{"id":"https://openalex.org/W2944947738","doi":"https://doi.org/10.1007/s10898-020-00906-y","title":"On the relation between the extended supporting hyperplane algorithm and Kelley\u2019s cutting plane algorithm","display_name":"On the relation between the extended supporting hyperplane algorithm and Kelley\u2019s cutting plane algorithm","publication_year":2020,"publication_date":"2020-05-13","ids":{"openalex":"https://openalex.org/W2944947738","doi":"https://doi.org/10.1007/s10898-020-00906-y","mag":"2944947738"},"language":"en","primary_location":{"id":"doi:10.1007/s10898-020-00906-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10898-020-00906-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10898-020-00906-y.pdf","source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Global Optimization","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/s10898-020-00906-y.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032461091","display_name":"Felipe Serrano","orcid":"https://orcid.org/0000-0002-7892-3951"},"institutions":[{"id":"https://openalex.org/I195893171","display_name":"Zuse Institute Berlin","ror":"https://ror.org/02eva5865","country_code":"DE","type":"facility","lineage":["https://openalex.org/I195893171"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Felipe Serrano","raw_affiliation_strings":["Department of Mathematical Optimization, Zuse Institute Berlin, Takustr. 7, 14195, Berlin, Germany","Department of Mathematical Optimization, Zuse Institute Berlin, Takustr.\u00a07, 14195, Berlin, Germany"],"raw_orcid":"https://orcid.org/0000-0002-7892-3951","affiliations":[{"raw_affiliation_string":"Department of Mathematical Optimization, Zuse Institute Berlin, Takustr. 7, 14195, Berlin, Germany","institution_ids":["https://openalex.org/I195893171"]},{"raw_affiliation_string":"Department of Mathematical Optimization, Zuse Institute Berlin, Takustr.\u00a07, 14195, Berlin, Germany","institution_ids":["https://openalex.org/I195893171"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020262360","display_name":"Robert Schwarz","orcid":"https://orcid.org/0000-0002-2536-026X"},"institutions":[{"id":"https://openalex.org/I195893171","display_name":"Zuse Institute Berlin","ror":"https://ror.org/02eva5865","country_code":"DE","type":"facility","lineage":["https://openalex.org/I195893171"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Robert Schwarz","raw_affiliation_strings":["Department of Mathematical Optimization, Zuse Institute Berlin, Takustr. 7, 14195, Berlin, Germany","Department of Mathematical Optimization, Zuse Institute Berlin, Takustr.\u00a07, 14195, Berlin, Germany"],"raw_orcid":"https://orcid.org/0000-0002-2536-026X","affiliations":[{"raw_affiliation_string":"Department of Mathematical Optimization, Zuse Institute Berlin, Takustr. 7, 14195, Berlin, Germany","institution_ids":["https://openalex.org/I195893171"]},{"raw_affiliation_string":"Department of Mathematical Optimization, Zuse Institute Berlin, Takustr.\u00a07, 14195, Berlin, Germany","institution_ids":["https://openalex.org/I195893171"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009130251","display_name":"Ambros Gleixner","orcid":"https://orcid.org/0000-0003-0391-5903"},"institutions":[{"id":"https://openalex.org/I195893171","display_name":"Zuse Institute Berlin","ror":"https://ror.org/02eva5865","country_code":"DE","type":"facility","lineage":["https://openalex.org/I195893171"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Ambros Gleixner","raw_affiliation_strings":["Department of Mathematical Optimization, Zuse Institute Berlin, Takustr. 7, 14195, Berlin, Germany","Department of Mathematical Optimization, Zuse Institute Berlin, Takustr.\u00a07, 14195, Berlin, Germany"],"raw_orcid":"https://orcid.org/0000-0003-0391-5903","affiliations":[{"raw_affiliation_string":"Department of Mathematical Optimization, Zuse Institute Berlin, Takustr. 7, 14195, Berlin, Germany","institution_ids":["https://openalex.org/I195893171"]},{"raw_affiliation_string":"Department of Mathematical Optimization, Zuse Institute Berlin, Takustr.