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Prof. Dr. Michael Stiebitz

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Publications at the institute since 1990

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Thomann, Jana; Eichfelder, Gabriele;
A trust region algorithm for heterogeneous multiobjective optimization. - Ilmenau : Technische Universität Ilmenau, Institut für Mathematik, 2018. - 1 Online-Ressource (30 Seiten). . - (Preprint. - M18,04)
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)
Knobloch, Jürgen; Lamb, Jeroen S. W.; Webster, Kevin N.;
Shift dynamics near non-elementary T-points with real eigenvalues. - In: Journal of difference equations and applications. - London [u.a.] : Taylor & Francis, ISSN 1563-5120, Bd. 24 (2018), 4, S. 609-654
Hassi, Seppo; Snoo, Henk; Winkler, Henrik;
Limit properties of eigenvalues in spectral gaps. - In: Indefinite inner product spaces, Schur analysis, and differential equations : a volume dedicated to Heinz Langer.. - Cham : Birkhäuser, (2018), S. 335-355
Brechtken, Stefan; Sasse, Thomas;
Normal, high order discrete velocity models of the Boltzmann equation. - In: Computers and mathematics with applications : an international journal.. - Amsterdam [u.a.] : Elsevier Science, ISSN 1873-7668, Bd. 75 (2018), 2, S. 503-519
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. - Amsterdam : Elsevier Ltd., ISSN 2468-6018, Bd. 3 (2018), S. 10-22
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.