Chance constrained optimal power flow with non-Gaussian distributed uncertain wind power generation. - In: 2013 12th International Conference on Environment and Electrical Engineering (EEEIC), ISBN 978-1-4673-3060-2, (2013), S. 265-270
http://dx.doi.org/10.1109/EEEIC.2013.6549628
Erratum to: On the set-semidefinite representation of nonconvex quadratic programs over arbitrary feasible sets. - In: Optimization letters, 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
On the set-semidefinite representation of nonconvex quadratic programs over arbitrary feasible sets. - In: Optimization letters, 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
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
Laser-induced circular nanostructures in fused silica assisted by a self-assembling chromium layer. - In: Applied surface science, Bd. 280 (2013), S. 933-939
http://dx.doi.org/10.1016/j.apsusc.2013.05.102
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)
Confidence sets for modes or level sets of densities are usually derived from the asymptotic distribution of a suitable statistic. Mostly one does not have further information about how close the asymptotic distribution comes to the true distribution for a fixed sample size n. In order to derive conservative cofindence sets for each sample size recently an approach was suggested that does not need full information about a distribution, but instead employs a quantified version of semi-convergence in probability of random sets. The application of this approach to modes or level sets of density functions requires uniform concentration-of-measure results for the density estimators. The aim of the present paper is to prove a result of that kind for the multivariate kernel density estimator. The inequality is also of own interest as it provides a conservative confidence band for the density function.
http://www.db-thueringen.de/servlets/DocumentServlet?id=22415
Optimality conditions for vector optimization problems with variable ordering structures. - In: Optimization, 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
Symmetry in de Branges almost Pontryagin spaces. - In: Integral equations and operator theory, ISSN 1420-8989, Bd. 76 (2013), 2, S. 179-212
http://dx.doi.org/10.1007/s00020-013-2051-7
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)
We study linear differential-algebraic multi-input multi-output systems which are not necessarily regular and investigate the asymptotic stability of the zero dynamics and stabilizability. To this end, the concepts of autonomous zero dynamics, transmission zeros, right-invertibility, stabilizability in the behavioral sense and detectability in the behavioral sense are introduced and algebraic characterizations are derived. It is then proved, for the class of right-invertible systems with autonomous zero dynamics, that asymptotic stability of the zero dynamics is equivalent to three conditions: stabilizability in the behavioral sense, detectability in the behavioral sense, and the condition that all transmission zeros of the system are in the open left complex half-plane. Furthermore, for the same class, it is shown that we can achieve, by a compatible control in the behavioral sense, that the Lyapunov exponent of the interconnected system equals the Lyapunov exponent of the zero dynamics.
http://www.db-thueringen.de/servlets/DocumentServlet?id=22328
Controllability of linear differential-algebraic systems - a survey. - In: Surveys in differential-algebraic equations, (2013), S. 1-61