S. 863-864