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Publications at the institute since 1990

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Eichfelder, Gabriele; Jahn, Johannes;
Vector and set optimization. - In: Multiple criteria decision analysis : state of the art surveys.. - New York : Springer, (2016), S. 695-737

This chapter is devoted to recent developments of vector and set optimization. Based on the concept of a pre-order optimal elements are defined. In vector optimization properties of optimal elements and existence results are gained. Further, an introduction to vector optimization with a variable ordering structure is given. In set optimization basic concepts are summed up.



http://dx.doi.org/10.1007/978-1-4939-3094-4_17
Przybyło, Jakub; Schreyer, Jens; Škrabul'áková, Erika;
On the facial Thue choice number of plane graphs via entropy compression method. - In: Graphs and combinatorics. - Tokyo : Springer-Verl. Tokyo, ISSN 1435-5914, Bd. 32 (2016), 3, S. 1137-1153

http://dx.doi.org/10.1007/s00373-015-1642-2
Behrndt, Jussi; Möws, Roland; Trunk, Carsten;
Eigenvalue estimates for operators with finitely many negative squares. - Ilmenau : Technische Universität, Institut für Mathematik, 2016. - 1 Online-Ressource (14 Seiten). . - (Preprint. - M16,02)

Let A and B be selfadjoint operators in a Krein space. Assume that the re- solvent difference of A and B is of rank one and that the spectrum of A consists in some interval I of isolated eigenvalues only. In the case that A is an operator with finitely many negative squares we prove sharp estimates on the number of eigenvalues of B in the interval I. The general results are applied to singular indefinite Sturm-Liouville problems.



https://www.db-thueringen.de/receive/dbt_mods_00029046
Harant, Jochen; Mohr, Samuel;
Maximum weighted induced subgraphs. - In: Discrete mathematics. - Amsterdam [u.a.] : Elsevier, Bd. 339 (2016), 7, S. 1954-1559

http://dx.doi.org/10.1016/j.disc.2015.07.013
Worthmann, Karl; Braun, Philipp; Proch, Michael; Schlüchtermann, Jörg; Pannek, Jürgen;
On contractual periods in supplier development. - In: IFAC-PapersOnLine. - Frankfurt : Elsevier, ISSN 2405-8963, Bd. 49 (2016), 2, S. 60-65

http://dx.doi.org/10.1016/j.ifacol.2016.03.011
Axenovich, Maria; Harant, Jochen; Przybyło, Jaromir; Soták, Roman; Voigt, Margit; Weidelich, Jenny;
A note on adjacent vertex distinguishing colorings of graphs. - In: Discrete applied mathematics. - [S.l.] : Elsevier, Bd. 205 (2016), S. 1-7

http://dx.doi.org/10.1016/j.dam.2015.12.005
Behrndt, Jussi; Leben, Leslie; Martínez Pería, Francisco; Möws, Roland; Trunk, Carsten;
Sharp eigenvalue estimates for rank one perturbations of nonnegative operators in Krein spaces. - In: Journal of mathematical analysis and applications. - Amsterdam [u.a.] : Elsevier, ISSN 1096-0813, Bd. 439 (2016), 2, S. 864-895

http://dx.doi.org/10.1016/j.jmaa.2016.03.012
Gernandt, Hannes; Trunk, Carsten;
Eigenvalue placement for regular matrix pencils with rank one perturbations. - Ilmenau : Technische Universität, Institut für Mathematik, 2016. - 1 Online-Ressource (15 Seiten). . - (Preprint. - M16,01)

A regular matrix pencil sE-A and its rank one perturbations are considered. We determine the sets in \C\cup\{\infty\} which are the eigenvalues of the perturbed pencil. We show that the largest Jordan chains at each eigenvalue of sE-A may disappear and the sum of the length of all destroyed Jordan chains is the number of eigenvalues (counted with multiplicities) which can be placed arbitrarily in \C\cup\{\infty\}. We prove sharp upper and lower bounds of the change of the algebraic and geometric multiplicity of an eigenvalue under rank one perturbations. Finally we apply our results to a pole placement problem for a single-input differential algebraic equation with feedback.



http://www.db-thueringen.de/servlets/DocumentServlet?id=27311
Eichfelder, Gabriele; Gerlach, Tobias; Sumi, Susanne;
A modification of the [alpha]BB method for box-constrained optimization and an application to inverse kinematics. - In: EURO journal on computational optimization. - Berlin : Springer, ISSN 2192-4414, Bd. 4 (2016), 1, S. 93-121

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. We extend the well-known alphaBB method such that it can be used to find an approximation of the set of globally optimal solutions with a predefined quality. We illustrate the properties and give a proof for the finiteness and correctness of our modified alphaBB method.



http://dx.doi.org/10.1007/s13675-015-0056-5
Knobloch, Jürgen; Vielitz, Martin
Non-conservative perturbations of homoclinic snaking scenarios. - In: Journal of differential equations. - Orlando, Fla. : Elsevier, ISSN 1090-2732, Bd. 260 (2016), 1, S. 517-566

http://dx.doi.org/10.1016/j.jde.2015.09.005