{"id":"https://openalex.org/W1966419611","doi":"https://doi.org/10.1137/110841576","title":"A Patchy Dynamic Programming Scheme for a Class of Hamilton--Jacobi--Bellman Equations","display_name":"A Patchy Dynamic Programming Scheme for a Class of Hamilton--Jacobi--Bellman Equations","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W1966419611","doi":"https://doi.org/10.1137/110841576","mag":"1966419611"},"language":"en","primary_location":{"id":"doi:10.1137/110841576","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110841576","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1109.3577","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5031296378","display_name":"Simone Cacace","orcid":"https://orcid.org/0000-0002-5864-0970"},"institutions":[{"id":"https://openalex.org/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I4210107641","display_name":"Centre de Math\u00e9matiques Appliqu\u00e9es","ror":"https://ror.org/012e1xn46","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I142476485","https://openalex.org/I4210107641","https://openalex.org/I4210141950","https://openalex.org/I4210145102"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Simone Cacace","raw_affiliation_strings":["Centre de Math\u00e9matiques Appliqu\u00e9es, \u00c9cole Polytechnique"],"affiliations":[{"raw_affiliation_string":"Centre de Math\u00e9matiques Appliqu\u00e9es, \u00c9cole Polytechnique","institution_ids":["https://openalex.org/I4210107641","https://openalex.org/I142476485"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006366581","display_name":"Emiliano Cristiani","orcid":"https://orcid.org/0000-0002-7015-2371"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Emiliano Cristiani","raw_affiliation_strings":["Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems"],"affiliations":[{"raw_affiliation_string":"Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044925835","display_name":"Maurizio Falcone","orcid":"https://orcid.org/0000-0002-4277-2370"},"institutions":[{"id":"https://openalex.org/I861853513","display_name":"Sapienza University of Rome","ror":"https://ror.org/02be6w209","country_code":"IT","type":"education","lineage":["https://openalex.org/I861853513"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Maurizio Falcone","raw_affiliation_strings":["Universita degli Studi di Roma La Sapienza, Rome"],"affiliations":[{"raw_affiliation_string":"Universita degli Studi di Roma La Sapienza, Rome","institution_ids":["https://openalex.org/I861853513"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036746144","display_name":"Athena Picarelli","orcid":"https://orcid.org/0000-0003-1103-5324"},"institutions":[{"id":"https://openalex.org/I4210164441","display_name":"Conservatorio Guido Cantelli di Novara","ror":"https://ror.org/05hfa9864","country_code":"IT","type":"education","lineage":["https://openalex.org/I4210164441"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Athena Picarelli","raw_affiliation_strings":["Dipartimento di Matematica Guido Castelnuovo [Roma I]"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica Guido Castelnuovo [Roma I]","institution_ids":["https://openalex.org/I4210164441"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5031296378"],"corresponding_institution_ids":["https://openalex.org/I142476485","https://openalex.org/I4210107641"],"apc_list":null,"apc_paid":null,"fwci":6.9107,"has_fulltext":false,"cited_by_count":59,"citation_normalized_percentile":{"value":0.97318509,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"34","issue":"5","first_page":"A2625","last_page":"A2649"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9908999800682068,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9908999800682068,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10462","display_name":"Reinforcement Learning in Robotics","score":0.979200005531311,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11615","display_name":"Control and Dynamics of Mobile Robots","score":0.975600004196167,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7222439646720886},{"id":"https://openalex.org/keywords/hamilton\u2013jacobi-equation","display_name":"Hamilton\u2013Jacobi equation","score":0.686933696269989},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6526620388031006},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.635184645652771},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.6018285155296326},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5695786476135254},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5646759867668152},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"Dynamic programming","score":0.5572510361671448},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.5220530033111572},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4788810610771179},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.44363173842430115},{"id":"https://openalex.org/keywords/subdivision","display_name":"Subdivision","score":0.42169880867004395},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29259926080703735},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.2254854142665863},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1718463897705078}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7222439646720886},{"id":"https://openalex.org/C2778860007","wikidata":"https://www.wikidata.org/wiki/Q1060137","display_name":"Hamilton\u2013Jacobi