{"id":"https://openalex.org/W2063917507","doi":"https://doi.org/10.1007/s10589-011-9454-7","title":"Convergence of the forward-backward sweep method in optimal control","display_name":"Convergence of the forward-backward sweep method in optimal control","publication_year":2012,"publication_date":"2012-01-13","ids":{"openalex":"https://openalex.org/W2063917507","doi":"https://doi.org/10.1007/s10589-011-9454-7","mag":"2063917507"},"language":"en","primary_location":{"id":"doi:10.1007/s10589-011-9454-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10589-011-9454-7","pdf_url":null,"source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Optimization and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5045824294","display_name":"Michael McAsey","orcid":"https://orcid.org/0000-0003-4882-7827"},"institutions":[{"id":"https://openalex.org/I24648388","display_name":"Bradley University","ror":"https://ror.org/04kmeaw70","country_code":"US","type":"education","lineage":["https://openalex.org/I24648388"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Michael McAsey","raw_affiliation_strings":["Department of Mathematics, Bradley University, Peoria, IL, 61625, USA","Department of Mathematics, Bradley University, Peoria, USA 61625"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Bradley University, Peoria, IL, 61625, USA","institution_ids":["https://openalex.org/I24648388"]},{"raw_affiliation_string":"Department of Mathematics, Bradley University, Peoria, USA 61625","institution_ids":["https://openalex.org/I24648388"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006599140","display_name":"Libin Mou","orcid":null},"institutions":[{"id":"https://openalex.org/I24648388","display_name":"Bradley University","ror":"https://ror.org/04kmeaw70","country_code":"US","type":"education","lineage":["https://openalex.org/I24648388"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Libin Mou","raw_affiliation_strings":["Department of Mathematics, Bradley University, Peoria, IL, 61625, USA","Department of Mathematics, Bradley University, Peoria, USA 61625"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Bradley University, Peoria, IL, 61625, USA","institution_ids":["https://openalex.org/I24648388"]},{"raw_affiliation_string":"Department of Mathematics, Bradley University, Peoria, USA 61625","institution_ids":["https://openalex.org/I24648388"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031753752","display_name":"Weimin Han","orcid":"https://orcid.org/0000-0002-0960-2281"},"institutions":[{"id":"https://openalex.org/I126307644","display_name":"University of Iowa","ror":"https://ror.org/036jqmy94","country_code":"US","type":"education","lineage":["https://openalex.org/I126307644"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Weimin Han","raw_affiliation_strings":["Department of Mathematics, University of Iowa, Iowa City, IA, 52242, USA","Department of Mathematics, University of Iowa, Iowa City, USA 52242#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Iowa, Iowa City, IA, 52242, USA","institution_ids":["https://openalex.org/I126307644"]},{"raw_affiliation_string":"Department of Mathematics, University of Iowa, Iowa City, USA 52242#TAB#","institution_ids":["https://openalex.org/I126307644"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5045824294"],"corresponding_institution_ids":["https://openalex.org/I24648388"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":74.7041,"has_fulltext":false,"cited_by_count":201,"citation_normalized_percentile":{"value":0.9967941,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"53","issue":"1","first_page":"207","last_page":"226"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11082","display_name":"Spacecraft Dynamics and Control","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11082","display_name":"Spacecraft Dynamics and Control","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8443106412887573},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.7928767204284668},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.6862612366676331},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.6810503602027893},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6734477877616882},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.6579407453536987},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.573483407497406},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.5420679450035095},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4829946756362915},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.44404253363609314},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.41504979133605957},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.27038460969924927},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11018091440200806},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.06682589650154114}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8443106412887573},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.7928767204284668},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.6862612366676331},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.6810503602027893},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6734477877616882},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6579407453536987},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.573483407497406},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5420679450035095},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4829946756362915},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.44404253363609314},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41504979133605957},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27038460969924927},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11018091440200806},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.06682589650154114},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10589-011-9454-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10589-011-9454-7","pdf_url":null,"source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Optimization and Applications","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:coopap:v:53:y:2012:i:1:p:207-226","is_oa":false,"landing_page_url":"http://hdl.handle.net/10.1007/s10589-011-9454-7","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":60,"referenced_works":["https://openalex.org/W9124626","https://openalex.org/W60908348","https://openalex.org/W176320170","https://openalex.org/W231975775","https://openalex.org/W565935782","https://openalex.org/W581347801","https://openalex.org/W613882012","https://openalex.org/W641945295","https://openalex.org/W1220922634","https://openalex.org/W1480679962","https://openalex.org/W1509923322","https://openalex.org/W1510003436","https://openalex.org/W1543326485","https://openalex.org/W1597944220","https://openalex.org/W1967011851","https://openalex.org/W1967455159","https://openalex.org/W1971947347","https://openalex.org/W1972344754","https://openalex.org/W1976377608","https://openalex.org/W1976616156","https://openalex.org/W1979851178","https://openalex.org/W1982048066","https://openalex.org/W1984170737","https://openalex.org/W1985249384","https://openalex.org/W1987694238","https://openalex.org/W1995504856","https://openalex.org/W1997283008","https://openalex.org/W1999698136","https://openalex.org/W2007770288","https://openalex.org/W2010069926","https://openalex.org/W2018816843","https://openalex.org/W2027181737","https://openalex.org/W2027472105","https://openalex.org/W2035273811","https://openalex.org/W2035904219","https://openalex.org/W2061840468","https://openalex.org/W2067772305","https://openalex.org/W2070389042","https://openalex.org/W2077617040","https://openalex.org/W2084436749","https://openalex.org/W2085740870","https://openalex.org/W2096517919","https://openalex.org/W2107345353","https://openalex.org/W2120688585","https://openalex.org/W2134298283","https://openalex.org/W2152058476","https://openalex.org/W2153132823","https://openalex.org/W2153425320","https://openalex.org/W2162218551","https://openalex.org/W2165126234","https://openalex.org/W2187565700","https://openalex.org/W2214807705","https://openalex.org/W2221321873","https://openalex.org/W2314485382","https://openalex.org/W2497660909","https://openalex.org/W2566565178","https://openalex.org/W2577663557","https://openalex.org/W2974720244","https://openalex.org/W4254671851","https://openalex.org/W4292079189"],"related_works":["https://openalex.org/W3185235544","https://openalex.org/W2364741597","https://openalex.org/W1492103595","https://openalex.org/W946352265","https://openalex.org/W2911623553","https://openalex.org/W3020787026","https://openalex.org/W2585010741","https://openalex.org/W3133842343","https://openalex.org/W2473609169","https://openalex.org/W2329573185"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":16},{"year":2025,"cited_by_count":31},{"year":2024,"cited_by_count":25},{"year":2023,"cited_by_count":24},{"year":2022,"cited_by_count":18},{"year":2021,"cited_by_count":24},{"year":2020,"cited_by_count":14},{"year":2019,"cited_by_count":15},{"year":2018,"cited_by_count":13},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3}],"updated_date":"2026-05-13T08:25:38.343686","created_date":"2025-10-10T00:00:00"}
