{"id":"https://openalex.org/W2086575862","doi":"https://doi.org/10.1007/s10957-014-0628-1","title":"Second-Order Necessary Optimality Conditions for a Class of Optimal Control Problems Governed by Partial Differential Equations with Pure State Constraints","display_name":"Second-Order Necessary Optimality Conditions for a Class of Optimal Control Problems Governed by Partial Differential Equations with Pure State Constraints","publication_year":2014,"publication_date":"2014-07-30","ids":{"openalex":"https://openalex.org/W2086575862","doi":"https://doi.org/10.1007/s10957-014-0628-1","mag":"2086575862"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-014-0628-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-014-0628-1","pdf_url":null,"source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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":"Journal of Optimization Theory 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/A5033764668","display_name":"B. T. Kien","orcid":"https://orcid.org/0000-0001-8370-7009"},"institutions":[{"id":"https://openalex.org/I4210148301","display_name":"Institute of Mathematics","ror":"https://ror.org/04jr71r83","country_code":"VN","type":"facility","lineage":["https://openalex.org/I4210148301","https://openalex.org/I70349855"]},{"id":"https://openalex.org/I70349855","display_name":"Vietnam Academy of Science and Technology","ror":"https://ror.org/02wsd5p50","country_code":"VN","type":"government","lineage":["https://openalex.org/I70349855"]}],"countries":["VN"],"is_corresponding":false,"raw_author_name":"B. T. Kien","raw_affiliation_strings":["Department of Optimization and Control Theory, Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet road, Hanoi, Vietnam","Department of Optimization and Control Theory, Institute of Mathematics, Vietnam Academy of Science and Technology, Hanoi, Vietnam"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Optimization and Control Theory, Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet road, Hanoi, Vietnam","institution_ids":["https://openalex.org/I4210148301","https://openalex.org/I70349855"]},{"raw_affiliation_string":"Department of Optimization and Control Theory, Institute of Mathematics, Vietnam Academy of Science and Technology, Hanoi, Vietnam","institution_ids":["https://openalex.org/I4210148301","https://openalex.org/I70349855"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058708435","display_name":"Vu Huu Nhu","orcid":"https://orcid.org/0000-0003-4279-3937"},"institutions":[{"id":"https://openalex.org/I194744927","display_name":"National Institute of Education","ror":"https://ror.org/02fhgbp51","country_code":null,"type":"education","lineage":["https://openalex.org/I172675005","https://openalex.org/I194744927"]},{"id":"https://openalex.org/I4210148490","display_name":"The Vietnam National Institute of Educational Sciences","ror":"https://ror.org/044nmzj55","country_code":"VN","type":"education","lineage":["https://openalex.org/I4210148490"]}],"countries":["VN"],"is_corresponding":false,"raw_author_name":"V. H. Nhu","raw_affiliation_strings":["Faculty of Information Technology, National Institute of Education Management, 31 Phan Dinh Giot, Hanoi, Vietnam","Faculty of Information Technology, National Institute of Education Management, Hanoi, Vietnam"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Information Technology, National Institute of Education Management, 31 Phan Dinh Giot, Hanoi, Vietnam","institution_ids":["https://openalex.org/I4210148490"]},{"raw_affiliation_string":"Faculty of Information Technology, National Institute of Education Management, Hanoi, Vietnam","institution_ids":["https://openalex.org/I194744927"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073486661","display_name":"Arnd R\u00f6sch","orcid":"https://orcid.org/0009-0001-2163-7153"},"institutions":[{"id":"https://openalex.org/I62318514","display_name":"University of Duisburg-Essen","ror":"https://ror.org/04mz5ra38","country_code":"DE","type":"education","lineage":["https://openalex.org/I62318514"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"A. R\u00f6sch","raw_affiliation_strings":["Faculty of Mathematics, University of Duisburg-Essen, Thea-Leymann-Stra\u00dfe 9, 45127 , Essen, Germany","Faculty of Mathematics, University of Duisburg-Essen, Essen, Germany 45127#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, University of Duisburg-Essen, Thea-Leymann-Stra\u00dfe 9, 45127 , Essen, Germany","institution_ids":["https://openalex.org/I62318514"]},{"raw_affiliation_string":"Faculty of Mathematics, University of Duisburg-Essen, Essen, Germany 