{"id":"https://openalex.org/W2042844238","doi":"https://doi.org/10.1007/s00211-007-0095-9","title":"Second-order nonsmooth optimization for H \u221e synthesis","display_name":"Second-order nonsmooth optimization for H \u221e synthesis","publication_year":2007,"publication_date":"2007-06-27","ids":{"openalex":"https://openalex.org/W2042844238","doi":"https://doi.org/10.1007/s00211-007-0095-9","mag":"2042844238"},"language":"de","primary_location":{"id":"doi:10.1007/s00211-007-0095-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-007-0095-9","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":"Numerische Mathematik","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/A5062242577","display_name":"Vincent Bompart","orcid":null},"institutions":[{"id":"https://openalex.org/I134560555","display_name":"Universit\u00e9 Toulouse III - Paul Sabatier","ror":"https://ror.org/02v6kpv12","country_code":"FR","type":"education","lineage":["https://openalex.org/I134560555","https://openalex.org/I4405258862"]},{"id":"https://openalex.org/I2799535048","display_name":"Centre National d'\u00c9tudes Spatiales","ror":"https://ror.org/04h1h0y33","country_code":"FR","type":"government","lineage":["https://openalex.org/I2799535048"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Vincent Bompart","raw_affiliation_strings":["Institut de Math\u00e9matiques, Universit\u00e9 Paul Sabatier, 118 route de Narbonne, 31062, Toulouse, France","ONERA-CERT, 2 av. Edouard Belin, 31055, Toulouse, France"],"affiliations":[{"raw_affiliation_string":"Institut de Math\u00e9matiques, Universit\u00e9 Paul Sabatier, 118 route de Narbonne, 31062, Toulouse, France","institution_ids":["https://openalex.org/I134560555"]},{"raw_affiliation_string":"ONERA-CERT, 2 av. Edouard Belin, 31055, Toulouse, France","institution_ids":["https://openalex.org/I2799535048"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030567369","display_name":"Dominikus Noll","orcid":"https://orcid.org/0000-0002-8638-2438"},"institutions":[{"id":"https://openalex.org/I134560555","display_name":"Universit\u00e9 Toulouse III - Paul Sabatier","ror":"https://ror.org/02v6kpv12","country_code":"FR","type":"education","lineage":["https://openalex.org/I134560555","https://openalex.org/I4405258862"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Dominikus Noll","raw_affiliation_strings":["Institut de Math\u00e9matiques, Universit\u00e9 Paul Sabatier, 118 route de Narbonne, 31062, Toulouse, France"],"affiliations":[{"raw_affiliation_string":"Institut de Math\u00e9matiques, Universit\u00e9 Paul Sabatier, 118 route de Narbonne, 31062, Toulouse, France","institution_ids":["https://openalex.org/I134560555"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033569810","display_name":"Pierre Apkarian","orcid":"https://orcid.org/0000-0003-1122-9153"},"institutions":[{"id":"https://openalex.org/I2799535048","display_name":"Centre National d'\u00c9tudes Spatiales","ror":"https://ror.org/04h1h0y33","country_code":"FR","type":"government","lineage":["https://openalex.org/I2799535048"]},{"id":"https://openalex.org/I134560555","display_name":"Universit\u00e9 Toulouse III - Paul Sabatier","ror":"https://ror.org/02v6kpv12","country_code":"FR","type":"education","lineage":["https://openalex.org/I134560555","https://openalex.org/I4405258862"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Pierre Apkarian","raw_affiliation_strings":["Institut de Math\u00e9matiques, Universit\u00e9 Paul Sabatier, 118 route de Narbonne, 31062, Toulouse, France","ONERA-CERT, 2 av. Edouard Belin, 31055, Toulouse, France"],"affiliations":[{"raw_affiliation_string":"Institut de Math\u00e9matiques, Universit\u00e9 Paul Sabatier, 118 route de Narbonne, 31062, Toulouse, France","institution_ids":["https://openalex.org/I134560555"]},{"raw_affiliation_string":"ONERA-CERT, 2 av. Edouard Belin, 31055, Toulouse, France","institution_ids":["https://openalex.org/I2799535048"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5062242577"],"corresponding_institution_ids":["https://openalex.org/I134560555","https://openalex.org/I2799535048"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":9.6717,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.97742852,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"107","issue":"3","first_page":"433","last_page":"454"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.9987999796867371,"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"}},{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7577975392341614},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5515949726104736},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5485174059867859},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5329756736755371},{"id":"https://openalex.org/keywords/algebraic-riccati-equation","display_name":"Algebraic Riccati equation","score":0.5182385444641113},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.500420093536377},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4988431930541992},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.4559841454029083},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.45210760831832886},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.44310829043388367},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4353882670402527},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.43184882402420044},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.41840076446533203},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3779282569885254},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.3774855434894562},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.2122105360031128},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20199179649353027},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08472654223442078}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7577975392341614},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5515949726104736},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5485174059867859},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5329756736755371},{"id":"https://openalex.org/C13847129","wikidata":"https://www.wikidata.org/wiki/Q4723989","display_name":"Algebraic Riccati equation","level":4,"score":0.5182385444641113},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.500420093536377},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4988431930541992},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4559841454029083},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.45210760831832886},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.44310829043388367},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4353882670402527},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.43184882402420044},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.41840076446533203},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3779282569885254},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.3774855434894562},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2122105360031128},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20199179649353027},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08472654223442078},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00211-007-0095-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-007-0095-9","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":"Numerische Mathematik","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-00632196v1","is_oa":false,"landing_page_url":"https://hal.archives-ouvertes.fr/hal-00632196","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 0029-599X","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:HAL:hal-01868767v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01868767","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Numerische Mathematik, 2007, 107 (3), pp.433 - 454. ⟨10.1007/s00211-007-0095-9⟩","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W26939431","https://openalex.org/W147998453","https://openalex.org/W1497976349","https://openalex.org/W1558831267","https://openalex.org/W1575147392","https://openalex.org/W1967969202","https://openalex.org/W1978606791","https://openalex.org/W1981188096","https://openalex.org/W1993433915","https://openalex.org/W2007179152","https://openalex.org/W2012604200","https://openalex.org/W2025051282","https://openalex.org/W2032206573","https://openalex.org/W2034235667","https://openalex.org/W2038648531","https://openalex.org/W2039606278","https://openalex.org/W2054155441","https://openalex.org/W2055506505","https://openalex.org/W2075887074","https://openalex.org/W2079629485","https://openalex.org/W2086594463","https://openalex.org/W2094507464","https://openalex.org/W2101926728","https://openalex.org/W2111946256","https://openalex.org/W2114792685","https://openalex.org/W2123556725","https://openalex.org/W2130515279","https://openalex.org/W2135229502","https://openalex.org/W2144787788","https://openalex.org/W2145546299","https://openalex.org/W2148589597","https://openalex.org/W2161496432","https://openalex.org/W2178909929","https://openalex.org/W2563720504","https://openalex.org/W2724565893","https://openalex.org/W2798909945","https://openalex.org/W3029645440","https://openalex.org/W3210839039","https://openalex.org/W4293775970","https://openalex.org/W4300657400","https://openalex.org/W6634336730","https://openalex.org/W6750968397"],"related_works":["https://openalex.org/W2005019312","https://openalex.org/W2105459831","https://openalex.org/W1546579375","https://openalex.org/W2127238600","https://openalex.org/W2096105566","https://openalex.org/W1563296412","https://openalex.org/W2114791549","https://openalex.org/W2097622270","https://openalex.org/W2126205885","https://openalex.org/W2093841944"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}