{"id":"https://openalex.org/W7203673485","doi":"https://doi.org/10.48550/arxiv.2608.16265","title":"ExaModels.jl: an Algebraic Modeling System for Nonlinear Programming on GPUs","display_name":"ExaModels.jl: an Algebraic Modeling System for Nonlinear Programming on GPUs","publication_year":2026,"publication_date":"2026-08-17","ids":{"openalex":"https://openalex.org/W7203673485","doi":"https://doi.org/10.48550/arxiv.2608.16265"},"language":null,"primary_location":{"id":"pmh:oai:arXiv.org:2608.16265","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.16265","pdf_url":"https://arxiv.org/pdf/2608.16265","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.16265","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5141201806","display_name":"Sungho Shin","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shin, Sungho","raw_affiliation_strings":["Department of Chemical Engineering , Massachusetts Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Chemical Engineering , Massachusetts Institute of Technology","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011552443","display_name":"Michel Schanen","orcid":"https://orcid.org/0000-0002-4164-027X","observed_orcids":["https://orcid.org/0000-0002-4164-027X"]},"institutions":[{"id":"https://openalex.org/I1282105669","display_name":"Argonne National Laboratory","ror":"https://ror.org/05gvnxz63","country_code":"US","type":"facility","lineage":["https://openalex.org/I1282105669","https://openalex.org/I1330989302","https://openalex.org/I39565521","https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Schanen, Michel","raw_affiliation_strings":["Mathematics and Computer Science Division , Argonne National Laboratory \u00b6 AMD"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics and Computer Science Division , Argonne National Laboratory \u00b6 AMD","institution_ids":["https://openalex.org/I1282105669"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010044940","display_name":"Fran\u00e7ois Pacaud","orcid":"https://orcid.org/0000-0002-9009-6573","observed_orcids":["https://orcid.org/0000-0002-9009-6573","https://orcid.org/0000-0003-0596-3554"]},"institutions":[{"id":"https://openalex.org/I2746051580","display_name":"Universit\u00e9 Paris Sciences et Lettres","ror":"https://ror.org/013cjyk83","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580"]},{"id":"https://openalex.org/I70768539","display_name":"\u00c9cole Nationale Sup\u00e9rieure des Mines de Paris","ror":"https://ror.org/04y8cs423","country_code":"FR","type":"education","lineage":["https://openalex.org/I190752583","https://openalex.org/I2746051580","https://openalex.org/I70768539"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Pacaud, Fran\u00e7ois","raw_affiliation_strings":["MINES Paris -PSL"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MINES Paris -PSL","institution_ids":["https://openalex.org/I2746051580","https://openalex.org/I70768539"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043783059","display_name":"Alexis Montoison","orcid":"https://orcid.org/0000-0002-3403-5450","observed_orcids":["https://orcid.org/0000-0002-3403-5450"]},"institutions":[{"id":"https://openalex.org/I1282105669","display_name":"Argonne National Laboratory","ror":"https://ror.org/05gvnxz63","country_code":"US","type":"facility","lineage":["https://openalex.org/I1282105669","https://openalex.org/I1330989302","https://openalex.org/I39565521","https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Montoison, Alexis","raw_affiliation_strings":["Mathematics and Computer Science Division , Argonne National Laboratory \u00b6 AMD"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics and Computer Science Division , Argonne National Laboratory \u00b6 AMD","institution_ids":["https://openalex.org/I1282105669"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000943506","display_name":"Mihai Anitescu","orcid":"https://orcid.org/0000-0002-0787-5462","observed_orcids":["https://orcid.org/0000-0002-0787-5462"]},"institutions":[{"id":"https://openalex.org/I1282105669","display_name":"Argonne National Laboratory","ror":"https://ror.org/05gvnxz63","country_code":"US","type":"facility","lineage":["https://openalex.org/I1282105669","https://openalex.org/I1330989302","https://openalex.org/I39565521","https://openalex.org/I40347166"]},{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Anitescu, Mihai","raw_affiliation_strings":["Department of Statistics , University of Chicago","Mathematics and Computer Science Division , Argonne National Laboratory \u00b6 AMD"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics , University of Chicago","institution_ids":["https://openalex.org/I40347166"]},{"raw_affiliation_string":"Mathematics and Computer Science Division , Argonne National Laboratory \u00b6 AMD","institution_ids":["https://openalex.org/I1282105669"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.5619999766349792,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.5619999766349792,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.4311999976634979,"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":0.000699999975040555,"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/nonlinear-programming","display_name":"nonlinear