On Optimal Sparse-Control Problems Governed by Jump-Diffusion Processes
Please always quote using this 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.…
Author: | Beatrice Gaviraghi, Andreas Schindele, Mario Annunziato, Alfio Borzì |
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URN: | urn:nbn:de:bvb:20-opus-147819 |
Document Type: | Journal article |
Faculties: | Fakultät für Mathematik und Informatik / Institut für Mathematik |
Language: | English |
Parent Title (English): | Applied Mathematics |
Year of Completion: | 2016 |
Volume: | 7 |
Issue: | 16 |
First Page: | 1978 |
Last Page: | 2004 |
Source: | Applied Mathematics , 7, 1978-2004. http://dx.doi.org/10.4236/am.2016.716162 |
DOI: | https://doi.org/10.4236/am.2016.716162 |
Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 519 Wahrscheinlichkeiten, angewandte Mathematik |
Tag: | jump-diffusion processes; nonsmooth optimization; optimal control theory; partial integro-differential Fokker-Planck Equation; proximal methods |
Release Date: | 2017/05/19 |
EU-Project number / Contract (GA) number: | 304617 |
OpenAIRE: | OpenAIRE |
Collections: | Open-Access-Publikationsfonds / Förderzeitraum 2016 |
Licence (German): | CC BY: Creative-Commons-Lizenz: Namensnennung |