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Prof. Dr. rer. nat. Thomas Hotz


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Eichfelder, Gabriele; Hotz, Thomas; Wieditz, Johannes;
An algorithm for computing Fréchet means on the sphere. - In: Optimization letters - Berlin : Springer, ISSN 1862-4480, (2019), insges. 11 S., First Online: 07 March 2019

For most optimisation methods an essential assumption is the vector space structure of the feasible set. This condition is not fulfilled if we consider optimisation problems over the sphere. We present an algorithm for solving a special global problem over the sphere, namely the determination of Fréchet means, which are points minimising the mean distance to a given set of points. The Branch and Bound method derived needs no further assumptions on the input data, but is able to cope with this objective function which is neither convex nor differentiable. The algorithms performance is tested on simulated and real data.
Semper, Sebastian; Römer, Florian; Hotz, Thomas; Del Galdo, Giovanni;
Grid-free Direction-of-Arrival estimation with compressed sensing and arbitrary antenna arrays. - In: 2018 IEEE International Conference on Acoustics, Speech, and Signal Processing : proceedings : April 15-20, 2018, Calgary Telus Convention Center, Calgary, Alberta, Canada. - Piscataway, NJ : IEEE, ISBN 978-1-5386-4658-8, (2018), S. 3251-3255
Semper, Sebastian; Römer, Florian; Hotz, Thomas; Del Galdo, Giovanni;
Sparsity order estimation from a single compressed observation vector. - In: IEEE transactions on signal processing : SP : a publication of the IEEE Signal Processing Society. - New York, NY : IEEE, Bd. 66 (2018), 15, S. 3958-3971
Dietrich, Thomas; Krug, Silvia; Hotz, Thomas; Zimmermann, Armin;
Towards energy consumption prediction with safety margins for multicopter systems. - In: Proceedings of the 11th EAI International Conference on Performance Evaluation Methodologies and Tools : VALUETOOLS 2017 : 5-7 December 2017, Venice, Italy. - New York, NY, USA : ACM, ISBN 978-1-4503-6346-4, (2017), S. 227-228
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Glock, Matthias; Hotz, Thomas;
Constructing universal, non-asymptotic confidence sets for intrinsic means on the circle. - In: Geometric science of information : third International Conference, GSI 2017, Paris, France, November 7-9, 2017 : proceedings. - Cham : Springer International Publishing, ISBN 978-3-319-68445-1, (2017), S. 477-485
Zimmermann, Armin; Hotz, Thomas; Canabal Lavista, Andrés;
A hybrid multi-trajectory simulation algorithm for the performance evaluation of stochastic petri nets. - In: Quantitative evaluation of systems : 14th international conference, QEST 2017, Berlin, Germany, September 5-7, 2017 : proceedings. - Cham : Springer International Publishing, ISBN 978-3-319-66335-7, (2017), S. 107-122
Vogel, Silvia;
Random approximations in multiobjective optimization - Ilmenau : Techn. Univ., Inst. für Mathematik, 2014 - Online-Ressource (PDF-Datei: 27 S., 304,7 KB). . - (Preprint. - M14,12)

Often decision makers have to cope with a programming problem with unknown quantitities. Then they will estimate these quantities and solve the problem as it then appears - the 'approximate problem'. Thus there is a need to establish conditions which will ensure that the solutions to the approximate problem will come close to the solutions to the true problem in a suitable manner. Confidence sets, i.e. sets that cover the true sets with a given prescribed probability, provide useful quantitative information. In this paper we consider multiobjective problems and derive confidence sets for the sets of efficient points, weakly efficient points, and the corresponding solution sets. Besides the crucial convergence conditions for the objective and/or constraint functions, one approach for the derivation of confidence sets requires some knowledge about the true problem, which may be not available. Therefore also another method, called relaxation, is suggested. This approach works without any knowledge about the true problem. The results are applied to the Markowitz model of portfolio optimization.
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)
Sinotina, Tatiana; Vogel, Silvia
Universal confidence sets for the mode of a regression function. - In: IMA journal of management mathematics - Oxford : Univ. Press, ISSN 1471-6798, Bd. 23 (2012), 4, S. 309-323
Vogel, Silvia;
Universal confidence sets - estimation and relaxation - Ilmenau : Techn. Univ., Inst. für Mathematik, 2011 - Online-Ressource (PDF-Datei: 14 S., 192,5 KB). . - (Preprint. - M11,12)