{"id":"https://openalex.org/W92780816","doi":"https://doi.org/10.1007/978-3-642-36062-6_1","title":"Second Order Conditions for L 2 Local Optimality in PDE Control","display_name":"Second Order Conditions for L 2 Local Optimality in PDE Control","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W92780816","doi":"https://doi.org/10.1007/978-3-642-36062-6_1","mag":"92780816"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-36062-6_1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-642-36062-6_1","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-642-36062-6_1.pdf","source":{"id":"https://openalex.org/S4210175514","display_name":"IFIP International Federation for Information Processing/IFIP","issn_l":"1571-5736","issn":["1571-5736","1861-2288"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IFIP Advances in Information and Communication Technology","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/978-3-642-36062-6_1.pdf","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067757319","display_name":"Eduardo Casas","orcid":"https://orcid.org/0000-0002-8364-9416"},"institutions":[{"id":"https://openalex.org/I13134134","display_name":"Universidad de Cantabria","ror":"https://ror.org/046ffzj20","country_code":"ES","type":"education","lineage":["https://openalex.org/I13134134"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Eduardo Casas","raw_affiliation_strings":["Departmento de Matem\u00e1tica Aplicada y Ciencias de la Computaci\u00f3n, E.T.S.I. Industriales y de Telecomunicaci\u00f3n, Universidad de Cantabria, Av. Los Castros s/n, 39005, Santander, Spain"],"affiliations":[{"raw_affiliation_string":"Departmento de Matem\u00e1tica Aplicada y Ciencias de la Computaci\u00f3n, E.T.S.I. Industriales y de Telecomunicaci\u00f3n, Universidad de Cantabria, Av. Los Castros s/n, 39005, Santander, Spain","institution_ids":["https://openalex.org/I13134134"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5067757319"],"corresponding_institution_ids":["https://openalex.org/I13134134"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01811806,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"12"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9980999827384949,"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"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9980999827384949,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9933000206947327,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9901999831199646,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/mathematics","display_name":"Mathematics","score":0.669276773929596},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.6155993342399597},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.606610894203186},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.541368842124939},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5380129218101501},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5208204984664917},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3535764217376709},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.11652621626853943},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.1139812171459198}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.669276773929596},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.6155993342399597},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.606610894203186},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.541368842124939},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5380129218101501},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5208204984664917},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3535764217376709},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.11652621626853943},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.1139812171459198},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/978-3-642-36062-6_1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-642-36062-6_1","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-642-36062-6_1.pdf","source":{"id":"https://openalex.org/S4210175514","display_name":"IFIP International Federation for Information Processing/IFIP","issn_l":"1571-5736","issn":["1571-5736","1861-2288"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IFIP Advances in Information and Communication Technology","raw_type":"book-chapter"},{"id":"pmh:oai:HAL:hal-01347511v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-01347511","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"25th System Modeling and Optimization (CSMO), Sep 2011, Berlin, Germany. pp.1-12, ⟨10.1007/978-3-642-36062-6_1⟩","raw_type":"Conference papers"}],"best_oa_location":{"id":"doi:10.1007/978-3-642-36062-6_1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-642-36062-6_1","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-642-36062-6_1.pdf","source":{"id":"https://openalex.org/S4210175514","display_name":"IFIP International Federation for Information Processing/IFIP","issn_l":"1571-5736","issn":["1571-5736","1861-2288"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IFIP Advances in Information and Communication Technology","raw_type":"book-chapter"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W92780816.pdf","grobid_xml":"https://content.openalex.org/works/W92780816.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W983098934","https://openalex.org/W1601741115","https://openalex.org/W1866311589","https://openalex.org/W1996088437","https://openalex.org/W2040772515","https://openalex.org/W2048164789","https://openalex.org/W2050434647","https://openalex.org/W2060073982","https://openalex.org/W2061162530","https://openalex.org/W2067024715","https://openalex.org/W2105253623","https://openalex.org/W2112867735","https://openalex.org/W4292360407"],"related_works":["https://openalex.org/W1987895267","https://openalex.org/W2350519135","https://openalex.org/W1892002403","https://openalex.org/W2390619334","https://openalex.org/W4309005041","https://openalex.org/W2962746246","https://openalex.org/W2052190160","https://openalex.org/W1989531755","https://openalex.org/W1967384683","https://openalex.org/W2375327612"],"abstract_inverted_index":{"In":[0,103],"the":[1,15,25,35,44,65,80,84,93,100,106,131,138],"second":[2,26,67,81,124],"order":[3,27,68,125],"analysis":[4],"of":[5,22,56,83,111,117,137],"infinite":[6],"dimension":[7],"optimization":[8],"problems,":[9],"we":[10,40,73,119],"have":[11,41],"to":[12,130],"deal":[13],"with":[14],"so-called":[16],"two-norm":[17],"discrepancy.":[18],"As":[19],"a":[20],"consequence":[21],"this":[23,71,104,115],"fact,":[24],"optimality":[28,33,48,126,136],"conditions":[29,127],"usually":[30,110],"imply":[31],"local":[32,47,135],"in":[34,99],"L":[36,45,133],"\u221e":[37],"sense.":[38],"However,":[39],"observed":[42],"that":[43,128],"2":[46,134],"can":[49,61],"be":[50,62],"proved":[51],"for":[52],"many":[53],"control":[54,94,108],"problems":[55,118],"partial":[57],"differential":[58],"equations.":[59],"This":[60],"deduced":[63],"from":[64],"standard":[66],"conditions.":[69],"To":[70],"end,":[72],"make":[74],"some":[75,122],"quite":[76],"realistic":[77],"assumptions":[78,88],"on":[79],"derivative":[82],"cost":[85,101],"functional.":[86,102],"These":[87],"do":[89],"not":[90,96],"hold":[91],"if":[92],"does":[95],"appear":[97],"explicitly":[98],"case,":[105],"optimal":[107],"is":[109],"bang-bang":[112,139],"type.":[113],"For":[114],"type":[116],"also":[120],"formulate":[121],"new":[123],"lead":[129],"strict":[132],"controls.":[140]},"counts_by_year":[],"updated_date":"2026-03-18T14:38:29.013473","created_date":"2025-10-10T00:00:00"}