{"id":"https://openalex.org/W7104552573","doi":"https://doi.org/10.1145/3747199.3747570","title":"Solving generic parametric linear matrix inequalities","display_name":"Solving generic parametric linear matrix inequalities","publication_year":2025,"publication_date":"2025-07-28","ids":{"openalex":"https://openalex.org/W7104552573","doi":"https://doi.org/10.1145/3747199.3747570"},"language":"en","primary_location":{"id":"doi:10.1145/3747199.3747570","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3747199.3747570","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3747199.3747570","source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2025 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://dl.acm.org/doi/pdf/10.1145/3747199.3747570","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Simone Naldi","orcid":"https://orcid.org/0000-0002-4556-6935"},"institutions":[{"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/I4210093397","display_name":"XLIM","ror":"https://ror.org/00f7srh09","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I32881790","https://openalex.org/I4210093397","https://openalex.org/I4210095849","https://openalex.org/I65806277"]},{"id":"https://openalex.org/I65806277","display_name":"Universit\u00e9 de Limoges","ror":"https://ror.org/02cp04407","country_code":"FR","type":"education","lineage":["https://openalex.org/I65806277"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Simone Naldi","raw_affiliation_strings":["Universit\u00e9 de Limoges, CNRS, XLIM, Limoges, France"],"raw_orcid":"https://orcid.org/0000-0002-4556-6935","affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Limoges, CNRS, XLIM, Limoges, France","institution_ids":["https://openalex.org/I65806277","https://openalex.org/I4210093397","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Mohab Safey El Din","orcid":"https://orcid.org/0000-0001-9463-1257"},"institutions":[{"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/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210159731","display_name":"LIP6","ror":"https://ror.org/05krcen59","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I39804081","https://openalex.org/I4210159245","https://openalex.org/I4210159731"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Mohab Safey El Din","raw_affiliation_strings":["Sorbonne Universit\u00e9, CNRS, LIP6, Paris, France"],"raw_orcid":"https://orcid.org/0000-0001-9463-1257","affiliations":[{"raw_affiliation_string":"Sorbonne Universit\u00e9, CNRS, LIP6, Paris, France","institution_ids":["https://openalex.org/I4210159731","https://openalex.org/I204730241","https://openalex.org/I1294671590","https://openalex.org/I39804081"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Adrien Taylor","orcid":"https://orcid.org/0009-0008-7305-6474"},"institutions":[{"id":"https://openalex.org/I4210103330","display_name":"\u00c9cole Normale Sup\u00e9rieure","ror":"https://ror.org/01dp7jr64","country_code":"BI","type":"education","lineage":["https://openalex.org/I4210103330"]}],"countries":["BI"],"is_corresponding":false,"raw_author_name":"Adrien Taylor","raw_affiliation_strings":["Inria, \u00c9cole normale sup\u00e9rieure, PSL Research University, Paris, France"],"raw_orcid":"https://orcid.org/0009-0008-7305-6474","affiliations":[{"raw_affiliation_string":"Inria, \u00c9cole normale sup\u00e9rieure, PSL Research University, Paris, France","institution_ids":["https://openalex.org/I4210103330"]}]},{"author_position":"last","author":{"id":null,"display_name":"Weijia Wang","orcid":"https://orcid.org/0009-0003-4299-2837"},"institutions":[{"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/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210159731","display_name":"LIP6","ror":"https://ror.org/05krcen59","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I39804081","https://openalex.org/I4210159245","https://openalex.org/I4210159731"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Weijia Wang","raw_affiliation_strings":["Sorbonne Universit\u00e9, CNRS, LIP6, Paris, France"],"raw_orcid":"https://orcid.org/0009-0003-4299-2837","affiliations":[{"raw_affiliation_string":"Sorbonne Universit\u00e9, CNRS, LIP6, Paris, France","institution_ids":["https://openalex.org/I4210159731","https://openalex.org/I204730241","https://openalex.org/I1294671590","https://openalex.org/I39804081"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210093397","https://openalex.org/I65806277"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.64316423,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"267","last_page":"276"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.439300000667572,"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":0.439300000667572,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.16609999537467957,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.16019999980926514,"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/parametric-statistics","display_name":"Parametric statistics","score":0.6047999858856201},{"id":"https://openalex.org/keywords/leverage","display_name":"Leverage (statistics)","score":0.565500020980835},{"id":"https://openalex.org/keywords/quantifier-elimination","display_name":"Quantifier elimination","score":0.5339999794960022},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.43130001425743103},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4228000044822693},{"id":"https://openalex.org/keywords/linear-matrix-inequality","display_name":"Linear matrix inequality","score":0.41920000314712524},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.41620001196861267},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.39800000190734863}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.782800018787384},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.6047999858856201},{"id":"https://openalex.org/C153083717","wikidata":"https://www.wikidata.org/wiki/Q6535263","display_name":"Leverage (statistics)","level":2,"score":0.565500020980835},{"id":"https://openalex.org/C32278780","wikidata":"https://www.wikidata.org/wiki/Q1849020","display_name":"Quantifier