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On Optimal Sparse-Control Problems Governed by Jump-Diffusion Processes
Zitieren Sie bitte immer diese URN: urn:nbn:de:bvb:20-opus-147819
- A framework for the optimal sparse-control of the probability density function of a jump-diffusion process is presented. This framework is based on the partial integro-differential Fokker-Planck (FP) equation that governs the time evolution of the probability density function of this process. In the stochastic process and, correspondingly, in the FP model the control function enters as a time-dependent coefficient. The objectives of the control are to minimize a discrete-in-time, resp. continuous-in-time, tracking functionals and its L2- andA framework for the optimal sparse-control of the probability density function of a jump-diffusion process is presented. This framework is based on the partial integro-differential Fokker-Planck (FP) equation that governs the time evolution of the probability density function of this process. In the stochastic process and, correspondingly, in the FP model the control function enters as a time-dependent coefficient. The objectives of the control are to minimize a discrete-in-time, resp. continuous-in-time, tracking functionals and its L2- and L1-costs, where the latter is considered to promote control sparsity. An efficient proximal scheme for solving these optimal control problems is considered. Results of numerical experiments are presented to validate the theoretical results and the computational effectiveness of the proposed control framework.…
Autor(en): | Beatrice Gaviraghi, Andreas Schindele, Mario Annunziato, Alfio Borzì |
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URN: | urn:nbn:de:bvb:20-opus-147819 |
Dokumentart: | Artikel / Aufsatz in einer Zeitschrift |
Institute der Universität: | Fakultät für Mathematik und Informatik / Institut für Mathematik |
Sprache der Veröffentlichung: | Englisch |
Titel des übergeordneten Werkes / der Zeitschrift (Englisch): | Applied Mathematics |
Erscheinungsjahr: | 2016 |
Band / Jahrgang: | 7 |
Heft / Ausgabe: | 16 |
Erste Seite: | 1978 |
Letzte Seite: | 2004 |
Originalveröffentlichung / Quelle: | Applied Mathematics , 7, 1978-2004. http://dx.doi.org/10.4236/am.2016.716162 |
DOI: | https://doi.org/10.4236/am.2016.716162 |
Allgemeine fachliche Zuordnung (DDC-Klassifikation): | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 519 Wahrscheinlichkeiten, angewandte Mathematik |
Freie Schlagwort(e): | jump-diffusion processes; nonsmooth optimization; optimal control theory; partial integro-differential Fokker-Planck Equation; proximal methods |
Datum der Freischaltung: | 19.05.2017 |
EU-Projektnummer / Contract (GA) number: | 304617 |
OpenAIRE: | OpenAIRE |
Sammlungen: | Open-Access-Publikationsfonds / Förderzeitraum 2016 |
Lizenz (Deutsch): | CC BY: Creative-Commons-Lizenz: Namensnennung |