{"id":"https://openalex.org/W2101719620","doi":"https://doi.org/10.1007/s10107-009-0282-9","title":"Lifting for conic mixed-integer programming","display_name":"Lifting for conic mixed-integer programming","publication_year":2009,"publication_date":"2009-05-18","ids":{"openalex":"https://openalex.org/W2101719620","doi":"https://doi.org/10.1007/s10107-009-0282-9","mag":"2101719620"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-009-0282-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-009-0282-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-009-0282-9.pdf","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":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","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":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10107-009-0282-9.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008007328","display_name":"Alper Atamt\u00fcrk","orcid":"https://orcid.org/0000-0003-1220-808X"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alper Atamt\u00fcrk","raw_affiliation_strings":["Industrial Engineering and Operations Research Department, University of California, 4141 Etcheverry Hall MC 1777, Berkeley, CA, 94720-1777, USA","University of California, Industrial Engineering and Operations Research Department, 4141 Etcheverry Hall MC 1777, 94720-1777, Berkeley, CA, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Industrial Engineering and Operations Research Department, University of California, 4141 Etcheverry Hall MC 1777, Berkeley, CA, 94720-1777, USA","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"University of California, Industrial Engineering and Operations Research Department, 4141 Etcheverry Hall MC 1777, 94720-1777, Berkeley, CA, USA#TAB#","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084488825","display_name":"Vishnu Narayanan","orcid":null},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Vishnu Narayanan","raw_affiliation_strings":["Industrial Engineering and Operations Research, Indian Institute of Technology Bombay, Powai, Mumbai, 400076, India","Indian Institute of Technology Bombay, Industrial Engineering and Operations Research, Powai, 400076, Mumbai, India#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Industrial Engineering and Operations Research, Indian Institute of Technology Bombay, Powai, Mumbai, 400076, India","institution_ids":["https://openalex.org/I162827531"]},{"raw_affiliation_string":"Indian Institute of Technology Bombay, Industrial Engineering and Operations Research, Powai, 400076, Mumbai, India#TAB#","institution_ids":["https://openalex.org/I162827531"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2190,"currency":"EUR","value_usd":2890},"fwci":9.0847,"has_fulltext":true,"cited_by_count":59,"citation_normalized_percentile":{"value":0.97613686,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"126","issue":"2","first_page":"351","last_page":"363"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9944999814033508,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/conic-section","display_name":"Conic section","score":0.9656919836997986},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.8063149452209473},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.7524032592773438},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7244127988815308},{"id":"https://openalex.org/keywords/conic-optimization","display_name":"Conic optimization","score":0.6840249300003052},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.527739405632019},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.47958698868751526},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.45280033349990845},{"id":"https://openalex.org/keywords/branch-and-price","display_name":"Branch and price","score":0.4368094801902771},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.24641433358192444},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16124087572097778},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07093781232833862},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.06102937459945679}],"concepts":[{"id":"https://openalex.org/C108598597","wikidata":"https://www.wikidata.org/wiki/Q124255","display_name":"Conic section","level":2,"score":0.9656919836997986},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.8063149452209473},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.7524032592773438},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7244127988815308},{"id":"https://openalex.org/C79187972","wikidata":"https://www.wikidata.org/wiki/Q2654791","display_name":"Conic optimization","level":5,"score":0.6840249300003052},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.527739405632019},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.47958698868751526},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.45280033349990845},{"id":"https://openalex.org/C123558587","wikidata":"https://www.wikidata.org/wiki/Q4956382","display_name":"Branch and price","level":3,"score":0.4368094801902771},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.24641433358192444},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16124087572097778},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07093781232833862},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.06102937459945679},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.0},{"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/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s10107-009-0282-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-009-0282-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-009-0282-9.pdf","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":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.386.9430","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.386.9430","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ieor.berkeley.edu/~atamturk/pubs/_published/mathprog126-2011.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.507.6112","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.507.6112","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.optimization-online.org/DB_FILE/2007/11/1846.pdf","raw_type":"text"},{"id":"pmh:oai:dsapce.library.iitb.ac.in:100/13953","is_oa":false,"landing_page_url":"http://dspace.library.iitb.ac.in/jspui/handle/100/13953","pdf_url":null,"source":{"id":"https://openalex.org/S4306400899","display_name":"DSpace (IIT Bombay)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I162827531","host_organization_name":"Indian Institute of Technology Bombay","host_organization_lineage":["https://openalex.org/I162827531"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.1007/s10107-009-0282-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-009-0282-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-009-0282-9.pdf","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":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5603195941","display_name":"Conic Integer Programming","funder_award_id":"0700203","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309321","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2101719620.pdf","grobid_xml":"https://content.openalex.org/works/W2101719620.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1481126596","https://openalex.org/W1508501959","https://openalex.org/W1549174816","https://openalex.org/W1568307856","https://openalex.org/W1922855725","https://openalex.org/W1964191135","https://openalex.org/W1975365958","https://openalex.org/W1995151259","https://openalex.org/W1997826608","https://openalex.org/W2007126271","https://openalex.org/W2024753861","https://openalex.org/W2034186905","https://openalex.org/W2047688435","https://openalex.org/W2100189126","https://openalex.org/W2105235982","https://openalex.org/W2106871914","https://openalex.org/W2107395148","https://openalex.org/W2112538451","https://openalex.org/W2158515702"],"related_works":["https://openalex.org/W3199026565","https://openalex.org/W4323321439","https://openalex.org/W3124564720","https://openalex.org/W4302819359","https://openalex.org/W2952330476","https://openalex.org/W2101719620","https://openalex.org/W4232431455","https://openalex.org/W2941986668","https://openalex.org/W2995925505","https://openalex.org/W3116484972"],"abstract_inverted_index":{"Lifting":[0,20],"is":[1],"a":[2,76],"procedure":[3],"for":[4,8,14,33,75,84,99,117],"deriving":[5],"valid":[6,12,31,73,83],"inequalities":[7,13,32,74,82],"mixed-integer":[9],"sets":[10],"from":[11,80],"suitable":[15],"restrictions":[16],"of":[17,55],"those":[18],"sets.":[19],"has":[21,39],"been":[22,40],"shown":[23],"to":[24,43,57,70,90,108,114],"be":[25],"very":[26],"effective":[27],"in":[28],"developing":[29],"strong":[30],"linear":[34,118],"integer":[35,59,62,78,101,119],"programming":[36,120],"and":[37],"it":[38],"successfully":[41],"used":[42],"solve":[44],"such":[45],"problems":[46],"with":[47,64],"branch-and-cut":[48],"algorithms.":[49],"Here":[50],"we":[51,94],"generalize":[52],"the":[53,92,104,115],"theory":[54],"lifting":[56,98,112,116],"conic":[58,65,72,77,81,100,111],"programming,":[60],"i.e.,":[61],"programs":[63],"constraints.":[66],"We":[67],"show":[68],"how":[69],"derive":[71],"program":[79],"its":[85],"lower-dimensional":[86],"restrictions.":[87],"In":[88],"order":[89],"simplify":[91],"computations,":[93],"also":[95],"discuss":[96],"sequence-independent":[97],"programs.":[102],"When":[103],"cones":[105],"are":[106],"restricted":[107],"nonnegative":[109],"orthants,":[110],"reduces":[113],"as":[121],"one":[122],"may":[123],"expect.":[124]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":4}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