equation","level":2,"score":0.686933696269989},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6526620388031006},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.635184645652771},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.6018285155296326},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5695786476135254},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5646759867668152},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.5572510361671448},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.5220530033111572},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4788810610771179},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.44363173842430115},{"id":"https://openalex.org/C143392562","wikidata":"https://www.wikidata.org/wiki/Q449111","display_name":"Subdivision","level":2,"score":0.42169880867004395},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29259926080703735},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.2254854142665863},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1718463897705078},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.0},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/110841576","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110841576","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1109.3577","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1109.3577","pdf_url":"https://arxiv.org/pdf/1109.3577","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.220.4201","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.220.4201","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hal.inria.fr/docs/00/62/81/08/PDF/CacaceChristianiFalconePicarelli_2011.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:inria-00628108v1","is_oa":true,"landing_page_url":"https://inria.hal.science/inria-00628108","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Scientific Computing, 2012, 34 (5), pp.A2625-A2649. ⟨10.1137/110841576⟩","raw_type":"Journal articles"},{"id":"pmh:oai:iris.uniroma1.it:11573/507037","is_oa":false,"landing_page_url":"http://hdl.handle.net/11573/507037","pdf_url":null,"source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:iris.uniroma3.it:11590/351094","is_oa":false,"landing_page_url":"http://hdl.handle.net/11590/351094","pdf_url":null,"source":{"id":"https://openalex.org/S4377196120","display_name":"Iris (Roma Tre University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I119003972","host_organization_name":"Roma Tre University","host_organization_lineage":["https://openalex.org/I119003972"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1109.3577","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1109.3577","pdf_url":"https://arxiv.org/pdf/1109.3577","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W16150225","https://openalex.org/W124620454","https://openalex.org/W587977125","https://openalex.org/W1487586009","https://openalex.org/W1567262822","https://openalex.org/W1916545658","https://openalex.org/W1986091057","https://openalex.org/W1988902760","https://openalex.org/W1999244633","https://openalex.org/W2000582360","https://openalex.org/W2003009438","https://openalex.org/W2010920261","https://openalex.org/W2011092576","https://openalex.org/W2017089923","https://openalex.org/W2020361400","https://openalex.org/W2027438381","https://openalex.org/W2040126557","https://openalex.org/W2049391017","https://openalex.org/W2055341194","https://openalex.org/W2055630271","https://openalex.org/W2064614799","https://openalex.org/W2070376330","https://openalex.org/W2076729694","https://openalex.org/W2087599797","https://openalex.org/W2092223234","https://openalex.org/W2099761232","https://openalex.org/W2108193376","https://openalex.org/W2141454876","https://openalex.org/W2143454084","https://openalex.org/W2152712142","https://openalex.org/W2321052409","https://openalex.org/W2561843528","https://openalex.org/W2998023265","https://openalex.org/W3104948387","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1985696076","https://openalex.org/W1977330547","https://openalex.org/W4255265352","https://openalex.org/W4239477580","https://openalex.org/W1974495512","https://openalex.org/W4226406511","https://openalex.org/W4390746698","https://openalex.org/W4286890456","https://openalex.org/W2061850819","https://openalex.org/W4285537323"],"abstract_inverted_index":{"Abstract.":[0],"In":[1],"this":[2,95],"paper":[3],"we":[4,67],"present":[5],"a":[6,43,80],"new":[7,124],"parallel":[8],"algorithm":[9],"for":[10],"the":[11,27,34,37,50,60,70,77,84,89,92,98,103,120,123],"solution":[12],"of":[13,29,36,91,122],"Hamilton-Jacobi-Bellman":[14],"equations":[15],"related":[16],"to":[17,25,59,79],"optimal":[18,61],"control":[19,38],"problems.":[20],"The":[21],"main":[22],"idea":[23],"is":[24,55],"divide":[26],"domain":[28],"computation":[30],"into":[31],"subdomains":[32,99],"following":[33],"dynamics":[35],"problem.":[39],"This":[40],"results":[41],"in":[42,73,102,110,114],"rather":[44],"complex":[45],"geometrical":[46],"subdivision,":[47],"but":[48],"has":[49],"advantage":[51],"that":[52,66],"every":[53],"subdomain":[54,75],"invariant":[56],"with":[57],"respect":[58],"controlled":[62],"vector":[63],"field,":[64],"so":[65],"can":[68],"compute":[69],"value":[71],"function":[72],"each":[74],"assigning":[76],"task":[78],"processor":[81],"and":[82,108,117],"avoiding":[83],"classical":[85],"transmission":[86],"condition":[87],"on":[88],"boundaries":[90],"subdomains.":[93],"For":[94],"specific":[96],"feature":[97],"are":[100],"patches":[101],"sense":[104],"introduced":[105],"by":[106],"Ancona":[107],"Bressan":[109],"[1].":[111],"Several":[112],"examples":[113],"dimension":[115],"two":[116],"three":[118],"illustrate":[119],"properties":[121],"method.":[125]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":5}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}