The Byrnes-Isidori form for infinite-dimensional systems. - In: SIAM journal on control and optimization, ISSN 1095-7138, Bd. 54 (2016), 3, S. 1504-1534
http://dx.doi.org/10.1137/130942413
Vector and set optimization. - In: Multiple criteria decision analysis, (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
On the facial Thue choice number of plane graphs via entropy compression method. - In: Graphs and combinatorics, ISSN 1435-5914, Bd. 32 (2016), 3, S. 1137-1153
http://dx.doi.org/10.1007/s00373-015-1642-2
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
Maximum weighted induced subgraphs. - In: Discrete mathematics, Bd. 339 (2016), 7, S. 1954-1559
http://dx.doi.org/10.1016/j.disc.2015.07.013
On contractual periods in supplier development. - In: IFAC-PapersOnLine, ISSN 2405-8963, Bd. 49 (2016), 2, S. 60-65
http://dx.doi.org/10.1016/j.ifacol.2016.03.011
A note on adjacent vertex distinguishing colorings of graphs. - In: Discrete applied mathematics, ISSN 1872-6771, Bd. 205 (2016), S. 1-7
https://doi.org/10.1016/j.dam.2015.12.005
Sharp eigenvalue estimates for rank one perturbations of nonnegative operators in Krein spaces. - In: Journal of mathematical analysis and applications, ISSN 1096-0813, Bd. 439 (2016), 2, S. 864-895
http://dx.doi.org/10.1016/j.jmaa.2016.03.012
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
A modification of the [alpha]BB method for box-constrained optimization and an application to inverse kinematics. - In: EURO journal on computational optimization, 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