elimination","level":2,"score":0.5339999794960022},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45680001378059387},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.43130001425743103},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4228000044822693},{"id":"https://openalex.org/C201829737","wikidata":"https://www.wikidata.org/wiki/Q2022760","display_name":"Linear matrix inequality","level":2,"score":0.41920000314712524},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41690000891685486},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.41620001196861267},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.39800000190734863},{"id":"https://openalex.org/C84135550","wikidata":"https://www.wikidata.org/wiki/Q3154022","display_name":"Linear inequality","level":3,"score":0.3889999985694885},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.3855000138282776},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.37450000643730164},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.35929998755455017},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.3447999954223633},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3375999927520752},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32670000195503235},{"id":"https://openalex.org/C2776045410","wikidata":"https://www.wikidata.org/wiki/Q25111241","display_name":"Parametric programming","level":3,"score":0.3027999997138977},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.2989000082015991},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.2728999853134155},{"id":"https://openalex.org/C126352355","wikidata":"https://www.wikidata.org/wiki/Q2562273","display_name":"Polynomial matrix","level":4,"score":0.2612000107765198},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.25870001316070557},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.2506999969482422}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/3747199.3747570","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3747199.3747570","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3747199.3747570","source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2025 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},{"id":"pmh:oai:HAL:hal-04973502v2","is_oa":true,"landing_page_url":"https://hal.sorbonne-universite.fr/hal-04973502","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSAC '25: International Symposium on Symbolic and Algebraic Computation, Jul 2025, Guanajuato, Mexico. pp.267-276, ⟨10.1145/3747199.3747570⟩","raw_type":"Conference papers"}],"best_oa_location":{"id":"doi:10.1145/3747199.3747570","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3747199.3747570","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3747199.3747570","source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2025 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.41750630736351013,"id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G7964329499","display_name":null,"funder_award_id":"ANR-21-CE48-0006-01 HYPERSPACE, ANR-23-IACL-0008 PR[AI]RIE-PSAI, ANR-22-CE91-0007 EAGLES","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7104552573.pdf"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1559760555","https://openalex.org/W1949239131","https://openalex.org/W1962121538","https://openalex.org/W1979896658","https://openalex.org/W2025561788","https://openalex.org/W2035153735","https://openalex.org/W2037381995","https://openalex.org/W2057105460","https://openalex.org/W2075348750","https://openalex.org/W2080480594","https://openalex.org/W2102074804","https://openalex.org/W2104223485","https://openalex.org/W2151549243","https://openalex.org/W2164838307","https://openalex.org/W2279788372","https://openalex.org/W2951335402","https://openalex.org/W2962893120","https://openalex.org/W3048571829","https://openalex.org/W3108459106","https://openalex.org/W3138767167","https://openalex.org/W3141384256","https://openalex.org/W4289931776","https://openalex.org/W4298290503","https://openalex.org/W4400648353"],"related_works":[],"abstract_inverted_index":{"We":[0,162],"consider":[1],"linear":[2],"matrix":[3],"inequalities":[4],"(LMIs)":[5],"A":[6],"=":[7],"A0":[8],"+":[9,11,13],"x1A1":[10],"\u22c5\u22c5\u22c5":[12],"xnAn\u2ab00":[14],"with":[15,24,98],"the":[16,36,43,62,69,76,79,83,111,115,131,164,173,189],"Ai\u2019s":[17],"being":[18],"m":[19,21,148,157],"\u00d7":[20],"symmetric":[22],"matrices,":[23],"entries":[25],"in":[26,40,104,146,154],"a":[27,50,66,99,123,127,167],"ring":[28],"\\(\\mathcal":[29,32,55],"{R}\\).":[30],"When":[31,54],"{R}=":[33,56],"\\mathbb":[34,57],"{R}\\),":[35],"feasibility":[37,190],"problem":[38,63,89,116,170],"consists":[39],"deciding":[41],"whether":[42],"xi\u2019s":[44],"can":[45,90],"be":[46,91,186],"instantiated":[47],"to":[48,117,166,172,185,188],"obtain":[49],"positive":[51],"semi-definite":[52],"matrix.":[53],"{Q}[y_1,":[58],"\\ldots":[59],",":[60],"y_t]\\),":[61],"asks":[64],"for":[65,81],"formula":[67,124],"on":[68],"parameters":[70,80],"y1,":[71],"\u2026,":[72],"yt,":[73],"which":[74,82,181],"describes":[75],"values":[77],"of":[78,114,130,134,141,176,191],"specialized":[84],"LMI":[85,112],"is":[86,102,144],"feasible.":[87],"This":[88],"solved":[92],"using":[93],"general":[94],"quantifier":[95],"elimination":[96],"algorithms,":[97],"complexity":[100,140],"that":[101,121],"exponential":[103,145],"n.":[105],"In":[106],"this":[107,142],"work,":[108],"we":[109],"leverage":[110],"structure":[113],"design":[118],"an":[119],"algorithm":[120,143,165],"computes":[122],"\u03a6":[125],"describing":[126],"dense":[128],"subset":[129],"feasible":[132],"region":[133],"parameters,":[135],"under":[136],"genericity":[137],"assumptions.":[138],"The":[139],"n,":[147],"and":[149,158,171],"t":[150,159],"but":[151],"becomes":[152],"polynomial":[153],"n":[155],"when":[156],"are":[160,182],"fixed.":[161],"apply":[163],"parametric":[168,193],"sum-of-squares":[169],"convergence":[174],"analyses":[175],"certain":[177,192],"first-order":[178],"optimization":[179],"methods,":[180],"both":[183],"known":[184],"equivalent":[187],"LMIs,":[194],"hence":[195],"demonstrating":[196],"its":[197],"practical":[198],"interest.":[199]},"counts_by_year":[],"updated_date":"2026-05-07T13:39:58.223016","created_date":"2025-11-10T00:00:00"}