{"id":"https://openalex.org/W2037850883","doi":"https://doi.org/10.1137/080734455","title":"Symmetry of Solutions to the Optimal Exit Time Control Problem","display_name":"Symmetry of Solutions to the Optimal Exit Time Control Problem","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2037850883","doi":"https://doi.org/10.1137/080734455","mag":"2037850883"},"language":"en","primary_location":{"id":"doi:10.1137/080734455","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080734455","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,"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"},"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/A5035753295","display_name":"Jianghai Hu","orcid":"https://orcid.org/0000-0002-4250-8852"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jianghai Hu","raw_affiliation_strings":["jianghai@purdue.edu#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"jianghai@purdue.edu#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100441734","display_name":"Wei Zhang","orcid":"https://orcid.org/0000-0003-0003-0341"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wei Zhang","raw_affiliation_strings":["weizhang@eecs.berkeley.edu#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"weizhang@eecs.berkeley.edu#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3962,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.58411011,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"48","issue":"8","first_page":"5488","last_page":"5509"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9952999949455261,"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"}},"topics":[{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9952999949455261,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9873999953269958,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9818000197410583,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8069918155670166},{"id":"https://openalex.org/keywords/isoperimetric-inequality","display_name":"Isoperimetric inequality","score":0.8022520542144775},{"id":"https://openalex.org/keywords/symmetrization","display_name":"Symmetrization","score":0.761239767074585},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.6789852380752563},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.6401181817054749},{"id":"https://openalex.org/keywords/ball","display_name":"Ball (mathematics)","score":0.5831555724143982},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5152950286865234},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4911324679851532},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.43238940834999084},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.4122586250305176},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.383655309677124},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15448671579360962},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15037000179290771},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.09204721450805664}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8069918155670166},{"id":"https://openalex.org/C140142295","wikidata":"https://www.wikidata.org/wiki/Q617417","display_name":"Isoperimetric inequality","level":2,"score":0.8022520542144775},{"id":"https://openalex.org/C64999384","wikidata":"https://www.wikidata.org/wiki/Q3507967","display_name":"Symmetrization","level":2,"score":0.761239767074585},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.6789852380752563},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6401181817054749},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.5831555724143982},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5152950286865234},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4911324679851532},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.43238940834999084},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.4122586250305176},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.383655309677124},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15448671579360962},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15037000179290771},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.09204721450805664},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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":2,"locations":[{"id":"doi:10.1137/080734455","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080734455","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,"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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.664.8442","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.664.8442","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://engineering.purdue.edu/%7Ejianghai/Publication/SICON2010_symmetry.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.46000000834465027}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W55674907","https://openalex.org/W1521776015","https://openalex.org/W1547997799","https://openalex.org/W1550621289","https://openalex.org/W1580445772","https://openalex.org/W1587799944","https://openalex.org/W1593038947","https://openalex.org/W1940627440","https://openalex.org/W1967753432","https://openalex.org/W1982357817","https://openalex.org/W2021204697","https://openalex.org/W2022977680","https://openalex.org/W2049374540","https://openalex.org/W2071428985","https://openalex.org/W2091603956","https://openalex.org/W2098916117","https://openalex.org/W2114277285","https://openalex.org/W2124497430","https://openalex.org/W2141436719","https://openalex.org/W2170316986","https://openalex.org/W2184067402","https://openalex.org/W2248038859","https://openalex.org/W2477983385","https://openalex.org/W2496229805","https://openalex.org/W2564087643","https://openalex.org/W2567832481","https://openalex.org/W3021722416","https://openalex.org/W3206777520"],"related_works":["https://openalex.org/W2027848045","https://openalex.org/W4386555441","https://openalex.org/W4323540055","https://openalex.org/W4291655786","https://openalex.org/W1603369162","https://openalex.org/W2066358007","https://openalex.org/W2024744103","https://openalex.org/W2028687365","https://openalex.org/W4361272590","https://openalex.org/W4300460696"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,72,94],"study":[4],"the":[5,8,20,32,43,47,59,76,82,105,108,114,127],"solutions":[6],"to":[7,18],"optimal":[9,83,117],"exit":[10,118],"time":[11,119],"control":[12,23,85],"problem.":[13],"Such":[14],"a":[15,26,35,40,80,102],"problem":[16,60,64],"tries":[17],"find":[19],"state":[21,33,44],"feedback":[22,84],"law":[24],"with":[25,65,101],"fixed":[27,103],"cost":[28],"that":[29,111],"can":[30],"keep":[31],"of":[34,42,126],"randomly":[36],"perturbed":[37],"system":[38],"inside":[39],"subset":[41],"space,":[45],"called":[46],"safe":[48,77,99],"set,":[49],"for":[50],"as":[51,53,61],"long":[52],"possible":[54],"on":[55],"average.":[56],"By":[57],"formulating":[58],"an":[62],"optimization":[63],"PDE":[66],"constraints":[67],"and":[68],"using":[69],"symmetrization":[70],"techniques,":[71],"show":[73,95],"that,":[74,96],"when":[75],"set":[78],"is":[79,107],"ball,":[81],"(if":[86],"it":[87,112],"exists)":[88],"must":[89],"be":[90],"radially":[91],"symmetric.":[92],"Furthermore,":[93],"among":[97],"all":[98],"sets":[100],"volume,":[104],"ball":[106],"best":[109],"in":[110],"yields":[113],"most":[115],"efficient":[116],"control.":[120],"The":[121],"proofs":[122],"make":[123],"essential":[124],"use":[125],"general":[128],"isoperimetric":[129],"inequality.":[130]},"counts_by_year":[],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}