\u00a07, 14195, Berlin, Germany","institution_ids":["https://openalex.org/I195893171"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5032461091"],"corresponding_institution_ids":["https://openalex.org/I195893171"],"apc_list":{"value":2780,"currency":"USD","value_usd":2780},"apc_paid":{"value":2780,"currency":"USD","value_usd":2780},"fwci":0.8217,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.66170324,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"78","issue":"1","first_page":"161","last_page":"179"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9997000098228455,"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":0.9997000098228455,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9980999827384949,"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"}},{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9954000115394592,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8562507033348083},{"id":"https://openalex.org/keywords/hyperplane","display_name":"Hyperplane","score":0.8238420486450195},{"id":"https://openalex.org/keywords/cutting-plane-method","display_name":"Cutting-plane method","score":0.7147330045700073},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6972305774688721},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.49036645889282227},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.4793732464313507},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.24940776824951172},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.16475948691368103},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1226053535938263},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.1088324785232544}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8562507033348083},{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.8238420486450195},{"id":"https://openalex.org/C109839438","wikidata":"https://www.wikidata.org/wiki/Q1762039","display_name":"Cutting-plane method","level":3,"score":0.7147330045700073},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6972305774688721},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.49036645889282227},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.4793732464313507},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.24940776824951172},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.16475948691368103},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1226053535938263},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.1088324785232544}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10898-020-00906-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10898-020-00906-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10898-020-00906-y.pdf","source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Global Optimization","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:jglopt:v:78:y:2020:i:1:d:10.1007_s10898-020-00906-y","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10898-020-00906-y","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":null,"raw_type":"article"},{"id":"pmh:oai:econstor.eu:10419/288454","is_oa":true,"landing_page_url":"https://hdl.handle.net/10419/288454","pdf_url":null,"source":{"id":"https://openalex.org/S4306401696","display_name":"Econstor (Econstor)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"doc-type:article"}],"best_oa_location":{"id":"doi:10.1007/s10898-020-00906-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10898-020-00906-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10898-020-00906-y.pdf","source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Global Optimization","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4192406653","display_name":null,"funder_award_id":"05M20ZBM","funder_id":"https://openalex.org/F4320321114","funder_display_name":"Bundesministerium f\u00fcr Bildung und Forschung"},{"id":"https://openalex.org/G5524815408","display_name":null,"funder_award_id":"05M14ZAM,05M20ZBM","funder_id":"https://openalex.org/F4320321114","funder_display_name":"Bundesministerium f\u00fcr Bildung und Forschung"},{"id":"https://openalex.org/G8129675556","display_name":null,"funder_award_id":"03ET1549D","funder_id":"https://openalex.org/F4320323803","funder_display_name":"Bundesministerium f\u00fcr Wirtschaft und Energie"},{"id":"https://openalex.org/G8921868790","display_name":null,"funder_award_id":"05M14ZAM","funder_id":"https://openalex.org/F4320321114","funder_display_name":"Bundesministerium