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Publications at the institute since 1990

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Terzijska, Dzulia; Porcelli, Margherita; Eichfelder, Gabriele
Multi-objective optimization in the Lorentz force velocimetry framework. - In: Book of digests & program. - Delft, (2014), S. 81-82

Bao, Truong Q.; Eichfelder, Gabriele; Soleimani, Behnam; Tammer, Christiane
Ekeland's variational principle for vector optimization with variable ordering structure. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2014. - Online-Ressource (PDF-Datei: 24 S., 351 KB). . - (Preprint. - M14,08)

There are many generalizations of Ekeland's variational principle for vector optimization problems with fixed ordering structures, i.e., ordering cones. These variational principles are useful for deriving optimality conditions, epsilon-Kolmogorov conditions in approximation theory, and epsilon-maximum principles in optimal control. Here, we present several generalizations of Ekeland's variational principle for vector optimization problems with respect to variable ordering structures. For deriving these variational principles we use nonlinear scalarization techniques. Furthermore, we derive necessary conditions for approximate solutions of vector optimization problems with respect to variable ordering structures using these variational principles and the subdifferential calculus by Mordukhovich.



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Boccia, Andrea; , ; ,
Stability and feasibility of state constrained MPC without stabilizing terminal constraints. - In: Systems & control letters. - Amsterdam [u.a.] : Elsevier, ISSN 1872-7956, Bd. 72 (2014), S. 14-21

http://dx.doi.org/10.1016/j.sysconle.2014.08.002
Walkling, Andreas; Neundorf, Werner; Schierz, Christoph; Stockmar, Axel
Erweitertes TI-Verfahren für eine präzisere Erfassung der physiologischen Blendung. - In: Licht 2014. - Ede : Nederlandse Stichting voor Verlichtingskunde (NSW), (2014), insges. 8 S.

Ilchmann, Achim; Reis, Timo
Outer transfer functions of differential-algebraic systems. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2014. - Online-Ressource (PDF-Datei: 39 S., 403,1 KB). . - (Preprint. - M14,07)

We consider differential-algebraic systems whose transfer function is outer: i.e., it has full row rank and all transmission zeros lie in the closed left half complex plane. We characterize outer, with the aid of the Kronecker structure of the system pencil and the Smith-McMillan structure of the transfer function, as the following property of a behavioural stabilizable and detectable realization: each consistent initial value can be asymptotically controlled to zero while the output can be made arbitrarily small in the L2-norm. The zero dynamics of systems with outer transfer functions are analyzed. We further show that our characterizations of outer provide a simple and very structured analysis of the linear-quadratic optimal control problem.



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Hildenbrandt, Regina;
The k-server problem with parallel requests and the compound Harmonic algorithm. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2014. - Online-Ressource (PDF-Datei: 21 S., 163,8 KB). . - (Preprint. - M14,06)

In this paper we consider a generalized k-server problem with parallel requests where several servers can also be located on one point (which was initiated by an operations research problem). In section 4 the ''compound Harmonic algorithm'' for the generalized k-server problem is presented. Certain multi-step transition probabilities and absorbing probabilities are used by the compound Harmonic algorithm. For their computation one step of the generalized k-server problem is replaced by a number of steps of other (generalized) specific k-server problems. We show that this algorithm is competitive against an adaptive online adversary. In the case of unit distances the Harmonic algorithm and the compound Harmonic algorithm are identical.



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Futschik, Andreas; Hotz, Thomas; Munk, Axel; Sieling, Hannes;
Multiscale DNA partitioning: statistical evidence for segments. - In: Bioinformatics. - Oxford : Oxford Univ. Press, ISSN 1460-2059, Bd. 30 (2014), 16, S. 2255-2262

http://dx.doi.org/10.1093/bioinformatics/btu180
Brás, Carmo; Eichfelder, Gabriele; Júdice, Joaquim
Copositivity tests based on the linear complementarity problem. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2014. - Online-Ressource (PDF-Datei: 28 S., 443 KB). . - (Preprint. - M14,05)

Copositivity tests are presented based on new necessary and suffcient conditions requiring the solution of linear complementarity problems (LCP). Methodologies involving Lemke's method, an enumerative algorithm and a linear mixed-integer programming formulation are proposed to solve the required LCPs. A new necessary condition for (strict) copositivity based on solving a Linear Program (LP) is also discussed, 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 up to dimension 496 x 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://www.db-thueringen.de/servlets/DocumentServlet?id=24543
Knobloch, Jürgen; Lamb, Jeroen S. W.; Webster, Kevin N.
Using Lin's method to solve Bykov's problems. - In: Journal of differential equations. - Orlando, Fla. : Elsevier, ISSN 1090-2732, Bd. 257 (2014), 8, S. 2984-3047

http://dx.doi.org/10.1016/j.jde.2014.06.006
Brandt, Stephan; Harant, Jochen; Naumann, Steffi
On degree sums of a triangle-free graph. - In: Discrete mathematics. - Amsterdam [u.a.] : Elsevier, Bd. 337 (2014), S. 76-82

http://dx.doi.org/10.1016/j.disc.2014.08.010