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Publications

Publications at the institute since 1990

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Reis, Timo; Selig, Tilman
Funnel control for the boundary controlled heat equation. - In: SIAM journal on control and optimization. - Philadelphia, Pa. : Soc., ISSN 1095-7138, Bd. 53 (2015), 1, S. 547-574

http://dx.doi.org/10.1137/140971567
Harant, Jochen; , ; Richter, Sebastian
Eigenvalue conditions for induced subgraphs. - In: Discussiones mathematicae. - Warsaw : De Gruyter Open, ISSN 2083-5892, Bd. 35 (2015), 2, S. 355-363

https://doi.org/10.7151/dmgt.1790
Harant, Jochen; Richter, Sebastian
A new eigenvalue bound for independent sets. - In: Discrete mathematics. - Amsterdam [u.a.] : Elsevier, Bd. 338 (2015), 10, S. 1763-1765

http://dx.doi.org/10.1016/j.disc.2014.12.008
Kemnitz, Arnfried; Marangio, Massimiliano; Pruchnewski, Anja; Voigt, Margit
(P,Q)-total (r,s)-colorings of graphs. - In: Discrete mathematics. - Amsterdam [u.a.] : Elsevier, Bd. 338 (2015), 10, S. 1722-1729

http://dx.doi.org/10.1016/j.disc.2014.09.012
Dempe, Stephan; Eichfelder, Gabriele; Fliege, Jörg
On the effects of combining objectives in multi-objective optimization. - In: Mathematical methods of operations research : ZOR.. - Berlin : Springer, ISSN 1432-5217, Bd. 82 (2015), 1, S. 1-18

In multi-objective optimization, one considers optimization problems with more than one objective function, and in general these objectives conflict each other. As the solution set of a multi-objective problem is often rather large and contains points of no interest to the decision-maker, strategies are sought that reduce the size of the solution set. One such strategy is to combine several objectives with each other, i.e. by summing them up, before employing tools to solve the resulting multi-objective optimization problem. This approach can be used to reduce the dimensionality of the objective space as well as to discard certain unwanted solutions, especially the 'extreme' ones found by minimizing just one of the objectives given in the classical sense while disregarding all others. In this paper, we discuss in detail how the strategy of combining objectives linearly influences the set of optimal, i.e. efficient solutions.



http://dx.doi.org/10.1007/s00186-015-0501-5
Eichfelder, Gabriele; Gerlach, Tobias; Sumi, Susanne
A modification of the [alpha]BB method for box-constrained optimization and an application to inverse kinematics. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2015. - Online-Ressource (PDF-Datei: 25 S., 1,58 MB). . - (Preprint. - M15,04)

For many practical applications it is important to determine not only a numerical approximation of one but a representation of the whole set of globally optimal solutions of a non-convex optimization problem. Then one element of this representation may be chosen based on additional information which cannot be formulated as a mathematical function or within a hierarchical problem formulation. We present such an application in the field of robotic design. This application problem can be modeled as a smooth box-constrained optimization problem. For determining a representation of the global optimal solution set with a predefined quality we modify the well known BB method. We illustrate the properties and give a proof for the finiteness and correctness of our modified BB method.



http://www.db-thueringen.de/servlets/DocumentServlet?id=26001
Behrndt, Jussi; Leben, Leslie; Martínez Pería, Francisco; Trunk, Carsten
The effect of finite rank perturbations on Jordan chains of linear operators. - In: Linear algebra and its applications : LAA.. - New York, NY : American Elsevier Publ., Bd. 479 (2015), S. 118-130

http://dx.doi.org/10.1016/j.laa.2015.04.007
Ilchmann, Achim; Reis, Timo
. - Surveys in differential-algebraic equations ; 2. - Cham [u.a.] : Springer, 2015. - VII, 339 S.. . - (Differential-algebraic equations forum, DAE-F) - Literaturangaben

Selig, Tilman;
Controller reduction by H∞ balanced truncation for infinite-dimensional, discrete-time systems. - In: Mathematics of control, signals, and systems : MCSS.. - London : Springer, ISSN 1435-568X, Bd. 27 (2015), 1, S. 111-147
- Im Titel ist "∞" tiefgestellt

https://doi.org/10.1007/s00498-014-0137-7
Ilchmann, Achim;
Zur gesellschaftlichen Funktion der angewandten Mathematik. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2015. - Online-Ressource (PDF-Datei: 31 S., 396 KB). . - (Preprint. - M15,02)

Der Begriff derWissenschaft wird expliziert; die Einzelwissenschaften Philosophie, Natur und Technikwissenschaften und Mathematik werden historisch und systematisch eingeordnet, um insbesondere den Unterschied zwischen Technologie und angewandter Mathematik zu verstehen. Es wird dann Peter Bulthaups These der "tendenziellen Transformation von Wissenschaft in Technologie" für die angewandte Mathematik untersucht.



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