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Publications

Publications at the institute since 1990

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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, 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
Berger, Thomas; Trunk, Carsten; Winkler, Henrik
Linear relations and the Kronecker canonical form. - In: Linear algebra and its applications : LAA.. - New York, NY : American Elsevier Publ., Bd. 488 (2016), S. 13-44

http://dx.doi.org/10.1016/j.laa.2015.09.033
Brás, Carmo; Eichfelder, Gabriele; Júdice, Joaquim;
Copositivity tests based on the linear complementarity problem. - In: Computational optimization and applications : an international journal.. - New York, NY [u.a.] : Springer Science + Business Media B.V., ISSN 1573-2894, Bd. 63 (2016), 2, S. 164-493

We present copositivity tests based on new necessary and sufficient conditions which require the solution of linear complementarity problems (LCP). We propose methodologies involving Lemkes method, an enumerative algorithm and a linear mixed-integer programming formulation to solve the required LCPs. Moreover, we discuss a new necessary condition for (strict) copositivity based on solving a linear program, which can be used as a preprocessing step. The algorithms with these three different variants are thoroughly applied to test matrices from the literature and to max-clique instances with matrices of order up to 496×496. We compare our procedures with three other copositivity tests from the literature as well as with a general global optimization solver. The numerical results are very promising and equally good and in many cases better than the results reported elsewhere.



http://dx.doi.org/10.1007/s10589-015-9772-2
Eichfelder, Gabriele; Gerlach, Tobias;
Characterization of properly optimal elements with variable ordering structures. - In: Optimization : a journal of mathematical programming and operations research.. - London [u.a.] : Taylor & Francis, ISSN 1029-4945, Bd. 65 (2016), 3, S. 571-588

In vector optimization with a variable ordering structure, the partial ordering defined by a convex cone is replaced by a whole family of convex cones, one associated with each element of the space. In recent publications, it was started to develop a comprehensive theory for these vector optimization problems. Thereby, also notions of proper efficiency were generalized to variable ordering structures. In this paper, we study the relation between several types of proper optimality. We give scalarization results based on new functionals defined by elements from the dual cones which allow complete characterizations also in the nonconvex case.



http://dx.doi.org/10.1080/02331934.2015.1040793
Philipp, Friedrich; Trunk, Carsten;
Spectral points of type π+ and type π- of closed operators in indefinite inner product spaces. - In: Operators and matrices : OaM.. - Zagreb : Element, Bd. 9 (2015), 3, S. 481-506
- Im Titel ist "+" und "-" tiefgestellt

http://dx.doi.org/10.7153/oam-09-30
Hotz, Thomas; Kelma, Florian; Wieditz, Johannes;
Universal, non-asymptotic confidence sets for circular means. - In: Geometric science of information : second international conference, GSI 2015, Palaiseau, France, October 28-30, 2015 : proceedings.. - Cham : Springer, ISBN 978-3-319-25040-3, (2015), S. 635-642

http://dx.doi.org/10.1007/978-3-319-25040-3_68
Biedl, Therese; Schmidt, Jens M.;
Small-area orthogonal drawings of 3-connected graphs. - In: Graph drawing and network visualization : 23rd international symposium, GD 2015, Los Angeles, CA, USA, September 24-26, 2015 : revised selected papers.. - Cham : Springer, ISBN 978-3-319-27261-0, (2015), S. 153-165

http://dx.doi.org/10.1007/978-3-319-27261-0_13