{"id":"https://openalex.org/W4211090019","doi":"https://doi.org/10.1007/s10898-022-01128-0","title":"The supporting hyperplane optimization toolkit for convex MINLP","display_name":"The supporting hyperplane optimization toolkit for convex MINLP","publication_year":2022,"publication_date":"2022-02-10","ids":{"openalex":"https://openalex.org/W4211090019","doi":"https://doi.org/10.1007/s10898-022-01128-0"},"language":"en","primary_location":{"id":"doi:10.1007/s10898-022-01128-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10898-022-01128-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10898-022-01128-0.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/s10898-022-01128-0.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030912699","display_name":"Andreas Lundell","orcid":"https://orcid.org/0000-0002-1548-1893"},"institutions":[{"id":"https://openalex.org/I130217899","display_name":"\u00c5bo Akademi University","ror":"https://ror.org/029pk6x14","country_code":"FI","type":"education","lineage":["https://openalex.org/I130217899"]}],"countries":["FI"],"is_corresponding":true,"raw_author_name":"Andreas Lundell","raw_affiliation_strings":["Department of Information Technology, Faculty of Science and Engineering, \u00c5bo Akademi University, Vaasa, Finland"],"raw_orcid":"https://orcid.org/0000-0002-1548-1893","affiliations":[{"raw_affiliation_string":"Department of Information Technology, Faculty of Science and Engineering, \u00c5bo Akademi University, Vaasa, Finland","institution_ids":["https://openalex.org/I130217899"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006006057","display_name":"Jan Kronqvist","orcid":"https://orcid.org/0000-0003-0299-5745"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]},{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["GB","SE"],"is_corresponding":true,"raw_author_name":"Jan Kronqvist","raw_affiliation_strings":["Department of Computing, Imperial College London, London, UK","Optimization and Systems Theory, Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden"],"raw_orcid":"https://orcid.org/0000-0003-0299-5745","affiliations":[{"raw_affiliation_string":"Department of Computing, Imperial College London, London, UK","institution_ids":["https://openalex.org/I47508984"]},{"raw_affiliation_string":"Optimization and Systems Theory, Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037388244","display_name":"Tapio Westerlund","orcid":"https://orcid.org/0000-0002-8979-9642"},"institutions":[{"id":"https://openalex.org/I130217899","display_name":"\u00c5bo Akademi University","ror":"https://ror.org/029pk6x14","country_code":"FI","type":"education","lineage":["https://openalex.org/I130217899"]}],"countries":["FI"],"is_corresponding":true,"raw_author_name":"Tapio Westerlund","raw_affiliation_strings":["Process Design and Systems Engineering, Faculty of Science and Engineering, \u00c5bo Akademi University, Turku, Finland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Process Design and Systems Engineering, Faculty of Science and Engineering, \u00c5bo Akademi University, Turku, Finland","institution_ids":["https://openalex.org/I130217899"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5006006057","https://openalex.org/A5030912699","https://openalex.org/A5037388244"],"corresponding_institution_ids":["https://openalex.org/I130217899","https://openalex.org/I47508984","https://openalex.org/I86987016"],"apc_list":{"value":2780,"currency":"USD","value_usd":2780},"apc_paid":{"value":2780,"currency":"USD","value_usd":2780},"fwci":4.6781,"has_fulltext":true,"cited_by_count":17,"citation_normalized_percentile":{"value":0.95973525,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"84","issue":"1","first_page":"1","last_page":"41"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9987999796867371,"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":0.9987999796867371,"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/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9937999844551086,"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/T11053","display_name":"Process Optimization and Integration","score":0.9915000200271606,"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/solver","display_name":"Solver","score":0.7377294301986694},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6691246032714844},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5644258260726929},{"id":"https://openalex.org/keywords/heuristics","display_name":"Heuristics","score":0.5522225499153137},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.5342017412185669},{"id":"https://openalex.org/keywords/hyperplane","display_name":"Hyperplane","score":0.5164197087287903},{"id":"https://openalex.org/keywords/cutting-plane-method","display_name":"Cutting-plane method","score":0.5041459798812866},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.4898640811443329},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.4555749297142029},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.4097920060157776},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.37308675050735474},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36210352182388306},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3447805345058441},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.07983627915382385}],"concepts":[{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.7377294301986694},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6691246032714844},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5644258260726929},{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.5522225499153137},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.5342017412185669},{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.5164197087287903},{"id":"https://openalex.org/C109839438","wikidata":"https://www.wikidata.org/wiki/Q1762039","display_name":"Cutting-plane