45127#TAB#","institution_ids":["https://openalex.org/I62318514"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5073486661"],"corresponding_institution_ids":["https://openalex.org/I62318514"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":1.2972,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.78915533,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"165","issue":"1","first_page":"30","last_page":"61"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9993000030517578,"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":0.9993000030517578,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9987999796867371,"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/optimal-control","display_name":"Optimal control","score":0.758826494216919},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7497462630271912},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6529254913330078},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.5725474953651428},{"id":"https://openalex.org/keywords/elliptic-partial-differential-equation","display_name":"Elliptic partial differential equation","score":0.5667898058891296},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4866264760494232},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.47755393385887146},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.46860966086387634},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.39048153162002563},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34410157799720764},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14675375819206238}],"concepts":[{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.758826494216919},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7497462630271912},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6529254913330078},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.5725474953651428},{"id":"https://openalex.org/C54067925","wikidata":"https://www.wikidata.org/wiki/Q3607962","display_name":"Elliptic partial differential equation","level":3,"score":0.5667898058891296},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4866264760494232},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.47755393385887146},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.46860966086387634},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39048153162002563},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34410157799720764},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14675375819206238},{"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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10957-014-0628-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-014-0628-1","pdf_url":null,"source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:joptap:v:165:y:2015:i:1:d:10.1007_s10957-014-0628-1","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10957-014-0628-1","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":[{"id":"https://openalex.org/F4320308269","display_name":"Alexander von Humboldt-Stiftung","ror":"https://ror.org/012kf4317"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":50,"referenced_works":["https://openalex.org/W85849956","https://openalex.org/W121328656","https://openalex.org/W345014192","https://openalex.org/W1493492050","https://openalex.org/W1516681311","https://openalex.org/W1537639429","https://openalex.org/W1545761024","https://openalex.org/W1551360398","https://openalex.org/W1577246751","https://openalex.org/W1601741115","https://openalex.org/W1604436244","https://openalex.org/W1973254632","https://openalex.org/W1978282183","https://openalex.org/W1979335926","https://openalex.org/W1983871704","https://openalex.org/W1986555670","https://openalex.org/W1990396147","https://openalex.org/W2012663305","https://openalex.org/W2018508199","https://openalex.org/W2020071646","https://openalex.org/W2024828886","https://openalex.org/W2039537159","https://openalex.org/W2039944282","https://openalex.org/W2040772515","https://openalex.org/W2041037772","https://openalex.org/W2042725568","https://openalex.org/W2042810077","https://openalex.org/W2043841940","https://openalex.org/W2045940260","https://openalex.org/W2048164789","https://openalex.org/W2071452176","https://openalex.org/W2076582418","https://openalex.org/W2078760286","https://openalex.org/W2080674898","https://openalex.org/W2085831953","https://openalex.org/W2089828300","https://openalex.org/W2094233096","https://openalex.org/W2103284380","https://openalex.org/W2110305719","https://openalex.org/W2122106895","https://openalex.org/W2149726831","https://openalex.org/W2153562582","https://openalex.org/W2164411545","https://openalex.org/W2282314551","https://openalex.org/W2477040106","https://openalex.org/W3148800415","https://openalex.org/W3157341860","https://openalex.org/W4250028192","https://openalex.org/W4285719527","https://openalex.org/W4294678829"],"related_works":["https://openalex.org/W2348093013","https://openalex.org/W2682190590","https://openalex.org/W2358589552","https://openalex.org/W4366197524","https://openalex.org/W935007796","https://openalex.org/W2027741235","https://openalex.org/W2066764747","https://openalex.org/W2079390358","https://openalex.org/W1974193032","https://openalex.org/W1994929327"],"abstract_inverted_index":null,"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
