{"id":"https://openalex.org/W3011357030","doi":"https://doi.org/10.1109/cdc40024.2019.9030176","title":"On second order necessary conditions in infinite dimensional optimal control with state constraints","display_name":"On second order necessary conditions in infinite dimensional optimal control with state constraints","publication_year":2019,"publication_date":"2019-12-01","ids":{"openalex":"https://openalex.org/W3011357030","doi":"https://doi.org/10.1109/cdc40024.2019.9030176","mag":"3011357030"},"language":"en","primary_location":{"id":"doi:10.1109/cdc40024.2019.9030176","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc40024.2019.9030176","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE 58th Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-02343395","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034818712","display_name":"H\u00e9l\u00e8ne Frankowska","orcid":"https://orcid.org/0000-0001-6237-4137"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I3017942884","display_name":"Institut de Math\u00e9matiques de Jussieu-Paris Rive Gauche","ror":"https://ror.org/03fk87k11","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I3017942884","https://openalex.org/I39804081","https://openalex.org/I4210141950"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"H. Frankowska","raw_affiliation_strings":["CNRS, Institut de Math\u00e9matiques de Jussieu-Paris Rive gauche, Sorbonne Universit\u00e9, Paris, France","IMJ-PRG (UMR_7586) - Institut de Math\u00e9matiques de Jussieu - Paris Rive Gauche (UPMC - 4 place Jussieu, Case 247 - 75252 Paris Cedex 5\r\nUP7D - Campus des Grands Moulins - B\u00e2timent Sophie Germain, Case 7012- 75205 PARIS Cedex 13 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CNRS, Institut de Math\u00e9matiques de Jussieu-Paris Rive gauche, Sorbonne Universit\u00e9, Paris, France","institution_ids":["https://openalex.org/I3017942884","https://openalex.org/I39804081","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"IMJ-PRG (UMR_7586) - Institut de Math\u00e9matiques de Jussieu - Paris Rive Gauche (UPMC - 4 place Jussieu, Case 247 - 75252 Paris Cedex 5\r\nUP7D - Campus des Grands Moulins - B\u00e2timent Sophie Germain, Case 7012- 75205 PARIS Cedex 13 - France)","institution_ids":["https://openalex.org/I39804081","https://openalex.org/I3017942884"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057087392","display_name":"Elsa M. Marchini","orcid":"https://orcid.org/0000-0003-3555-5105"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"E. M. Marchini","raw_affiliation_strings":["Dipartimento di Matematica, Politecnico di Milano, Milano, Italy","POLIMI - Politecnico di Milano [Milan] (Piazza Leonardo da Vinci, 32 20133 Milano - Italy)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Politecnico di Milano, Milano, Italy","institution_ids":["https://openalex.org/I93860229"]},{"raw_affiliation_string":"POLIMI - Politecnico di Milano [Milan] (Piazza Leonardo da Vinci, 32 20133 Milano - Italy)","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061876866","display_name":"Marco Mazzola","orcid":"https://orcid.org/0000-0001-6445-0279"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I3017942884","display_name":"Institut de Math\u00e9matiques de Jussieu-Paris Rive Gauche","ror":"https://ror.org/03fk87k11","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I3017942884","https://openalex.org/I39804081","https://openalex.org/I4210141950"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"M. Mazzola","raw_affiliation_strings":["Institut de Math\u00e9matiques de Jussieu-Paris Rive gauche, CNRS, Sorbonne Universit\u00e9, Paris, France","IMJ-PRG (UMR_7586) - Institut de Math\u00e9matiques de Jussieu - Paris Rive Gauche (UPMC - 4 place Jussieu, Case 247 - 75252 Paris Cedex 5\r\nUP7D - Campus des Grands Moulins - B\u00e2timent Sophie Germain, Case 7012- 75205 PARIS Cedex 13 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut de Math\u00e9matiques de Jussieu-Paris Rive gauche, CNRS, Sorbonne Universit\u00e9, Paris, France","institution_ids":["https://openalex.org/I3017942884","https://openalex.org/I39804081","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"IMJ-PRG (UMR_7586) - Institut de Math\u00e9matiques de Jussieu - Paris Rive Gauche (UPMC - 4 place Jussieu, Case 247 - 75252 Paris Cedex 5\r\nUP7D - Campus des Grands Moulins - B\u00e2timent Sophie Germain, Case 7012- 75205 PARIS Cedex 13 - France)","institution_ids":["https://openalex.org/I39804081","https://openalex.org/I3017942884"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1926,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.58341916,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":93},"biblio":{"volume":null,"issue":null,"first_page":"2416","last_page":"2421"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998000264167786,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9962000250816345,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9951000213623047,"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/optimal-control","display_name":"Optimal control","score":0.6428514719009399},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5861430168151855},{"id":"https://openalex.org/keywords/variational-analysis","display_name":"Variational