{"id":"https://openalex.org/W2052284267","doi":"https://doi.org/10.1137/0328049","title":"On the Existence of Optimal Controls","display_name":"On the Existence of Optimal Controls","publication_year":1990,"publication_date":"1990-05-01","ids":{"openalex":"https://openalex.org/W2052284267","doi":"https://doi.org/10.1137/0328049","mag":"2052284267"},"language":"en","primary_location":{"id":"doi:10.1137/0328049","doi":"https://doi.org/10.1137/0328049","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0328049","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-a","jufo-3","ki-jl-1","norway-2","poland-100","russia-white-list-1","vabb-shw"],"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 Control and Optimization","raw_type":"journal-article"},"volume":null,"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":null,"display_name":"U. G. Haussmann","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"U. G. Haussmann","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5087794190","display_name":"J. P. Lepeltier","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. P. Lepeltier","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9132,"has_fulltext":false,"cited_by_count":136,"citation_normalized_percentile":{"value":0.83030739,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"28","issue":"4","first_page":"851","last_page":"902"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.6689000129699707,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.6689000129699707,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.18619999289512634,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.06849999725818634,"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/optimal-control","display_name":"optimal control","score":0.8209999799728394},{"id":"https://openalex.org/keywords/stochastic-differential-equations","display_name":"stochastic differential equations","score":0.8220000267028809},{"id":"https://openalex.org/keywords/ito-equations","display_name":"It\u00f4 equations","score":0.7070000171661377},{"id":"https://openalex.org/keywords/existence-of-optimal-control","display_name":"existence of optimal control","score":0.8560000061988831},{"id":"https://openalex.org/keywords/coercivity-conditions","display_name":"coercivity conditions","score":0.9020000100135803},{"id":"https://openalex.org/keywords/convexity-conditions","display_name":"convexity conditions","score":0.8930000066757202},{"id":"https://openalex.org/keywords/direct-method","display_name":"direct method","score":0.6710000038146973},{"id":"https://openalex.org/keywords/soft-constraints","display_name":"soft constraints","score":0.7070000171661377},{"id":"https://openalex.org/keywords/hard-constraints","display_name":"hard constraints","score":0.9629999995231628},{"id":"https://openalex.org/keywords/synthesis-problem","display_name":"synthesis problem","score":0.9380000233650208}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9090337753295898},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.7128777503967285},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.6885759830474854},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.6610227227210999},{"id":"https://openalex.org/C70834904","wikidata":"https://www.wikidata.org/wiki/Q1054638","display_name":"Differential inclusion","level":2,"score":0.5493799448013306},{"id":"https://openalex.org/C48406656","wikidata":"https://www.wikidata.org/wiki/Q534112","display_name":"Martingale (probability theory)","level":2,"score":0.49834370613098145},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45685556530952454},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.4245189428329468},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.412596732378006},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3898216485977173},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.37107497453689575},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35181546211242676},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0328049","doi":"https://doi.org/10.1137/0328049","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0328049","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-a","jufo-3","ki-jl-1","norway-2","poland-100","russia-white-list-1","vabb-shw"],"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 Control and Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W119526149","https://openalex.org/W204533568","https://openalex.org/W265084489","https://openalex.org/W1513091520","https://openalex.org/W1979834002","https://openalex.org/W2011951499","https://openalex.org/W2075574287","https://openalex.org/W2094649962","https://openalex.org/W2126634394","https://openalex.org/W2149081875","https://openalex.org/W2156574545","https://openalex.org/W2156580702","https://openalex.org/W3140571750","https://openalex.org/W4245159036","https://openalex.org/W4253755470","https://openalex.org/W4302609762"],"related_works":["https://openalex.org/W2011951499","https://openalex.org/W2045766027","https://openalex.org/W2483893678","https://openalex.org/W2148859451","https://openalex.org/W2011060629","https://openalex.org/W2095521749","https://openalex.org/W2068098627","https://openalex.org/W2134184061","https://openalex.org/W2255041893","https://openalex.org/W4210382664"],"abstract_inverted_index":{"The":[0,99],"optimal":[1,57,79],"control":[2,37,80],"problem":[3,95],"where":[4],"the":[5,36,47,53,67,87,93],"state":[6],"is":[7,21,31,50,73,82,103],"governed":[8],"by":[9,52],"an":[10,17,78],"It\u00f4":[11],"stochastic":[12],"differential":[13,19],"equation":[14],"(possibly":[15],"just":[16],"ordinary":[18],"equation)":[20],"formulated":[22],"in":[23],"martingale":[24],"terms.":[25],"Under":[26],"a":[27,39,83,97],"coercivity":[28],"condition":[29],"(which":[30],"weaker":[32],"than":[33],"compactness":[34],"of":[35,69,86],"set),":[38],"convexity":[40],"condition,":[41],"and":[42,61,90],"mild":[43],"continuity":[44],"hypotheses":[45],"on":[46],"data,":[48],"it":[49,72],"shown":[51,74],"direct":[54],"method":[55],"that":[56,75,81],"controls":[58],"exist.":[59],"Hard":[60],"soft":[62,70],"constraints":[63,71],"are":[64],"allowed.":[65],"In":[66],"absence":[68],"there":[76],"exists":[77],"function":[84],"only":[85],"present":[88],"time":[89],"state,":[91],"i.e.,":[92],"synthesis":[94],"has":[96],"solution.":[98],"main":[100],"tool":[101],"here":[102],"Krylov\u2019s":[104],"Markovian":[105],"Selection":[106],"Theorem.":[107]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2025-10-10T00:00:00"}