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- Publisher Website: 10.1109/CDC.2011.6161386
- Scopus: eid_2-s2.0-84860654722
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Conference Paper: Curse of dimensionality reduction in max-plus based approximation methods: Theoretical estimates and improved pruning algorithms
Title | Curse of dimensionality reduction in max-plus based approximation methods: Theoretical estimates and improved pruning algorithms |
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Authors | |
Issue Date | 2011 |
Citation | Proceedings of the IEEE Conference on Decision and Control, 2011, p. 1054-1061 How to Cite? |
Abstract | Max-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 Identifier | http://hdl.handle.net/10722/219665 |
ISSN | 2020 SCImago Journal Rankings: 0.395 |
DC Field | Value | Language |
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dc.contributor.author | Gaubert, Stéphane | - |
dc.contributor.author | McEneaney, William | - |
dc.contributor.author | Qu, Zheng | - |
dc.date.accessioned | 2015-09-23T02:57:40Z | - |
dc.date.available | 2015-09-23T02:57:40Z | - |
dc.date.issued | 2011 | - |
dc.identifier.citation | Proceedings of the IEEE Conference on Decision and Control, 2011, p. 1054-1061 | - |
dc.identifier.issn | 0191-2216 | - |
dc.identifier.uri | http://hdl.handle.net/10722/219665 | - |
dc.description.abstract | Max-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.language | eng | - |
dc.relation.ispartof | Proceedings of the IEEE Conference on Decision and Control | - |
dc.title | Curse of dimensionality reduction in max-plus based approximation methods: Theoretical estimates and improved pruning algorithms | - |
dc.type | Conference_Paper | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1109/CDC.2011.6161386 | - |
dc.identifier.scopus | eid_2-s2.0-84860654722 | - |
dc.identifier.spage | 1054 | - |
dc.identifier.epage | 1061 | - |
dc.identifier.issnl | 0191-2216 | - |