http://www.tu-ilmenau.de

Logo TU Ilmenau



Photo of the Contact Person
Contact Person

Prof. Dr. Michael Stiebitz

Head of Institute

Phone +49 3677 69-3633

Send email


INHALTE

Publications

Publications at the institute since 1990

Anzahl der Treffer: 1185
Erstellt: Mon, 13 Jul 2020 23:05:59 +0200 in 0.0307 sec


Dickinson, Peter J. C.; Eichfelder, Gabriele; Povh, Janez
Erratum to: On the set-semidefinite representation of nonconvex quadratic programs over arbitrary feasible sets. - In: Optimization letters. - Berlin : Springer, ISSN 1862-4480, Bd. 7 (2013), 6, S. 1387-1397

In this paper, an erratum is provided to the article "On the set-semidefinite representation of nonconvex quadratic programs over arbitrary feasible sets", published in Optim Lett, 2012. Due to precise observation of the first author, it has been found that the proof of Lemma 9 has a nontrivial gap, and consequently the main result (Theorem 10) is incorrect. In this erratum, we prove that Corollary 14 is still correct in the original setting while to fix the proof of Theorem 10 we need additional assumptions. We provide a list of different commonly used assumptions making this theorem to be true, and a new version of this theorem, which is now Theorem 17.



http://dx.doi.org/10.1007/s11590-013-0645-2
Eichfelder, Gabriele; Povh, Janez
On the set-semidefinite representation of nonconvex quadratic programs over arbitrary feasible sets. - In: Optimization letters. - Berlin : Springer, ISSN 1862-4480, Bd. 7 (2013), 6, S. 1373-1386

In the paper we prove that any nonconvex quadratic problem over some set K R^n with additional linear and binary constraints can be rewritten as a linear problem over the cone, dual to the cone of K-semidefinite matrices. We show that when K is defined by one quadratic constraint or by one concave quadratic constraint and one linear inequality, then the resulting K-semidefinite problem is actually a semidefinite programming problem. This generalizes results obtained by Sturm and Zhang (Math Oper Res 28:246-267, 2003). Our result also generalizes thewell-known completely positive representation result from Burer (Math Program 120:479-495, 2009), which is actually a special instance of our result with K = R^n_+.



http://dx.doi.org/10.1007/s11590-012-0450-3
Möws, Roland;
Spektrallücken von indefiniten Sturm-Liouville-Operatoren, 2013. - Online-Ressource (PDF-Datei: XI, 67 S., 820,4 KB). : Ilmenau, Techn. Univ., Diss., 2013
- Unterschiede zwischen dem gedruckten Dokument und der elektronischen Ressource können nicht ausgeschlossen werden

In der Dissertationsschrift "Spektrallücken von indefiniten Sturm-Liouville-Operatoren" werden verschiedene Klassen von selbstadjungierten Operatoren und Relationen in indefiniten Innenprodukträumen betrachtet. Die Arbeit enthält zwei Hauptergebnisse: (A) Für lokal definisierbare Relationen wird gezeigt, dass die Endlichkeit der Anzahl der Eigenwerte in einer reellen Spektrallücke des essentiellen Spektrums unter endlichdimensionalen Störungen erhalten bleibt. (B) Für eine Unterklasse der lokal definisierbare Relationen, nämlich für Relationen mit endlich vielen negativen Quadraten, werden die Anzahl der Eigenwerte der gestörten Relation in einer reellen Spektrallücke des essentiellen Spektrums nach oben/unten durch die Anzahl der Eigenwerte derungestörten Relation und weiteren Korrekturgrößen abgeschätzt. Dabei werden hier nur eindimensionale Störungen betrachtet. Zudem gelingt der Nachweis, dass die in dieser Promotionsschrift vorgestellten Abschätzungen scharf sind.Diese abstrakten Ergebnisse aus dem ersten Teil der Arbeit werden im zweiten Teil auf Sturm-Liouville-Differentialoperatoren mit einer indefinitenGewichtsfunktion angewandt. In vielen Fällen werden die Abschätzungen leicht verbessert.



http://www.db-thueringen.de/servlets/DocumentServlet?id=22550
Hildenbrandt, Regina;
A new competitive ratio of the Harmonic algorithm for a k-server problem with parallel requests and unit distances. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2013. - Online-Ressource (PDF-Datei: 15 S., 152,8 KB). . - (Preprint. - M13,10)
http://www.db-thueringen.de/servlets/DocumentServlet?id=22488
Lorenz, Pierre; Klöppel, Michaell; Frost, Frank; Ehrhardt, Martin; Zimmer, Klaus; Li, Pu
Laser-induced circular nanostructures in fused silica assisted by a self-assembling chromium layer. - In: Applied surface science : a journal devoted to applied physics and chemistry of surfaces and interfaces.. - Amsterdam : Elsevier, Bd. 280 (2013), S. 933-939

http://dx.doi.org/10.1016/j.apsusc.2013.05.102
Vogel, Silvia; Schettler, Anne
A uniform concentration-of-measure inequality for multivariate kernel density estimators. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2013. - Online-Ressource (PDF-Datei: 10 S., 264,6 KB). . - (Preprint. - M13,09)
http://www.db-thueringen.de/servlets/DocumentServlet?id=22415
Eichfelder, Gabriele; Ha, Truong Xuan Duc
Optimality conditions for vector optimization problems with variable ordering structures. - In: Optimization : a journal of mathematical programming and operations research.. - London [u.a.] : Taylor & Francis, ISSN 1029-4945, Bd. 62 (2013), 5, S. 597-627

Our main concern in this article are concepts of nondominatedness w.r.t. a variable ordering structure introduced by Yu [P.L. Yu, Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives, J. Optim. Theory Appl. 14 (1974), pp. 319-377]. Our studies are motivated by some recent applications e.g. in medical image registration. Restricting ourselves to the case when the values of a cone-valued map defining the ordering structure are Bishop-Phelps cones, we obtain for the first time scalarizing functionals for nondominated elements, Fermat rule, Lagrange multiplier rule and duality results for a single- or set-valued vector optimization problem with a variable ordering structure.



http://dx.doi.org/10.1080/02331934.2011.575939
Winkler, Henrik; Woracek, Harald
Symmetry in de Branges almost Pontryagin spaces. - In: Integral equations and operator theory : IEOT.. - Berlin : Springer, ISSN 1420-8989, Bd. 76 (2013), 2, S. 179-212

http://dx.doi.org/10.1007/s00020-013-2051-7
Berger, Thomas;
Zero dynamics and stabilization for linear DAEs. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2013. - Online-Ressource (PDF-Datei: 19 S., 140 KB). . - (Preprint. - M13,08)
http://www.db-thueringen.de/servlets/DocumentServlet?id=22328
Berger, Thomas; Reis, Timo
Controllability of linear differential-algebraic systems - a survey. - In: Berlin [u.a.] : Springer, ISBN 978-3-642-34927-0, (2013), S. 1-61