{"id":"https://openalex.org/W2113615120","doi":"https://doi.org/10.1109/cdc.2011.6160364","title":"Inverse polynomial optimization","display_name":"Inverse polynomial optimization","publication_year":2011,"publication_date":"2011-12-01","ids":{"openalex":"https://openalex.org/W2113615120","doi":"https://doi.org/10.1109/cdc.2011.6160364","mag":"2113615120"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2011.6160364","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2011.6160364","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Conference on Decision and Control and European Control Conference","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/A5006670993","display_name":"Jean B. Lasserre","orcid":"https://orcid.org/0000-0003-0860-9913"},"institutions":[{"id":"https://openalex.org/I17866349","display_name":"Universit\u00e9 F\u00e9d\u00e9rale de Toulouse Midi-Pyr\u00e9n\u00e9es","ror":"https://ror.org/004raaa70","country_code":"FR","type":"education","lineage":["https://openalex.org/I17866349"]},{"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/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/I190497903","display_name":"Laboratoire d'Analyse et d'Architecture des Syst\u00e8mes","ror":"https://ror.org/03vcm6439","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I134560555","https://openalex.org/I190497903","https://openalex.org/I196454796","https://openalex.org/I205747304","https://openalex.org/I205747304","https://openalex.org/I4210095849","https://openalex.org/I4210159245","https://openalex.org/I4387153255","https://openalex.org/I4405258862","https://openalex.org/I4405258862","https://openalex.org/I4405258862","https://openalex.org/I4405258862"]},{"id":"https://openalex.org/I4210098964","display_name":"Toulouse Mathematics Institute","ror":null,"country_code":"FR","type":null,"lineage":["https://openalex.org/I4210098964"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Jean B. Lasserre","raw_affiliation_strings":["LAAS-CNRS and the Institute of Mathematics, University of Toulouse III, France","LAAS-CNRS and the Institute of Mathematics, University of Toulouse, France"],"affiliations":[{"raw_affiliation_string":"LAAS-CNRS and the Institute of Mathematics, University of Toulouse III, France","institution_ids":["https://openalex.org/I134560555","https://openalex.org/I4210098964","https://openalex.org/I1294671590","https://openalex.org/I190497903"]},{"raw_affiliation_string":"LAAS-CNRS and the Institute of Mathematics, University of Toulouse, France","institution_ids":["https://openalex.org/I17866349","https://openalex.org/I1294671590","https://openalex.org/I190497903"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5006670993"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I134560555","https://openalex.org/I17866349","https://openalex.org/I190497903","https://openalex.org/I4210098964"],"apc_list":null,"apc_paid":null,"fwci":0.4538,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.6515587,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"2794","last_page":"2799"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":1.0,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9973999857902527,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.996999979019165,"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/inverse","display_name":"Inverse","score":0.733240008354187},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6677477955818176},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5490126013755798},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5191530585289001},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5034064650535583},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.4314552843570709},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3919592499732971},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11721223592758179},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08174601197242737},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07390725612640381},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.05650562047958374}],"concepts":[{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.733240008354187},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6677477955818176},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5490126013755798},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5191530585289001},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5034064650535583},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.4314552843570709},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3919592499732971},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11721223592758179},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08174601197242737},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07390725612640381},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05650562047958374},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2011.6160364","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2011.6160364","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Conference on Decision and Control and European Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W572922989","https://openalex.org/W1964603869","https://openalex.org/W1966229055","https://openalex.org/W1967344706","https://openalex.org/W1970832114","https://openalex.org/W1977828554","https://openalex.org/W1979134936","https://openalex.org/W2001334051","https://openalex.org/W2001452717","https://openalex.org/W2003486810","https://openalex.org/W2021388365","https://openalex.org/W2042349733","https://openalex.org/W2047329156","https://openalex.org/W2049225870","https://openalex.org/W2068913356","https://openalex.org/W2071550336","https://openalex.org/W2089318869","https://openalex.org/W2090967418","https://openalex.org/W2153170581","https://openalex.org/W2166798101","https://openalex.org/W2911796152","https://openalex.org/W4255442211"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2399035783","https://openalex.org/W3161230432","https://openalex.org/W4367190712","https://openalex.org/W2168900540","https://openalex.org/W1487201914","https://openalex.org/W4301429470","https://openalex.org/W280458463","https://openalex.org/W1170131723","https://openalex.org/W2125310826"],"abstract_inverted_index":{"We":[0,30],"consider":[1],"the":[2,8,60,104,111,144],"inverse":[3,39],"optimization":[4],"problem":[5],"associated":[6],"with":[7,59,73,77,98],"polynomial":[9,47],"program":[10,106,130],"f":[11,56,116,148],"<sup":[12,149],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[13,93,150],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">*</sup>":[14,151],"=":[15],"min{f(x)":[16],":":[17],"x":[18],"\u2208":[19,28],"K}":[20],"and":[21,85,122],"a":[22,32,46,66,74,79,118,128,136],"given":[23],"current":[24],"feasible":[25],"solution":[26],"y":[27,64],"K.":[29],"provide":[31],"systematic":[33],"numerical":[34],"scheme":[35],"to":[36,110,126],"compute":[37,45],"an":[38,78],"optimal":[40,132,146],"solution.":[41],"That":[42],"is,":[43],"we":[44],"f\u0303":[48,70,87,124],"(which":[49],"may":[50],"be":[51,108],"of":[52,69,103],"same":[53],"degree":[54,81],"as":[55],"if":[57],"desired)":[58],"following":[61],"properties:":[62],"(a)":[63],"is":[65,141],"global":[67],"minimizer":[68],"on":[71,138],"K":[72],"Putinar's":[75],"certificate":[76],"priori":[80],"bound":[82,137],"d":[83],"fixed,":[84],"(b),":[86],"minimizes":[88],"||f":[89],"-":[90],"f\u0303||":[91],"<sub":[92],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1</sub>":[94],"over":[95],"all":[96],"polynomials":[97],"such":[99],"properties.":[100],"The":[101],"size":[102],"semidefinite":[105,129],"can":[107],"adapted":[109],"computational":[112],"capabilities":[113],"available.":[114],"Moreover,":[115],"takes":[117],"simple":[119],"canonical":[120],"form,":[121],"computing":[123],"reduces":[125],"solving":[127],"whose":[131],"value":[133,147],"also":[134,156],"provides":[135],"how":[139],"far":[140],"f(y)":[142],"from":[143],"unknown":[145],".":[152],"Some":[153],"variations":[154],"are":[155],"discussed.":[157]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}