{"id":"https://openalex.org/W3128000806","doi":"https://doi.org/10.1145/3452143.3465516","title":"The Constant Trace Property in Noncommutative Optimization","display_name":"The Constant Trace Property in Noncommutative Optimization","publication_year":2021,"publication_date":"2021-07-13","ids":{"openalex":"https://openalex.org/W3128000806","doi":"https://doi.org/10.1145/3452143.3465516","mag":"3128000806"},"language":"en","primary_location":{"id":"doi:10.1145/3452143.3465516","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3452143.3465516","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2021 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2102.02162","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066109597","display_name":"Ngoc Hoang Anh","orcid":"https://orcid.org/0000-0002-1688-4336"},"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"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Ngoc Hoang Anh Mai","raw_affiliation_strings":["Laboratoire d'Analyse et d'Architecture des Syst\u00e8mes (LAAS), Toulouse, France"],"affiliations":[{"raw_affiliation_string":"Laboratoire d'Analyse et d'Architecture des Syst\u00e8mes (LAAS), Toulouse, France","institution_ids":["https://openalex.org/I190497903"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039423885","display_name":"Abhishek Bhardwaj","orcid":"https://orcid.org/0000-0002-5346-877X"},"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"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Abhishek Bhardwaj","raw_affiliation_strings":["Laboratoire d'Analyse et d'Architecture des Syst\u00e8mes (LAAS), Toulouse, France"],"affiliations":[{"raw_affiliation_string":"Laboratoire d'Analyse et d'Architecture des Syst\u00e8mes (LAAS), Toulouse, France","institution_ids":["https://openalex.org/I190497903"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066095974","display_name":"Victor Magron","orcid":"https://orcid.org/0000-0003-1147-3738"},"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"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Victor Magron","raw_affiliation_strings":["Laboratoire d'Analyse et d'Architecture des Syst\u00e8mes (LAAS), Toulouse, France"],"affiliations":[{"raw_affiliation_string":"Laboratoire d'Analyse et d'Architecture des Syst\u00e8mes (LAAS), Toulouse, France","institution_ids":["https://openalex.org/I190497903"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5066109597"],"corresponding_institution_ids":["https://openalex.org/I190497903"],"apc_list":null,"apc_paid":null,"fwci":0.312,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.48939022,"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":"297","last_page":"304"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9993000030517578,"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":0.9993000030517578,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.996399998664856,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/noncommutative-geometry","display_name":"Noncommutative geometry","score":0.9294143915176392},{"id":"https://openalex.org/keywords/trace","display_name":"TRACE (psycholinguistics)","score":0.8256088495254517},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.6404182314872742},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5121181011199951},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.47960150241851807},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.4437800347805023},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.4379267990589142},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4350108504295349},{"id":"https://openalex.org/keywords/ball","display_name":"Ball (mathematics)","score":0.42434489727020264},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3991900384426117},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33953607082366943},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2534688711166382},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2007777988910675},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1889273226261139}],"concepts":[{"id":"https://openalex.org/C68797384","wikidata":"https://www.wikidata.org/wiki/Q2746792","display_name":"Noncommutative geometry","level":2,"score":0.9294143915176392},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.8256088495254517},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.6404182314872742},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5121181011199951},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.47960150241851807},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.4437800347805023},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.4379267990589142},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4350108504295349},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.42434489727020264},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3991900384426117},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33953607082366943},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2534688711166382},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2007777988910675},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1889273226261139},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/3452143.3465516","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3452143.3465516","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2021 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},{"id":"mag:3128000806","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2102.02162","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null}],"best_oa_location":{"id":"mag:3128000806","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2102.02162","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3320808828","display_name":null,"funder_award_id":"ANR-19-PI3A-0004, ANR-18-ERC2-0004-01","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G4535932799","display_name":null,"funder_award_id":"813211","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320332999","display_name":"Horizon 2020 Framework Programme","ror":"https://ror.org/00k4n6c32"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W91728630","https://openalex.org/W99708544","https://openalex.org/W1506690472","https://openalex.org/W1527351491","https://openalex.org/W1596877211","https://openalex.org/W1967344706","https://openalex.org/W1980431326","https://openalex.org/W1995320256","https://openalex.org/W1999471332","https://openalex.org/W2000320746","https://openalex.org/W2033813180","https://openalex.org/W2051306216","https://openalex.org/W2051634716","https://openalex.org/W2166798101","https://openalex.org/W2476213965","https://openalex.org/W2752158681","https://openalex.org/W2909168925","https://openalex.org/W2962999299","https://openalex.org/W2963297919","https://openalex.org/W2971613073","https://openalex.org/W3023939313","https://openalex.org/W3043614436","https://openalex.org/W3105661328","https://openalex.org/W3112841258","https://openalex.org/W3119965387","https://openalex.org/W3120760274","https://openalex.org/W3129033895","https://openalex.org/W3141641421","https://openalex.org/W3183816071","https://openalex.org/W4254742099","https://openalex.org/W4255442211","https://openalex.org/W6633965154","https://openalex.org/W6685170767","https://openalex.org/W6767450992"],"related_works":["https://openalex.org/W2041470464","https://openalex.org/W3100496417","https://openalex.org/W3043614436","https://openalex.org/W2101601284","https://openalex.org/W2000836604","https://openalex.org/W1966332181","https://openalex.org/W1967184028","https://openalex.org/W2941716933","https://openalex.org/W2745738375","https://openalex.org/W3127872418","https://openalex.org/W1979692659","https://openalex.org/W2013153664","https://openalex.org/W2996395503","https://openalex.org/W2540130351","https://openalex.org/W184815837","https://openalex.org/W2113615120","https://openalex.org/W2037887312","https://openalex.org/W2924423110","https://openalex.org/W2990870152","https://openalex.org/W2073476612"],"abstract_inverted_index":{"In":[0],"this":[1,33],"article,":[2],"we":[3],"show":[4],"that":[5],"each":[6],"semidefinite":[7,21,49],"relaxation":[8],"of":[9,51],"a":[10,20,24],"ball-constrained":[11],"noncommutative":[12,53],"polynomial":[13],"optimization":[14],"problem":[15],"can":[16,37],"be":[17,38],"cast":[18],"as":[19],"program":[22],"with":[23],"constant":[25,34],"trace":[26,35],"matrix":[27],"variable.":[28],"We":[29],"then":[30],"demonstrate":[31],"how":[32],"property":[36],"exploited":[39],"via":[40],"first":[41],"order":[42],"numerical":[43],"methods":[44],"to":[45],"solve":[46],"efficiently":[47],"the":[48,52],"relaxations":[50],"problem.":[54]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}