f\u00fcr Bildung und Forschung"}],"funders":[{"id":"https://openalex.org/F4320321114","display_name":"Bundesministerium f\u00fcr Bildung und Forschung","ror":"https://ror.org/04pz7b180"},{"id":"https://openalex.org/F4320323803","display_name":"Bundesministerium f\u00fcr Wirtschaft und Energie","ror":"https://ror.org/02vgg2808"},{"id":"https://openalex.org/F4320334763","display_name":"Leibniz-Gemeinschaft","ror":"https://ror.org/01n6r0e97"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2944947738.pdf","grobid_xml":"https://content.openalex.org/works/W2944947738.grobid-xml"},"referenced_works_count":53,"referenced_works":["https://openalex.org/W73692560","https://openalex.org/W75157487","https://openalex.org/W90642534","https://openalex.org/W637898570","https://openalex.org/W805566928","https://openalex.org/W1551360398","https://openalex.org/W1553702074","https://openalex.org/W1667969928","https://openalex.org/W1960239420","https://openalex.org/W1972848751","https://openalex.org/W1980908866","https://openalex.org/W2001741445","https://openalex.org/W2005435282","https://openalex.org/W2007231110","https://openalex.org/W2009683816","https://openalex.org/W2043155593","https://openalex.org/W2057338659","https://openalex.org/W2061962896","https://openalex.org/W2066875914","https://openalex.org/W2067945915","https://openalex.org/W2069808690","https://openalex.org/W2071334094","https://openalex.org/W2072004299","https://openalex.org/W2088836601","https://openalex.org/W2089492119","https://openalex.org/W2093324910","https://openalex.org/W2098297761","https://openalex.org/W2102379475","https://openalex.org/W2117160627","https://openalex.org/W2156245681","https://openalex.org/W2163062359","https://openalex.org/W2293133283","https://openalex.org/W2346910096","https://openalex.org/W2485305008","https://openalex.org/W2502743114","https://openalex.org/W2590058109","https://openalex.org/W2605907306","https://openalex.org/W2610216665","https://openalex.org/W2611155867","https://openalex.org/W2791984320","https://openalex.org/W2798344481","https://openalex.org/W2808856084","https://openalex.org/W2902723719","https://openalex.org/W3104448045","https://openalex.org/W3106992008","https://openalex.org/W3152358675","https://openalex.org/W4212766343","https://openalex.org/W4246092883","https://openalex.org/W4247489173","https://openalex.org/W4249667877","https://openalex.org/W4249840661","https://openalex.org/W4285719527","https://openalex.org/W6944489308"],"related_works":["https://openalex.org/W2067732528","https://openalex.org/W1641727897","https://openalex.org/W2373677839","https://openalex.org/W2316556093","https://openalex.org/W2148606335","https://openalex.org/W2019207072","https://openalex.org/W2985447680","https://openalex.org/W3024295069","https://openalex.org/W3080467265","https://openalex.org/W3210618"],"abstract_inverted_index":{"Abstract":[0],"Recently,":[1],"Kronqvist":[2],"et":[3],"al.":[4],"(J":[5,63],"Global":[6],"Optim":[7],"64(2):249\u2013272,":[8],"2016)":[9],"rediscovered":[10],"the":[11,38,52,76,83,86],"supporting":[12,53,87],"hyperplane":[13,54,88],"algorithm":[14,39,55,62,89],"of":[15,44,75,85,97],"Veinott":[16],"(Oper":[17],"Res":[18],"15(1):147\u2013152,":[19],"1967)":[20],"and":[21],"demonstrated":[22],"its":[23],"computational":[24],"benefits":[25],"for":[26],"solving":[27],"convex":[28,91,101],"mixed":[29],"integer":[30],"nonlinear":[31],"programs.":[32],"In":[33],"this":[34],"paper":[35],"we":[36,81],"derive":[37],"from":[40],"a":[41,72,79,95],"geometric":[42],"point":[43],"view.":[45],"This":[46],"enables":[47],"us":[48],"to":[49,58,71,90],"show":[50],"that":[51],"is":[56],"equivalent":[57],"Kelley\u2019s":[59],"cutting":[60],"plane":[61],"Soc":[64],"Ind":[65],"Appl":[66],"Math":[67],"8(4):703\u2013712,":[68],"1960)":[69],"applied":[70],"particular":[73],"reformulation":[74],"problem.":[77],"As":[78],"result,":[80],"extend":[82],"applicability":[84],"problems":[92],"represented":[93],"by":[94],"class":[96],"general,":[98],"not":[99],"necessarily":[100],"nor":[102],"differentiable,":[103],"functions.":[104]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}
