{"id":"https://openalex.org/W2901816197","doi":"https://doi.org/10.1007/s10107-020-01474-5","title":"Strong mixed-integer programming formulations for trained neural networks","display_name":"Strong mixed-integer programming formulations for trained neural networks","publication_year":2020,"publication_date":"2020-02-13","ids":{"openalex":"https://openalex.org/W2901816197","doi":"https://doi.org/10.1007/s10107-020-01474-5","mag":"2901816197"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-020-01474-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-020-01474-5","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-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/A5111970827","display_name":"Ross Anderson","orcid":null},"institutions":[{"id":"https://openalex.org/I1291425158","display_name":"Google (United States)","ror":"https://ror.org/00njsd438","country_code":"US","type":"company","lineage":["https://openalex.org/I1291425158","https://openalex.org/I4210128969"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ross Anderson","raw_affiliation_strings":["Google Inc, Cambridge, MA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Google Inc, Cambridge, MA, USA","institution_ids":["https://openalex.org/I1291425158"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039507401","display_name":"Joey Huchette","orcid":"https://orcid.org/0000-0003-3552-0316"},"institutions":[{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Joey Huchette","raw_affiliation_strings":["Rice University, Houston, TX, USA"],"raw_orcid":"https://orcid.org/0000-0003-3552-0316","affiliations":[{"raw_affiliation_string":"Rice University, Houston, TX, USA","institution_ids":["https://openalex.org/I74775410"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070149920","display_name":"Will Ma","orcid":null},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Will Ma","raw_affiliation_strings":["Columbia University, New York, NY, USA"],"raw_orcid":"https://orcid.org/0000-0002-2420-4468","affiliations":[{"raw_affiliation_string":"Columbia University, New York, NY, USA","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021227744","display_name":"Christian Tjandraatmadja","orcid":"https://orcid.org/0000-0002-0881-3511"},"institutions":[{"id":"https://openalex.org/I1291425158","display_name":"Google (United States)","ror":"https://ror.org/00njsd438","country_code":"US","type":"company","lineage":["https://openalex.org/I1291425158","https://openalex.org/I4210128969"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Christian Tjandraatmadja","raw_affiliation_strings":["Google Inc, Cambridge, MA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Google Inc, Cambridge, MA, USA","institution_ids":["https://openalex.org/I1291425158"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008961628","display_name":"Juan Pablo Vielma","orcid":"https://orcid.org/0000-0003-4335-7248"},"institutions":[{"id":"https://openalex.org/I1291425158","display_name":"Google (United States)","ror":"https://ror.org/00njsd438","country_code":"US","type":"company","lineage":["https://openalex.org/I1291425158","https://openalex.org/I4210128969"]},{"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":"Juan Pablo Vielma","raw_affiliation_strings":["Google Inc, Cambridge, MA, USA","Massachusetts Institute of Technology, Cambridge, MA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Google Inc, Cambridge, MA, USA","institution_ids":["https://openalex.org/I1291425158"]},{"raw_affiliation_string":"Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5039507401"],"corresponding_institution_ids":["https://openalex.org/I74775410"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":11.4232,"has_fulltext":false,"cited_by_count":165,"citation_normalized_percentile":{"value":0.98780594,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"183","issue":"1-2","first_page":"3","last_page":"39"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11689","display_name":"Adversarial Robustness in Machine Learning","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10036","display_name":"Advanced Neural Network Applications","score":0.9902999997138977,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/integer-programming","display_name":"Integer programming","score":0.6398279070854187},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6139948964118958},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6086669564247131},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5465986728668213},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5375933051109314},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.5290576219558716},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.49589094519615173},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.48654356598854065},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.44512248039245605},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4403465688228607},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.4379822015762329},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40468457341194153},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4031727910041809},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3350165784358978}],"concepts":[{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.6398279070854187},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6139948964