File Download

There are no files associated with this item.

  Links for fulltext
     (May Require Subscription)
Supplementary

Conference Paper: Curse of dimensionality reduction in max-plus based approximation methods: Theoretical estimates and improved pruning algorithms

TitleCurse of dimensionality reduction in max-plus based approximation methods: Theoretical estimates and improved pruning algorithms
Authors
Issue Date2011
Citation
Proceedings of the IEEE Conference on Decision and Control, 2011, p. 1054-1061 How to Cite?
AbstractMax-plus based methods have been recently developed to approximate the value function of possibly high dimensional optimal control problems. A critical step of these methods consists in approximating a function by a supremum of a small number of functions (max-plus "basis functions") taken from a prescribed dictionary. We study several variants of this approximation problem, which we show to be continuous versions of the facility location and k-center combinatorial optimization problems, in which the connection costs arise from a Bregman distance. We give theoretical error estimates, quantifying the number of basis functions needed to reach a prescribed accuracy. We derive from our approach a refinement of the curse of dimensionality free method introduced previously by McEneaney, with a higher accuracy for a comparable computational cost. © 2011 IEEE.
Persistent Identifierhttp://hdl.handle.net/10722/219665
ISSN

 

DC FieldValueLanguage
dc.contributor.authorGaubert, Stéphane-
dc.contributor.authorMcEneaney, William-
dc.contributor.authorQu, Zheng-
dc.date.accessioned2015-09-23T02:57:40Z-
dc.date.available2015-09-23T02:57:40Z-
dc.date.issued2011-
dc.identifier.citationProceedings of the IEEE Conference on Decision and Control, 2011, p. 1054-1061-
dc.identifier.issn0191-2216-
dc.identifier.urihttp://hdl.handle.net/10722/219665-
dc.description.abstractMax-plus based methods have been recently developed to approximate the value function of possibly high dimensional optimal control problems. A critical step of these methods consists in approximating a function by a supremum of a small number of functions (max-plus "basis functions") taken from a prescribed dictionary. We study several variants of this approximation problem, which we show to be continuous versions of the facility location and k-center combinatorial optimization problems, in which the connection costs arise from a Bregman distance. We give theoretical error estimates, quantifying the number of basis functions needed to reach a prescribed accuracy. We derive from our approach a refinement of the curse of dimensionality free method introduced previously by McEneaney, with a higher accuracy for a comparable computational cost. © 2011 IEEE.-
dc.languageeng-
dc.relation.ispartofProceedings of the IEEE Conference on Decision and Control-
dc.titleCurse of dimensionality reduction in max-plus based approximation methods: Theoretical estimates and improved pruning algorithms-
dc.typeConference_Paper-
dc.description.natureLink_to_subscribed_fulltext-
dc.identifier.doi10.1109/CDC.2011.6161386-
dc.identifier.scopuseid_2-s2.0-84860654722-
dc.identifier.spage1054-
dc.identifier.epage1061-

Export via OAI-PMH Interface in XML Formats


OR


Export to Other Non-XML Formats