{"id":"https://openalex.org/W2092622790","doi":"https://doi.org/10.1137/100801731","title":"Error Estimates of Stochastic Optimal Neumann Boundary Control Problems","display_name":"Error Estimates of Stochastic Optimal Neumann Boundary Control Problems","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2092622790","doi":"https://doi.org/10.1137/100801731","mag":"2092622790"},"language":"en","primary_location":{"id":"doi:10.1137/100801731","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100801731","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","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/A5076283476","display_name":"Max Gunzburger","orcid":"https://orcid.org/0000-0003-0921-9079"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Max D. Gunzburger","raw_affiliation_strings":["gunzburg@fsu.edu#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"gunzburg@fsu.edu#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091000193","display_name":"Hyung\u2010Chun Lee","orcid":"https://orcid.org/0000-0002-3168-3858"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hyung-Chun Lee","raw_affiliation_strings":["hclee@ajou.ac.kr#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"hclee@ajou.ac.kr#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063818739","display_name":"Jangwoon Lee","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jangwoon Lee","raw_affiliation_strings":["[email\u00a0protected]#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"[email\u00a0protected]#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":3.4925,"has_fulltext":false,"cited_by_count":60,"citation_normalized_percentile":{"value":0.93513803,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"49","issue":"4","first_page":"1532","last_page":"1552"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9976999759674072,"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/T10067","display_name":"Stochastic processes and financial applications","score":0.9969000220298767,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8681721091270447},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.7780219316482544},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.6249759793281555},{"id":"https://openalex.org/keywords/neumann-boundary-condition","display_name":"Neumann boundary condition","score":0.6169214248657227},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5538594722747803},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5370034575462341},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5179092288017273},{"id":"https://openalex.org/keywords/stochastic-control","display_name":"Stochastic control","score":0.4567990303039551},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3504871726036072},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33997270464897156}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8681721091270447},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.7780219316482544},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.6249759793281555},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.6169214248657227},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5538594722747803},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5370034575462341},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5179092288017273},{"id":"https://openalex.org/C170131372","wikidata":"https://www.wikidata.org/wiki/Q7617811","display_name":"Stochastic control","level":3,"score":0.4567990303039551},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3504871726036072},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33997270464897156}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/100801731","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100801731","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W89839489","https://openalex.org/W1502252680","https://openalex.org/W1538934584","https://openalex.org/W1674659126","https://openalex.org/W1968340635","https://openalex.org/W1971773540","https://openalex.org/W1983156129","https://openalex.org/W2003315290","https://openalex.org/W2003629765","https://openalex.org/W2027201301","https://openalex.org/W2033721384","https://openalex.org/W2039146619","https://openalex.org/W2040768145","https://openalex.org/W2044390636","https://openalex.org/W2055460625","https://openalex.org/W2058362163","https://openalex.org/W2068691144","https://openalex.org/W2080348404","https://openalex.org/W2080928812","https://openalex.org/W2135329423","https://openalex.org/W2160786691","https://openalex.org/W2185141813","https://openalex.org/W2884403958","https://openalex.org/W3021722416","https://openalex.org/W4250533253"],"related_works":["https://openalex.org/W2943897807","https://openalex.org/W3120484221","https://openalex.org/W4366198066","https://openalex.org/W3047748938","https://openalex.org/W2358522863","https://openalex.org/W278441094","https://openalex.org/W4386034604","https://openalex.org/W3099285423","https://openalex.org/W2336173978","https://openalex.org/W2060950178"],"abstract_inverted_index":{"We":[0],"study":[1],"mathematically":[2],"and":[3,29,47,63,82,94],"computationally":[4],"optimal":[5,45],"control":[6,18,31],"problems":[7],"for":[8],"stochastic":[9],"partial":[10],"differential":[11],"equations":[12],"with":[13,89],"Neumann":[14],"boundary":[15],"conditions.":[16],"The":[17],"objective":[19],"is":[20,32],"to":[21,91],"minimize":[22],"the":[23,30,34,41,54,65,74,79,87],"expectation":[24],"of":[25,33,43,48,59,69,78],"a":[26,49],"cost":[27],"functional,":[28],"deterministic,":[35],"boundary-value":[36],"type.":[37],"Mathematically,":[38],"we":[39,52,72],"prove":[40],"existence":[42],"an":[44],"solution":[46,77],"Lagrange":[50],"multiplier;":[51],"represent":[53],"input":[55],"data":[56],"in":[57],"terms":[58],"their":[60],"Karhunen\u2013Lo\u00e8ve":[61],"expansions":[62],"deduce":[64],"deterministic":[66],"optimality":[67,80],"system":[68,81],"equations.":[70],"Computationally,":[71],"approximate":[73],"finite":[75],"element":[76],"estimate":[83],"its":[84],"error":[85],"through":[86],"discretizations":[88],"respect":[90],"both":[92],"spatial":[93],"random":[95],"parameter":[96],"spaces.":[97]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
