{"id":"https://openalex.org/W2037405845","doi":"https://doi.org/10.1109/acc.2000.879261","title":"An augmented Lagrangian method for a class of LMI-constrained problems in robust control theory","display_name":"An augmented Lagrangian method for a class of LMI-constrained problems in robust control theory","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2037405845","doi":"https://doi.org/10.1109/acc.2000.879261","mag":"2037405845"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2000.879261","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2000.879261","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334)","raw_type":"proceedings-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/A5016816379","display_name":"B. Fares","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"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"B. Fares","raw_affiliation_strings":["Applied Mathematics Department, UPS-MIP, Toulouse, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Applied Mathematics Department, UPS-MIP, Toulouse, France","institution_ids":["https://openalex.org/I134560555"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033569810","display_name":"Pierre Apkarian","orcid":"https://orcid.org/0000-0003-1122-9153"},"institutions":[{"id":"https://openalex.org/I2801658355","display_name":"Office National d'\u00c9tudes et de Recherches A\u00e9rospatiales","ror":"https://ror.org/005y2ap84","country_code":"FR","type":"facility","lineage":["https://openalex.org/I2801658355"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"P. Apkarian","raw_affiliation_strings":["Control Systems and Flight Mechanics Department, ONERA/CERT, Toulouse, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Control Systems and Flight Mechanics Department, ONERA/CERT, Toulouse, France","institution_ids":["https://openalex.org/I2801658355"]}]},{"author_position":"last","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"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"D. Noll","raw_affiliation_strings":["Applied Mathematics Department, UPS-MIP, Toulouse, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Applied Mathematics Department, UPS-MIP, Toulouse, France","institution_ids":["https://openalex.org/I134560555"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.9867,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.94105163,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"3702","last_page":"3706 vol.5"},"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":0.9998000264167786,"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":0.9998000264167786,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9966999888420105,"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/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9937000274658203,"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/augmented-lagrangian-method","display_name":"Augmented Lagrangian method","score":0.8653005361557007},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6147364377975464},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6074696779251099},{"id":"https://openalex.org/keywords/sequential-quadratic-programming","display_name":"Sequential quadratic programming","score":0.5824042558670044},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.5693862438201904},{"id":"https://openalex.org/keywords/robust-control","display_name":"Robust control","score":0.44924965500831604},{"id":"https://openalex.org/keywords/line-search","display_name":"Line search","score":0.43580421805381775},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4336612820625305},{"id":"https://openalex.org/keywords/linear-matrix-inequality","display_name":"Linear matrix inequality","score":0.42108866572380066},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.4125105142593384},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4122149348258972},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.41150158643722534},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.32770130038261414},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2873842716217041}],"concepts":[{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.8653005361557007},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6147364377975464},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6074696779251099},{"id":"https://openalex.org/C198927703","wikidata":"https://www.wikidata.org/wiki/Q4373881","display_name":"Sequential quadratic programming","level":3,"score":0.5824042558670044},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.5693862438201904},{"id":"https://openalex.org/C31531917","wikidata":"https://www.wikidata.org/wiki/Q915157","display_name":"Robust control","level":3,"score":0.44924965500831604},{"id":"https://openalex.org/C85522705","wikidata":"https://www.wikidata.org/wiki/Q3278015","display_name":"Line search","level":3,"score":0.43580421805381775},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4336612820625305},{"id":"https://openalex.org/C201829737","wikidata":"https://www.wikidata.org/wiki/Q2022760","display_name":"Linear matrix inequality","level":2,"score":0.42108866572380066},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.4125105142593384},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4122149348258972},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.41150158643722534},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.32770130038261414},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2873842716217041},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/acc.2000.879261","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2000.879261","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334)","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.26.9061","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.26.9061","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://mip.ups-tlse.fr/publi/rapp99/99.40.ps.gz","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1669104078","https://openalex.org/W2039867272","https://openalex.org/W2077658674","https://openalex.org/W2124426742","https://openalex.org/W2143973155","https://openalex.org/W2144449623","https://openalex.org/W2171096559","https://openalex.org/W2563720504","https://openalex.org/W4212997115","https://openalex.org/W6681401255","https://openalex.org/W6684979664"],"related_works":["https://openalex.org/W2015060724","https://openalex.org/W2058578573","https://openalex.org/W2012871340","https://openalex.org/W3046535663","https://openalex.org/W3035320230","https://openalex.org/W4287694146","https://openalex.org/W3207854495","https://openalex.org/W4317581747","https://openalex.org/W2915353907","https://openalex.org/W2267953278"],"abstract_inverted_index":{"This":[0,112],"paper":[1],"present":[2],"a":[3,8,29,64,68,119],"new":[4],"approach":[5,99],"to":[6,33,45,79,149],"solve":[7,49],"class":[9],"of":[10,28,55,97,169],"nonconvex":[11,42,73],"LMI-constrained":[12,104],"problem":[13],"in":[14,39,89,132,155],"robust":[15,156],"control":[16],"theory.":[17],"The":[18,60,75,135],"problems":[19,51,160],"we":[20],"consider":[21],"may":[22,114],"be":[23,116],"recast":[24],"as":[25,118],"the":[26,56,72,90,127,150,165],"minimization":[27],"linear":[30,34],"objective":[31],"subject":[32],"matrix":[35],"inequality":[36],"(LMI)":[37],"constraints":[38,43],"tandem":[40],"with":[41,140],"related":[44],"rank":[46],"conditions.":[47],"We":[48,145],"these":[50],"using":[52],"an":[53],"extension":[54],"augmented":[57],"Lagrangian":[58,61],"technique.":[59],"function":[62],"combines":[63],"multiplier":[65],"term":[66,70],"and":[67,86,93,163,167],"penalty":[69],"governing":[71],"constraints.":[74],"LMI":[76],"constraints,":[77],"due":[78],"their":[80],"special":[81],"structure,":[82],"are":[83,161],"handled":[84],"explicitly":[85],"not":[87],"included":[88],"Lagrangian.":[91],"Global":[92],"fast":[94],"local":[95],"convergence":[96],"our":[98,170],"is":[100,137],"then":[101],"obtained":[102],"by":[103,126],"Newton":[105],"type":[106],"method":[107,136],"including":[108],"line":[109],"search":[110],"strategy.":[111],"procedure":[113],"therefore":[115],"regarded":[117],"sequential":[120,128],"semi-definite":[121],"programming":[122,130],"(SSDP)":[123],"method,":[124],"inspired":[125],"quadratic":[129],"(SQP)":[131],"nonlinear":[133],"optimization.":[134],"conveniently":[138],"implemented":[139],"available":[141],"SDP":[142],"interior-point":[143],"solvers.":[144],"compare":[146],"its":[147],"performance":[148],"well-known":[151],"D-K":[152],"iteration":[153],"scheme":[154],"control.":[157],"Two":[158],"test":[159],"investigated":[162],"demonstrate":[164],"power":[166],"efficiency":[168],"approach.":[171]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
