{"id":"https://openalex.org/W2133861730","doi":"https://doi.org/10.1109/cdc.2010.5717659","title":"A &amp;#x201C;joint+marginal&amp;#x201D; algorithm for polynomial optimization","display_name":"A &amp;#x201C;joint+marginal&amp;#x201D; algorithm for polynomial optimization","publication_year":2010,"publication_date":"2010-12-01","ids":{"openalex":"https://openalex.org/W2133861730","doi":"https://doi.org/10.1109/cdc.2010.5717659","mag":"2133861730"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2010.5717659","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2010.5717659","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"49th IEEE Conference on Decision and Control (CDC)","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/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/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/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/I4210098964","display_name":"Toulouse Mathematics Institute","ror":null,"country_code":"FR","type":null,"lineage":["https://openalex.org/I4210098964"]},{"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"]}],"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"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055818583","display_name":"Tung Phan Thanh","orcid":null},"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/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/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/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":"Tung Phan Thanh","raw_affiliation_strings":["LAAS-CNRS, University of Toulouse III, France","LAAS, CNRS, University of Toulouse, France"],"affiliations":[{"raw_affiliation_string":"LAAS-CNRS, University of Toulouse III, France","institution_ids":["https://openalex.org/I134560555","https://openalex.org/I17866349","https://openalex.org/I1294671590","https://openalex.org/I190497903"]},{"raw_affiliation_string":"LAAS, CNRS, 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":2,"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":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.19508804,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"3871","last_page":"3876"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998999834060669,"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":0.9998999834060669,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9972000122070312,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9962000250816345,"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/joint","display_name":"Joint (building)","score":0.6149970889091492},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5494590401649475},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4639887809753418},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.45686954259872437},{"id":"https://openalex.org/keywords/optimization-algorithm","display_name":"Optimization algorithm","score":0.41466736793518066},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.41159766912460327},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.316627562046051},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.16120439767837524},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.10627347230911255},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06467044353485107}],"concepts":[{"id":"https://openalex.org/C18555067","wikidata":"https://www.wikidata.org/wiki/Q8375051","display_name":"Joint (building)","level":2,"score":0.6149970889091492},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5494590401649475},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4639887809753418},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45686954259872437},{"id":"https://openalex.org/C2987595161","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Optimization algorithm","level":2,"score":0.41466736793518066},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41159766912460327},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.316627562046051},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.16120439767837524},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.10627347230911255},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06467044353485107}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2010.5717659","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2010.5717659","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"49th IEEE Conference on Decision and Control (CDC)","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":6,"referenced_works":["https://openalex.org/W1563737017","https://openalex.org/W1967344706","https://openalex.org/W1985123706","https://openalex.org/W2036726769","https://openalex.org/W2079089353","https://openalex.org/W2090967418"],"related_works":["https://openalex.org/W4366549320","https://openalex.org/W4287863136","https://openalex.org/W3006015132","https://openalex.org/W2965078190","https://openalex.org/W2140656843","https://openalex.org/W3040644038","https://openalex.org/W4394870774","https://openalex.org/W4311207076","https://openalex.org/W3203633096","https://openalex.org/W2355226480"],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2,7,40,117,204,213,281],"new":[3,267],"algorithm":[4],"for":[5,23,232],"solving":[6],"polynomial":[8,25,121,186],"program":[9],"P":[10],"based":[11],"on":[12,96,196,223],"the":[13,20,33,44,67,105,140,184,197,220,240,245],"recent":[14],"\u201cjoint":[15],"+":[16],"marginal\u201d":[17],"approach":[18],"of":[19,107,119,154,219],"first":[21,31],"author":[22],"parametric":[24],"optimization.":[26],"The":[27,217],"idea":[28],"is":[29,73,239],"to":[30,139,278],"consider":[32],"variable":[34],"x":[35,55,69,123,144,261],"<inf":[36,50,56,62,70,82,91,98,124,129,133,145,150,157,173,179,188,192,200,255,262,270],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[37,51,57,63,71,83,92,99,125,130,134,146,151,158,174,180,189,193,201,256,263,271,287],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1</inf>":[38,64,72,84,93,100,126,135,147,152,159,175,181,194,202],"as":[39,161,277],"parameter":[41,68,260],"and":[42,75],"solve":[43],"associated":[45],"(n":[46,250],"\u2212":[47,251],"1)-variable":[48],"(x":[49,132,191],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</inf>":[52,257,264,272],",":[53,203],"\u2026,":[54],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</inf>":[58],")":[59,65,136,153,195,258],"problem":[60,155,207,253],"P(x":[61,156,254],"where":[66],"fixed":[74,167],"takes":[76],"values":[77],"in":[78,265],"some":[79,88,266],"interval":[80,198,268],"Y":[81,97,178,199,269],"\u2282":[85,273],"\u211d,":[86,274],"with":[87,165,247,259],"probability":[89],"\u03d5":[90],"uniformly":[94],"distributed":[95],".":[101,289],"Then":[102,164],"one":[103,170],"considers":[104],"hierarchy":[106],"what":[108],"we":[109],"call":[110],"\u201cjoint+marginal\u201d":[111],"semidefinite":[112,215],"relaxations,":[113],"whose":[114],"duals":[115],"provide":[116],"sequence":[118],"univariate":[120,185],"approximations":[122],"\u21a6":[127,148],"p":[128,187],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">k</inf>":[131,190],"that":[137,208],"converges":[138],"optimal":[141],"value":[142],"function":[143],"J(x":[149],"),":[160],"k":[162,166,226,236],"increases.":[163],"\u00e0":[168],"priori,":[169],"computes":[171],"x\u0303":[172,283],"*":[176],"\u2208":[177,284],"which":[182],"minimizes":[183],"convex":[205],"optimization":[206],"can":[209,227],"be":[210,228],"solved":[211],"via":[212],"single":[214],"program.":[216],"quality":[218],"approximation":[221],"depends":[222],"how":[224],"large":[225],"chosen":[229],"(in":[230],"general":[231],"significant":[233],"size":[234],"problems":[235],"=":[237],"1":[238],"only":[241],"choice).":[242],"One":[243],"iterates":[244],"procedure":[246],"now":[248],"an":[249],"2)-variable":[252],"etc.":[275],"so":[276],"finally":[279],"obtain":[280],"vector":[282],"\u211d":[285],"<sup":[286],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</sup>":[288],"Preliminary":[290],"numerical":[291],"results":[292],"are":[293],"provided.":[294]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