programming","score":0.9929999709129333},{"id":"https://openalex.org/keywords/gpu-parallelization","display_name":"GPU parallelization","score":0.7490000128746033},{"id":"https://openalex.org/keywords/simd","display_name":"SIMD","score":0.8100000023841858},{"id":"https://openalex.org/keywords/derivative-evaluation","display_name":"derivative evaluation","score":0.6520000100135803},{"id":"https://openalex.org/keywords/julia-programming-language","display_name":"Julia","score":0.7139999866485596},{"id":"https://openalex.org/keywords/cops","display_name":"COPS","score":0.6669999957084656}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.734499990940094},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.7081000208854675},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.6359999775886536},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.5005000233650208},{"id":"https://openalex.org/C124304363","wikidata":"https://www.wikidata.org/wiki/Q673661","display_name":"Abstraction","level":2,"score":0.48590001463890076},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4832000136375427},{"id":"https://openalex.org/C169590947","wikidata":"https://www.wikidata.org/wiki/Q47506","display_name":"Compiler","level":2,"score":0.4796999990940094},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.46970000863075256},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.43070000410079956},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.39419999718666077},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3813999891281128},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3711000084877014},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.34779998660087585},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.31769999861717224},{"id":"https://openalex.org/C78766204","wikidata":"https://www.wikidata.org/wiki/Q555032","display_name":"Multi-core processor","level":2,"score":0.3158000111579895},{"id":"https://openalex.org/C67186912","wikidata":"https://www.wikidata.org/wiki/Q367664","display_name":"Data modeling","level":2,"score":0.30390000343322754},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.2937000095844269},{"id":"https://openalex.org/C138958017","wikidata":"https://www.wikidata.org/wiki/Q190087","display_name":"Data type","level":2,"score":0.2930999994277954},{"id":"https://openalex.org/C63000827","wikidata":"https://www.wikidata.org/wiki/Q3080428","display_name":"Software portability","level":2,"score":0.29019999504089355},{"id":"https://openalex.org/C21080849","wikidata":"https://www.wikidata.org/wiki/Q13611879","display_name":"Data point","level":2,"score":0.27070000767707825},{"id":"https://openalex.org/C2778119891","wikidata":"https://www.wikidata.org/wiki/Q477690","display_name":"CUDA","level":2,"score":0.2703999876976013},{"id":"https://openalex.org/C2781172179","wikidata":"https://www.wikidata.org/wiki/Q853109","display_name":"Parallelism (grammar)","level":2,"score":0.26969999074935913},{"id":"https://openalex.org/C2778361913","wikidata":"https://www.wikidata.org/wiki/Q7248437","display_name":"Program transformation","level":2,"score":0.26910001039505005},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.2685999870300293},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.26669999957084656},{"id":"https://openalex.org/C94523830","wikidata":"https://www.wikidata.org/wiki/Q11203","display_name":"System of linear equations","level":2,"score":0.266400009393692},{"id":"https://openalex.org/C110963975","wikidata":"https://www.wikidata.org/wiki/Q12070446","display_name":"Systems modeling","level":2,"score":0.2648000121116638},{"id":"https://openalex.org/C34165917","wikidata":"https://www.wikidata.org/wiki/Q188267","display_name":"Programming paradigm","level":2,"score":0.2583000063896179},{"id":"https://openalex.org/C61483411","wikidata":"https://www.wikidata.org/wiki/Q3124522","display_name":"Data parallelism","level":3,"score":0.2572999894618988},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.25690001249313354},{"id":"https://openalex.org/C165696696","wikidata":"https://www.wikidata.org/wiki/Q11287","display_name":"Exploit","level":2,"score":0.25619998574256897},{"id":"https://openalex.org/C164155591","wikidata":"https://www.wikidata.org/wiki/Q2067766","display_name":"Satisfiability modulo theories","level":2,"score":0.25380000472068787}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.16265","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.16265","pdf_url":"https://arxiv.org/pdf/2608.16265","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.16265","doi":"https://doi.org/10.48550/arxiv.2608.16265","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.16265","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.16265","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.16265","pdf_url":"https://arxiv.org/pdf/2608.16265","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G102163711","display_name":null,"funder_award_id":"DE\u2010 