dc.contributor.author
Guth, Philipp A.
dc.contributor.author
Kaarnioja, Vesa
dc.contributor.author
Kuo, Frances Y.
dc.contributor.author
Schillings, Claudia
dc.contributor.author
Sloan, Ian H.
dc.date.accessioned
2024-04-22T08:03:31Z
dc.date.available
2024-04-22T08:03:31Z
dc.identifier.uri
https://refubium.fu-berlin.de/handle/fub188/42939
dc.identifier.uri
http://dx.doi.org/10.17169/refubium-42653
dc.description.abstract
We study the application of a tailored quasi-Monte Carlo (QMC) method to a class of optimal control problems subject to parabolic partial differential equation (PDE) constraints under uncertainty: the state in our setting is the solution of a parabolic PDE with a random thermal diffusion coefficient, steered by a control function. To account for the presence of uncertainty in the optimal control problem, the objective function is composed with a risk measure. We focus on two risk measures, both involving high-dimensional integrals over the stochastic variables: the expected value and the (nonlinear) entropic risk measure. The high-dimensional integrals are computed numerically using specially designed QMC methods and, under moderate assumptions on the input random field, the error rate is shown to be essentially linear, independently of the stochastic dimension of the problem—and thereby superior to ordinary Monte Carlo methods. Numerical results demonstrate the effectiveness of our method.
en
dc.format.extent
44 Seiten
dc.rights.uri
https://creativecommons.org/licenses/by/4.0/
dc.subject
parabolic partial differential equation
en
dc.subject
optimal control
en
dc.subject.ddc
500 Naturwissenschaften und Mathematik::510 Mathematik::510 Mathematik
dc.title
Parabolic PDE-constrained optimal control under uncertainty with entropic risk measure using quasi-Monte Carlo integration
dc.type
Wissenschaftlicher Artikel
dcterms.bibliographicCitation.doi
10.1007/s00211-024-01397-9
dcterms.bibliographicCitation.journaltitle
Numerische Mathematik
dcterms.bibliographicCitation.number
2
dcterms.bibliographicCitation.pagestart
565
dcterms.bibliographicCitation.pageend
608
dcterms.bibliographicCitation.volume
156
dcterms.bibliographicCitation.url
https://doi.org/10.1007/s00211-024-01397-9
refubium.affiliation
Mathematik und Informatik
refubium.affiliation.other
Institut für Mathematik

refubium.funding
Springer Nature DEAL
refubium.note.author
Die Publikation wurde aus Open Access Publikationsgeldern der Freien Universität Berlin gefördert.
refubium.resourceType.isindependentpub
no
dcterms.accessRights.openaire
open access
dcterms.isPartOf.eissn
0945-3245