analysis","score":0.5640060901641846},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.562720537185669},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.537259042263031},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.4855160713195801},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4783165752887726},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4780229330062866},{"id":"https://openalex.org/keywords/novelty","display_name":"Novelty","score":0.4218425452709198},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.4190235435962677},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4165147840976715},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3708152770996094},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3624304533004761},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.10761070251464844}],"concepts":[{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.6428514719009399},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5861430168151855},{"id":"https://openalex.org/C523394659","wikidata":"https://www.wikidata.org/wiki/Q17086892","display_name":"Variational analysis","level":2,"score":0.5640060901641846},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.562720537185669},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.537259042263031},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.4855160713195801},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4783165752887726},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4780229330062866},{"id":"https://openalex.org/C2778738651","wikidata":"https://www.wikidata.org/wiki/Q16546687","display_name":"Novelty","level":2,"score":0.4218425452709198},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.4190235435962677},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4165147840976715},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3708152770996094},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3624304533004761},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.10761070251464844},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"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/C27206212","wikidata":"https://www.wikidata.org/wiki/Q34178","display_name":"Theology","level":1,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","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/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/cdc40024.2019.9030176","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc40024.2019.9030176","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE 58th Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},{"id":"pmh:oai:HAL:hal-02343395v1","is_oa":true,"landing_page_url":"https://hal.science/hal-02343395","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"58th IEEE Conference on Decision and Control, Dec 2019, Nice, France. pp.2416-2421, ⟨10.1109/CDC40024.2019.9030176⟩","raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"pmh:oai:re.public.polimi.it:11311/1102875","is_oa":false,"landing_page_url":"http://hdl.handle.net/11311/1102875","pdf_url":null,"source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-02343395v1","is_oa":true,"landing_page_url":"https://hal.science/hal-02343395","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"58th IEEE Conference on Decision and Control, Dec 2019, Nice, France. pp.2416-2421, ⟨10.1109/CDC40024.2019.9030176⟩","raw_type":"info:eu-repo/semantics/conferenceObject"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1527296550","https://openalex.org/W1528796636","https://openalex.org/W1594759473","https://openalex.org/W1601741115","https://openalex.org/W1974139228","https://openalex.org/W1983766238","https://openalex.org/W1991309447","https://openalex.org/W2029123910","https://openalex.org/W2033992723","https://openalex.org/W2043446027","https://openalex.org/W2046745855","https://openalex.org/W2085831953","https://openalex.org/W2112867735","https://openalex.org/W2270276724","https://openalex.org/W2283798739","https://openalex.org/W2525969799","https://openalex.org/W2770072546","https://openalex.org/W2791004733","https://openalex.org/W2810166019","https://openalex.org/W3021828133"],"related_works":["https://openalex.org/W2381242807","https://openalex.org/W3126131230","https://openalex.org/W2347541121","https://openalex.org/W2080951048","https://openalex.org/W4288804799","https://openalex.org/W3032237421","https://openalex.org/W2390346111","https://openalex.org/W3153752017","https://openalex.org/W2135400743","https://openalex.org/W2895393822"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,22,62,76],"devoted":[3],"to":[4,57,63,129],"second":[5,90,108],"order":[6,39,91,109],"necessary":[7,59,95],"optimality":[8,60,96],"conditions":[9,61,97],"for":[10,41],"control":[11,42,66,85],"problems":[12,43],"in":[13,36,50,99,116],"infinite":[14],"dimensions.":[15],"The":[16,53,94],"main":[17],"novelty":[18],"of":[19,25,82,102,119,121],"our":[20],"work":[21],"the":[23,37,51,65,80,83,100,117],"presence":[24],"pure":[26],"state":[27],"constraints":[28],"together":[29],"with":[30],"end":[31],"point":[32],"constraints,":[33],"quite":[34],"useful":[35],"applications.Second":[38],"analysis":[40],"involving":[44],"PDEs":[45],"has":[46],"been":[47],"extensively":[48],"discussed":[49],"literature.":[52],"most":[54],"usual":[55],"approach":[56,75],"derive":[58],"rewrite":[64],"problem":[67,86],"as":[68],"an":[69],"abstract":[70],"mathematical":[71],"programming":[72],"one.":[73],"Our":[74],"different,":[77],"we":[78],"avoid":[79],"reformulation":[81],"optimal":[84],"and":[87,106],"use":[88],"instead":[89],"variational":[92,110],"analysis.":[93],"are":[98,113],"form":[101,118],"a":[103,107],"maximum":[104],"principle":[105],"inequality.":[111],"They":[112],"first":[114],"obtained":[115],"nonintersection":[120],"convex":[122],"sets.":[123],"A":[124],"suitable":[125],"separation":[126],"theorem":[127],"allows":[128],"deduce":[130],"their":[131],"dual":[132],"characterization.":[133]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}