AC02\u201006CH11357","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G107546177","display_name":null,"funder_award_id":"DE- AC02-06-CH11357","funder_id":"https://openalex.org/F4320338284","funder_display_name":"Argonne National Laboratory"},{"id":"https://openalex.org/G1313983767","display_name":null,"funder_award_id":"DE-AC02","funder_id":"https://openalex.org/F4320338284","funder_display_name":"Argonne National Laboratory"},{"id":"https://openalex.org/G1664757510","display_name":null,"funder_award_id":"AC02\u201306CH11357","funder_id":"https://openalex.org/F4320338284","funder_display_name":"Argonne National Laboratory"},{"id":"https://openalex.org/G2287611682","display_name":null,"funder_award_id":"AC02\u201006CH11357","funder_id":"https://openalex.org/F4320332359","funder_display_name":"Office of Science"},{"id":"https://openalex.org/G262962599","display_name":null,"funder_award_id":"AC02\u201006CH11357","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G3075337988","display_name":null,"funder_award_id":"06CH11357","funder_id":"https://openalex.org/F4320338284","funder_display_name":"Argonne National Laboratory"},{"id":"https://openalex.org/G498139845","display_name":null,"funder_award_id":"DE-AC02","funder_id":"https://openalex.org/F4320332359","funder_display_name":"Office of Science"},{"id":"https://openalex.org/G5398989114","display_name":null,"funder_award_id":"AC02-06CH11357","funder_id":"https://openalex.org/F4320337506","funder_display_name":"Advanced Scientific Computing Research"},{"id":"https://openalex.org/G6848031779","display_name":null,"funder_award_id":"06CH11357","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G6918803902","display_name":null,"funder_award_id":"06CH11357","funder_id":"https://openalex.org/F4320332359","funder_display_name":"Office of Science"},{"id":"https://openalex.org/G878601127","display_name":null,"funder_award_id":"DE-AC02-06CH11357","funder_id":"https://openalex.org/F4320337506","funder_display_name":"Advanced Scientific Computing Research"},{"id":"https://openalex.org/G969889393","display_name":null,"funder_award_id":"DE-AC02-","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G993149817","display_name":null,"funder_award_id":"DE-AC02-06CH11357 ","funder_id":"https://openalex.org/F4320332359","funder_display_name":"Office of Science"}],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320309480","display_name":"Nvidia","ror":"https://ror.org/03jdj4y14"},{"id":"https://openalex.org/F4320332359","display_name":"Office of Science","ror":"https://ror.org/00mmn6b08"},{"id":"https://openalex.org/F4320337506","display_name":"Advanced Scientific Computing Research","ror":"https://ror.org/0012c7r22"},{"id":"https://openalex.org/F4320338284","display_name":"Argonne National Laboratory","ror":"https://ror.org/05gvnxz63"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7203673485.pdf","grobid_xml":"https://content.openalex.org/works/W7203673485.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Large-scale":[0],"nonlinear":[1,24,85],"programs":[2],"almost":[3],"always":[4],"exhibit":[5],"partially":[6],"separable":[7],"and":[8,32,69,111,170,175],"repetitive":[9],"structure,":[10],"yet":[11],"most":[12],"existing":[13],"algebraic":[14,56,92],"modeling":[15,57],"systems":[16],"do":[17],"not":[18],"take":[19],"advantage":[20],"of":[21,41,91,143,146,153],"it.":[22],"A":[23],"optimization":[25],"solver":[26],"queries":[27],"the":[28,30,39,47,65,67,101,125,144,150,154],"objective,":[29,66],"constraints,":[31,68],"their":[33,70],"derivatives":[34,71],"at":[35,105],"every":[36],"iteration,":[37],"so":[38],"speed":[40],"these":[42],"evaluations":[43],"bears":[44],"directly":[45],"on":[46,173,177],"overall":[48],"solution":[49],"time.":[50],"We":[51],"present":[52],"ExaModels.jl,":[53],"a":[54,78,84,88,108],"Julia-based":[55],"system":[58],"that":[59,82,121],"exploits":[60],"this":[61],"structure":[62],"to":[63],"evaluate":[64],"in":[72],"parallel.":[73],"At":[74],"its":[75],"core":[76],"is":[77,115],"single-instruction,":[79],"multiple-data":[80],"abstraction":[81],"represents":[83],"program":[86],"as":[87],"small":[89],"number":[90,145],"patterns,":[93],"each":[94,118],"repeated":[95],"over":[96,166],"many":[97,136],"data":[98,126,147],"points.":[99,148],"Because":[100],"patterns":[102],"are":[103],"visible":[104],"compile":[106],"time,":[107],"specialized":[109],"model":[110],"derivative":[112],"evaluation":[113,140,163],"kernel":[114,122],"compiled":[116],"for":[117],"pattern.":[119],"Applying":[120],"independently":[123],"across":[124],"points":[127],"maps":[128],"naturally":[129],"onto":[130],"GPU":[131,157],"parallelism":[132],"and,":[133],"with":[134],"sufficiently":[135],"threads,":[137],"yields":[138],"O(1)":[139],"time":[141],"regardless":[142],"On":[149],"largest":[151],"instances":[152],"Luksan-Vlcek":[155],"library,":[156],"execution":[158],"speeds":[159],"up":[160],"sparse":[161],"Hessian":[162],"by":[164,171],"76x":[165],"single-threaded":[167],"CPU":[168],"evaluation,":[169],"30x":[172],"COPS":[174],"7.3x":[176],"PGLIB-OPF.":[178]},"counts_by_year":[],"updated_date":"2026-10-01T08:54:57.152042","created_date":"2026-08-19T00:00:00"}