118958},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6086669564247131},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5465986728668213},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5375933051109314},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.5290576219558716},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.49589094519615173},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.48654356598854065},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.44512248039245605},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4403465688228607},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.4379822015762329},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40468457341194153},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4031727910041809},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3350165784358978},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10107-020-01474-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-020-01474-5","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.7799999713897705,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":101,"referenced_works":["https://openalex.org/W10227180","https://openalex.org/W127277165","https://openalex.org/W155963807","https://openalex.org/W205043357","https://openalex.org/W1019830208","https://openalex.org/W1531900088","https://openalex.org/W1557310162","https://openalex.org/W1663973292","https://openalex.org/W1762430620","https://openalex.org/W1924619199","https://openalex.org/W1965897919","https://openalex.org/W1967284207","https://openalex.org/W1972997295","https://openalex.org/W1974401856","https://openalex.org/W1981276685","https://openalex.org/W2004548680","https://openalex.org/W2009086942","https://openalex.org/W2027627501","https://openalex.org/W2036898642","https://openalex.org/W2066071727","https://openalex.org/W2073576149","https://openalex.org/W2090042335","https://openalex.org/W2098425563","https://openalex.org/W2105527809","https://openalex.org/W2112796928","https://openalex.org/W2135588736","https://openalex.org/W2151308681","https://openalex.org/W2156387975","https://openalex.org/W2156439985","https://openalex.org/W2180612164","https://openalex.org/W2186729226","https://openalex.org/W2215378786","https://openalex.org/W2232834753","https://openalex.org/W2276412021","https://openalex.org/W2278356837","https://openalex.org/W2294059674","https://openalex.org/W2345492474","https://openalex.org/W2433743436","https://openalex.org/W2555745781","https://openalex.org/W2594877703","https://openalex.org/W2715235799","https://openalex.org/W2721006554","https://openalex.org/W2741534749","https://openalex.org/W2742154030","https://openalex.org/W2746573794","https://openalex.org/W2752814746","https://openalex.org/W2766462876","https://openalex.org/W2766820687","https://openalex.org/W2768915615","https://openalex.org/W2784871291","https://openalex.org/W2791251367","https://openalex.org/W2797572905","https://openalex.org/W2801079363","https://openalex.org/W2802557767","https://openalex.org/W2803392236","https://openalex.org/W2846823501","https://openalex.org/W2892354372","https://openalex.org/W2894812324","https://openalex.org/W2895089194","https://openalex.org/W2896122372","https://openalex.org/W2898422183","https://openalex.org/W2908984973","https://openalex.org/W2909107555","https://openalex.org/W2919115771","https://openalex.org/W2945033152","https://openalex.org/W2947319091","https://openalex.org/W2962943487","https://openalex.org/W2963054787","https://openalex.org/W2963266548","https://openalex.org/W2963491246","https://openalex.org/W2963496101","https://openalex.org/W2963565751","https://openalex.org/W2963600714","https://openalex.org/W2963669882","https://openalex.org/W2963770044","https://openalex.org/W2963784236","https://openalex.org/W2963857521","https://openalex.org/W2963950090","https://openalex.org/W2964121744","https://openalex.org/W2964153729","https://openalex.org/W2969714402","https://openalex.org/W2970297683","https://openalex.org/W2976145414","https://openalex.org/W2998329861","https://openalex.org/W2998757566","https://openalex.org/W3022023007","https://openalex.org/W3099132019","https://openalex.org/W3100789280","https://openalex.org/W3103957401","https://openalex.org/W3109541805","https://openalex.org/W4285719527","https://openalex.org/W6600340058","https://openalex.org/W6600728650","https://openalex.org/W6601357468","https://openalex.org/W6601760687","https://openalex.org/W6604257626","https://openalex.org/W6607167723","https://openalex.org/W6633963571","https://openalex.org/W6634721097","https://openalex.org/W6702878494","https://openalex.org/W6824754410"],"related_works":["https://openalex.org/W1596838019","https://openalex.org/W3182827720","https://openalex.org/W2133947431","https://openalex.org/W2983685817","https://openalex.org/W2490196280","https://openalex.org/W3208509670","https://openalex.org/W2100864966","https://openalex.org/W2109304297","https://openalex.org/W3173321515","https://openalex.org/W4285278887"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":13},{"year":2025,"cited_by_count":28},{"year":2024,"cited_by_count":36},{"year":2023,"cited_by_count":38},{"year":2022,"cited_by_count":21},{"year":2021,"cited_by_count":18},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-05-03T08:25:01.440150","created_date":"2025-10-10T00:00:00"}
