{"id":"https://openalex.org/W2151462369","doi":"https://doi.org/10.1287/opre.18.3.404","title":"Cutting-Plane Methods without Nested Constraint Sets","display_name":"Cutting-Plane Methods without Nested Constraint Sets","publication_year":1970,"publication_date":"1970-06-01","ids":{"openalex":"https://openalex.org/W2151462369","doi":"https://doi.org/10.1287/opre.18.3.404","mag":"2151462369"},"language":"en","primary_location":{"id":"doi:10.1287/opre.18.3.404","is_oa":false,"landing_page_url":"https://doi.org/10.1287/opre.18.3.404","pdf_url":null,"source":{"id":"https://openalex.org/S125775545","display_name":"Operations Research","issn_l":"0030-364X","issn":["0030-364X","1526-5463"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315699","host_organization_name":"Institute for Operations Research and the Management Sciences","host_organization_lineage":["https://openalex.org/P4310315699"],"host_organization_lineage_names":["Institute for Operations Research and the Management Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Operations Research","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/A5043984862","display_name":"Donald M. Topkis","orcid":null},"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":true,"raw_author_name":"Donald M. Topkis","raw_affiliation_strings":["University of California, Berkeley, California"],"affiliations":[{"raw_affiliation_string":"University of California, Berkeley, California","institution_ids":["https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5043984862"],"corresponding_institution_ids":["https://openalex.org/I95457486"],"apc_list":null,"apc_paid":null,"fwci":15.4581,"has_fulltext":false,"cited_by_count":49,"citation_normalized_percentile":{"value":0.9874739,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"18","issue":"3","first_page":"404","last_page":"413"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12176","display_name":"Optimization and Packing Problems","score":0.9916999936103821,"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/T12176","display_name":"Optimization and Packing Problems","score":0.9916999936103821,"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/T10698","display_name":"Transportation Planning and Optimization","score":0.9900000095367432,"subfield":{"id":"https://openalex.org/subfields/3313","display_name":"Transportation"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9789999723434448,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.7298777103424072},{"id":"https://openalex.org/keywords/cutting-plane-method","display_name":"Cutting-plane method","score":0.7178717851638794},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.7081471681594849},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6824559569358826},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6138966083526611},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5358551740646362},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4834374189376831},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.44701871275901794},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41084423661231995},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.34877294301986694},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.17452892661094666},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08739033341407776},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06597289443016052}],"concepts":[{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.7298777103424072},{"id":"https://openalex.org/C109839438","wikidata":"https://www.wikidata.org/wiki/Q1762039","display_name":"Cutting-plane method","level":3,"score":0.7178717851638794},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.7081471681594849},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6824559569358826},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6138966083526611},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5358551740646362},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4834374189376831},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.44701871275901794},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41084423661231995},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34877294301986694},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.17452892661094666},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08739033341407776},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06597289443016052},{"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1287/opre.18.3.404","is_oa":false,"landing_page_url":"https://doi.org/10.1287/opre.18.3.404","pdf_url":null,"source":{"id":"https://openalex.org/S125775545","display_name":"Operations Research","issn_l":"0030-364X","issn":["0030-364X","1526-5463"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315699","host_organization_name":"Institute for Operations Research and the Management Sciences","host_organization_lineage":["https://openalex.org/P4310315699"],"host_organization_lineage_names":["Institute for Operations Research and the Management Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:inm:oropre:v:18:y:1970:i:3:p:404-413","is_oa":false,"landing_page_url":"http://doi.org/10.1287/opre.18.3.404","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W2013243898","https://openalex.org/W2038614136","https://openalex.org/W2069808690","https://openalex.org/W2084684483","https://openalex.org/W2089492119","https://openalex.org/W2127470768","https://openalex.org/W2136885855","https://openalex.org/W2152122625"],"related_works":["https://openalex.org/W2362705850","https://openalex.org/W3162204513","https://openalex.org/W2371138613","https://openalex.org/W2379672298","https://openalex.org/W2048963458","https://openalex.org/W3169499720","https://openalex.org/W1513565830","https://openalex.org/W3012113686","https://openalex.org/W1996239617","https://openalex.org/W3197304203"],"abstract_inverted_index":{"This":[0],"paper":[1,98],"gives":[2,99],"general":[3],"conditions":[4,69],"for":[5,20,40,79],"the":[6,17,21,54,87,97],"convergence":[7,102],"of":[8,11,45,53,75,77,89],"a":[9,51,72],"class":[10],"cutting-plane":[12],"algorithms":[13,63,88],"without":[14],"requiring":[15],"that":[16],"constraint":[18,66],"sets":[19],"sub-problems":[22],"be":[23,34],"sequentially":[24],"nested.":[25],"Conditions":[26],"are":[27],"given":[28],"under":[29],"which":[30],"inactive":[31],"constraints":[32],"may":[33],"dropped":[35],"after":[36],"each":[37],"subproblem.":[38],"Procedures":[39],"generating":[41],"cutting-planes":[42],"include":[43,83],"those":[44,76],"Kelley,":[46,90],"Cheney":[47,91],"and":[48,50,60,82,92,94],"Goldstein,":[49,93],"generalization":[52],"one":[55],"used":[56],"by":[57],"both":[58],"Zoutendijk":[59],"Veinott.":[61,95],"For":[62],"with":[64],"nested":[65],"sets,":[67],"these":[68],"reduce":[70],"to":[71],"special":[73,85],"case":[74],"Zangwill":[78],"such":[80],"problems":[81],"as":[84],"cases":[86],"Finally,":[96],"an":[100],"arithmetic":[101],"rate.":[103]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
