Mathematik und Statistikhttp://kops.uni-konstanz.de:80/handle/123456789/82019-10-16T21:00:39Z2019-10-16T21:00:39ZPOD-Based Bicriterial Optimal Control by the Reference Point MethodBanholzer, Stefanpop216783Beermann, Dennispop212145Volkwein, Stefanpop214121Macchelli, Alessandro123456789/34156.22019-10-15T11:51:42Z2016POD-Based Bicriterial Optimal Control by the Reference Point Method
Banholzer, Stefan; Beermann, Dennis; Volkwein, Stefan
In the present paper a bicriterial optimal control problem governed by a parabolic partial differential equation (PDE) and bilateral control constraints is considered. For the numerical optimization the reference point method is utilized. The PDE is discretized by a Galerkin approximation utilizing the method of proper orthogonal decomposition (POD). POD is a powerful approach to derive reduced-order approximations for evolution problems. Numerical examples illustrate the efficiency of the proposed strategy.
2016Banholzer, StefanBeermann, DennisVolkwein, Stefan510In the present paper a bicriterial optimal control problem governed by a parabolic partial differential equation (PDE) and bilateral control constraints is considered. For the numerical optimization the reference point method is utilized. The PDE is discretized by a Galerkin approximation utilizing the method of proper orthogonal decomposition (POD). POD is a powerful approach to derive reduced-order approximations for evolution problems. Numerical examples illustrate the efficiency of the proposed strategy.IFACMacchelli, AlessandroINPROCEEDINGSeng10.1016/j.ifacol.2016.07.443IFAC-Papers Online49,82405-89632102152nd IFAC Workshop on Control of Systems Governed by Partial Differential Equations2019-10-15T13:51:42+02:00123456789/392nd IFAC Workshop on Control of Systems Governed by Partial Differential Equations / Macchelli, Alessandro (Hrsg.). - Laxenburg : IFAC, 2016. - (IFAC-Papers Online ; 49,8). - S. 210-215. - eISSN 2405-8963Bertinoro, Italy2016-06-13Laxenburg2nd IFAC Workshop on Control of Systems Governed by Partial Differential Equations2016-06-152019-10-15T11:51:42ZExtended Laplace principle for empirical measures of a Markov chainEckstein, Stephanpop233432123456789/471282019-10-11T01:14:23Z2019Extended Laplace principle for empirical measures of a Markov chain
Eckstein, Stephan
We consider discrete-time Markov chains with Polish state space. The large deviations principle for empirical measures of a Markov chain can equivalently be stated in Laplace principle form, which builds on the convex dual pair of relative entropy (or Kullback– Leibler divergence) and cumulant generating functional f ↦ ln ʃ exp (f). Following the approach by Lacker (2016) in the independent and identically distributed case, we generalize the Laplace principle to a greater class of convex dual pairs. We present in depth one application arising from this extension, which includes large deviation results and a weak law of large numbers for certain robust Markov chains—similar to Markov set chains—where we model robustness via the first Wasserstein distance. The setting and proof of the extended Laplace principle are based on the weak convergence approach to large deviations by Dupuis and Ellis (2011).
2019Eckstein, Stephan510We consider discrete-time Markov chains with Polish state space. The large deviations principle for empirical measures of a Markov chain can equivalently be stated in Laplace principle form, which builds on the convex dual pair of relative entropy (or Kullback– Leibler divergence) and cumulant generating functional f ↦ ln ʃ exp (f). Following the approach by Lacker (2016) in the independent and identically distributed case, we generalize the Laplace principle to a greater class of convex dual pairs. We present in depth one application arising from this extension, which includes large deviation results and a weak law of large numbers for certain robust Markov chains—similar to Markov set chains—where we model robustness via the first Wasserstein distance. The setting and proof of the extended Laplace principle are based on the weak convergence approach to large deviations by Dupuis and Ellis (2011).JOURNAL_ARTICLEeng10.1017/apr.2019.60001-86781475-6064136167511Advances in Applied Probability2019-10-07T15:57:34+02:00123456789/39Advances in Applied Probability ; 51 (2019), 1. - S. 136-167. - ISSN 0001-8678. - eISSN 1475-6064true2019-10-07T13:57:34ZDefinable valuations induced by multiplicative subgroups and NIP fieldsDupont, Katharinapop89854Hasson, AssafKuhlmann, Salmapop215914123456789/40757.22019-10-07T09:03:35Z2019Definable valuations induced by multiplicative subgroups and NIP fields
Dupont, Katharina; Hasson, Assaf; Kuhlmann, Salma
We study the algebraic implications of the non-independence property and variants thereof (dp-minimality) on infinite fields, motivated by the conjecture that all such fields which are neither real closed nor separably closed admit a (definable) henselian valuation. Our results mainly focus on Hahn fields and build up on Will Johnson’s “The canonical topology on dp-minimal fields” (J Math Log 18(2):1850007, 2018).
2019Dupont, KatharinaHasson, AssafKuhlmann, Salma510We study the algebraic implications of the non-independence property and variants thereof (dp-minimality) on infinite fields, motivated by the conjecture that all such fields which are neither real closed nor separably closed admit a (definable) henselian valuation. Our results mainly focus on Hahn fields and build up on Will Johnson’s “The canonical topology on dp-minimal fields” (J Math Log 18(2):1850007, 2018).JOURNAL_ARTICLEeng10.1007/s00153-019-00661-20933-58461432-0665819839587-8Archive for Mathematical Logic2019-10-07T11:03:34+02:00123456789/39Archive for Mathematical Logic ; 58 (2019), 7-8. - S. 819-839. - ISSN 0933-5846. - eISSN 1432-0665true2019-10-07T09:03:34ZtrueImplementierung von Innere-Punkte-Verfahren in PythonHoffmann, Danielpop250322123456789/470912019-10-02T01:04:41Z2019Implementierung von Innere-Punkte-Verfahren in Python
Hoffmann, Daniel
2019Hoffmann, Daniel510BSC_THESISurn:nbn:de:bsz:352-2-ek81av8rgix01deu2019-10-01T13:27:24+02:00123456789/392019-10-01T11:27:24Z