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Prof. Dr. rer. nat. habil. Matthias Kriesell


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Veröffentlichungen am Institut für Mathematik seit 1990

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Schmid, Andreas; Schmidt, Jens M.;
Computing Tutte paths. - In: 45th International Colloquium on Automata, Languages, and Programming : ICALP 2018, Prague, Czech Republic, July 9-13, 2018.. - Saarbrücken/Wadern, Germany : Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH, Dagstuhl Publishing, (2018), Seite 98:1-98.14
Lo, On-Hei Solomon; Schmidt, Jens M.;
Longest cycles in cyclically 4-edge-connected cubic planar graphs. - In: The Australasian journal of combinatorics. - Queensland : Centre for Discrete Mathematics and Computing, Univ. of Queensland, ISSN 1034-4942, Bd. 72 (2018), Part 1, Seite 155-162
Jacob, Birgit; Tretter, Christiane; Trunk, Carsten; Vogt, Hendrik;
Systems with strong damping and their spectra. - In: Mathematical methods in the applied sciences. - Chichester, West Sussex : Wiley, ISSN 1099-1476, Bd. 41 (2018), 16, S. 6546-6573
Eichfelder, Gabriele; Niebling, Julia; Rocktäschel, Stefan;
An algorithmic approach to multiobjective optimization with decision uncertainty. - Ilmenau : Technische Universität Ilmenau, Institut für Mathematik, 2018. - 1 Online-Ressource (23 Seiten). . - (Preprint. - M18,11)

In real life applications optimization problems with more than one objective function are often of interest. Next to handling multiple objective functions, another challenge is to deal with uncertainties concerning the realization of the decision variables. One approach to handle these uncertainties is to consider the objectives as set-valued functions. Hence, the image of one variable is a whole set, which includes all possible outcomes of this variable. We choose a robust approach and thus these sets have to be compared using the so called upper-type less order relation. We propose a numerical method to calculate a covering of the set of optimal solutions of such an uncertain multiobjective optimization problem. We use a branchand-bound approach and lower and upper bound sets for being able to compare the arising sets. The calculation of these lower and upper bound sets uses techniques known from global optimization as convex underestimators as well as techniques used in convex multiobjective optimization as outer approximation techniques. We also give first numerical results for this algorithm.
Semper, Sebastian; Römer, Florian; Hotz, Thomas; Del Galdo, Giovanni;
Grid-free Direction-of-Arrival estimation with compressed sensing and arbitrary antenna arrays. - In: 2018 IEEE International Conference on Acoustics, Speech, and Signal Processing : proceedings : April 15-20, 2018, Calgary Telus Convention Center, Calgary, Alberta, Canada.. - Piscataway, NJ : IEEE, ISBN 978-1-5386-4658-8, (2018), S. 3251-3255
Eichfelder, Gabriele; Pilecka, Maria;
Ordering structures and their applications. - In: Applications of Nonlinear Analysis. - Cham : Springer, (2018), S. 265-304

Ordering structures play a fundamental role in many mathematical areas. These include important topics in optimization theory such as vector optimization and set optimization, but also other subjects as decision theory use ordering structures as well. Due to strong connections between ordering structures and cones in the considered space, order theory is also used every time two elements of a space, which is more general than the real line, are compared with each other. Therefore, also cone programming possessing restrictions defined using cones, and especially semidefinite optimization where the variables are symmetric matrices, make use of ordering structures. These structures may, on the one hand, be independent of the considered element of a given space or, on the other hand, vary for each element of this space. In the last case, we speak of variable ordering structures, which is one of the important topics in the newest research on vector optimization.
Kriesell, Matthias;
Nonseparating K4-subdivisions in graphs of minimum degree at least 4. - In: Journal of graph theory. - New York, NY [u.a.] : Wiley, ISSN 1097-0118, Bd. 89 (2018), 2, S. 194-213
- Im Titel ist "4" tiefgestellt
Kriesell, Matthias; Schmidt, Jens M.;
More on foxes. - In: Journal of graph theory. - New York, NY [u.a.] : Wiley, ISSN 1097-0118, Bd. 89 (2018), 2, S. 101-114
Behrndt, Jussi; Schmitz, Philipp; Trunk, Carsten;
Spectral bounds for singular indefinite Sturm-Liouville operators with L1-potentials. - In: Proceedings of the American Mathematical Society. - Providence, RI : Soc., ISSN 1088-6826, Bd. 146 (2018), 9, S. 3935-3942
- Im Titel ist "1" hochgestellt
Berger, Thomas; Giribet, Juan; Martínez Pería, Francisco; Trunk, Carsten;
On a class of non-Hermitian matrices with positive definite Schur complements. - Ilmenau : Technische Universität Ilmenau, Institut für Mathematik, 2018. - 1 Online-Ressource (11 Seiten). . - (Preprint. - M18,09)

Given a positive definite nXn matrix A and a Hermitian mXm matrix D, we characterize under which conditions there exists a strictly contractive matrix K such that the non-Hermitian block-matrix with the enties A and -AK in the first row and K^*A and D in the second has a positive definite Schur complement with respect to its submatrix A. Additionally, we show that K can be chosen such that diagonalizability of the block-matrix is guaranteed and we compute its spectrum. Moreover, we show a connection to the recently developed frame theory for Krein spaces.