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Veröffentlichungen am Institut für Mathematik seit 1990

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Babovsky, Hans;
Shocks in the light of discrete velocity models. - In: AIP conference proceedings - Melville, NY : Inst, ISSN 15517616, Bd. 2132 (2019), S. 060002-1-060002-8

https://doi.org/10.1063/1.5119542
Eichfelder, Gabriele; Niebling, Julia; Rocktäschel, Stefan;
An algorithmic approach to multiobjective optimization with decision uncertainty. - In: Journal of global optimization : an international journal dealing with theoretical and computational aspects of seeking global optima and their applications in science, management and engineering. - Dordrecht [u.a.] : Springer Science + Business Media B.V, ISSN 1573-2916, (2019), first online: 29 July 2019, 23 Seiten

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 decision variable is a whole set, which includes all possible outcomes of this decision 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 branch-and-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.



https://doi.org/10.1007/s10898-019-00815-9
Thomann, Jana; Eichfelder, Gabriele;
A trust-region algorithm for heterogeneous multiobjective optimization. - In: SIAM journal on optimization - Philadelphia, Pa. : SIAM, ISSN 1095-7189, Bd. 29 (2019), 2, S. 1017-1047

https://doi.org/10.1137/18M1173277
Harant, Jochen; Mohr, Samuel;
On Selkow's bound on the independence number of graphs. - In: Discussiones mathematicae - Warsaw : De Gruyter Open, ISSN 20835892, Bd. 39 (2019), 3, S. 655-657

https://doi.org/10.7151/dmgt.2100
Kubek, Mario; Böhme, Thomas; Unger, Herwig;
Empiric experiments with text-representing centroids. - In: Theory and application of text-representing centroids - Düsseldorf : VDI Verlag GmbH, (2019), S. 39-54

Kubek, Mario; Böhme, Thomas; Unger, Herwig;
Spreading activation: a fast calculation method for text centroids. - In: Theory and application of text-representing centroids - Düsseldorf : VDI Verlag GmbH, (2019), S. 27-38

Berger, Thomas; Giribet, Juan; Martínez Pería, Francisco; Trunk, Carsten;
On a class of non-Hermitian matrices with positive definite Schur complements. - In: Proceedings of the American Mathematical Society - Providence, RI : Soc., ISSN 1088-6826, Bd. 147 (2019), 6, S. 2375-2388

https://doi.org/10.1090/proc/14412
De Santis, Marianna; Eichfelder, Gabriele; Niebling, Julia; Rocktäschel, Stefan;
Solving multiobjective mixed integer convex optimization problems - Ilmenau : Technische Universität Ilmenau, Institut für Mathematik, 2019 - 1 Online-Ressource (26 Seiten). . - (Preprint. - M19,06)

Multiobjective mixed integer convex optimization refers to mathematical programming problems where more than one convex objective function needs to be optimized simultaneously and some of the variables are constrained to take integer values. We present a branch-and-bound method based on the use of properly defined lower bounds. We do not simply rely on convex relaxations, but we built linear outer approximations of the image set in an adaptive way. We are able to guarantee correctness in terms of detecting both the efficient and the nondominated set of multiobjective mixed integer convex problems according to a prescribed precision. As far as we know, the procedure we present is the first deterministic algorithm devised to handle this class of problems. Our numerical experiments show results on biobjective and triobjective mixed integer convex instances.



https://www.db-thueringen.de/receive/dbt_mods_00038620
Thomann, Jana; Eichfelder, Gabriele;
Numerical results for the multiobjective trust region algorithm MHT. - In: Data in Brief - Amsterdam [u.a.] : Elsevier, ISSN 23523409, Volume 25 (2019), article 104103, Seite 1-18

https://doi.org/10.1016/j.dib.2019.104103
Behrndt, Jussi; Schmitz, Philipp; Trunk, Carsten;
The non-real spectrum of a singular indefinite Sturm-Liouville operator with regular left endpoint - Ilmenau : Technische Universität Ilmenau, Institut für Mathematik, 2019 - 1 Online-Ressource (3 Seiten). . - (Preprint. - M19,05)
https://www.db-thueringen.de/receive/dbt_mods_00038524