method","level":3,"score":0.5041459798812866},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.4898640811443329},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.4555749297142029},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.4097920060157776},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.37308675050735474},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36210352182388306},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3447805345058441},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.07983627915382385},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10898-022-01128-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10898-022-01128-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10898-022-01128-0.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:pure.atira.dk:openaire/23596f5f-0aea-402b-a29e-bcc67737be60","is_oa":true,"landing_page_url":"https://research.abo.fi/en/publications/23596f5f-0aea-402b-a29e-bcc67737be60","pdf_url":null,"source":{"id":"https://openalex.org/S4406923060","display_name":"\u00c5bo Akademi University Research Portal","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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lundell, A, Kronqvist, J & Westerlund, T 2022, 'The supporting hyperplane optimization toolkit for convex MINLP', Journal of Global Optimization, vol. 84, no. 1, 1, pp. 1-41. https://doi.org/10.1007/s10898-022-01128-0","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:RePEc:spr:jglopt:v:84:y:2022:i:1:d:10.1007_s10898-022-01128-0","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10898-022-01128-0","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"}],"best_oa_location":{"id":"doi:10.1007/s10898-022-01128-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10898-022-01128-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10898-022-01128-0.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/G3038228801","display_name":null,"funder_award_id":"NIF\\R1\\182194","funder_id":"https://openalex.org/F4320320006","funder_display_name":"Royal Society"}],"funders":[{"id":"https://openalex.org/F4320320006","display_name":"Royal Society","ror":"https://ror.org/03wnrjx87"},{"id":"https://openalex.org/F4320322400","display_name":"Magnus Ehrnroothin S\u00e4\u00e4ti\u00f6","ror":"https://ror.org/02cdzet69"},{"id":"https://openalex.org/F4320324257","display_name":"Svenska Kulturfonden","ror":"https://ror.org/04a31ep84"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4211090019.pdf","grobid_xml":"https://content.openalex.org/works/W4211090019.grobid-xml"},"referenced_works_count":58,"referenced_works":["https://openalex.org/W54096403","https://openalex.org/W128066468","https://openalex.org/W805566928","https://openalex.org/W1855884329","https://openalex.org/W1918816242","https://openalex.org/W1963753892","https://openalex.org/W1972459914","https://openalex.org/W1989774703","https://openalex.org/W1997215277","https://openalex.org/W2004407575","https://openalex.org/W2007231110","https://openalex.org/W2009815418","https://openalex.org/W2011970986","https://openalex.org/W2017151271","https://openalex.org/W2021674665","https://openalex.org/W2033735555","https://openalex.org/W2045622192","https://openalex.org/W2050339136","https://openalex.org/W2057338659","https://openalex.org/W2057443868","https://openalex.org/W2061962896","https://openalex.org/W2065034096","https://openalex.org/W2066875914","https://openalex.org/W2067569795","https://openalex.org/W2071334094","https://openalex.org/W2072881663","https://openalex.org/W2073135589","https://openalex.org/W2078328524","https://openalex.org/W2082471977","https://openalex.org/W2123871098","https://openalex.org/W2124515075","https://openalex.org/W2160783673","https://openalex.org/W2166797227","https://openalex.org/W2170213261","https://openalex.org/W2176812374","https://openalex.org/W2242422634","https://openalex.org/W2411933627","https://openalex.org/W2489773810","https://openalex.org/W2766511395","https://openalex.org/W2767656582","https://openalex.org/W2767791580","https://openalex.org/W2767914269","https://openalex.org/W2790736634","https://openalex.org/W2791984320","https://openalex.org/W2793437242","https://openalex.org/W2798425997","https://openalex.org/W2801755592","https://openalex.org/W2902723719","https://openalex.org/W2904818131","https://openalex.org/W2916638179","https://openalex.org/W2943368153","https://openalex.org/W2963990227","https://openalex.org/W3007543531","https://openalex.org/W3103379443","https://openalex.org/W3105558219","https://openalex.org/W3106195685","https://openalex.org/W4232598359","https://openalex.org/W4297688559"],"related_works":["https://openalex.org/W2048233275","https://openalex.org/W2110818895","https://openalex.org/W2045076853","https://openalex.org/W1973064890","https://openalex.org/W2002159391","https://openalex.org/W2065369945","https://openalex.org/W3126345618","https://openalex.org/W2038141985","https://openalex.org/W1991394924","https://openalex.org/W3006617646"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2,181],"paper,":[3,182],"an":[4],"open-source":[5,132],"solver":[6,110],"for":[7],"mixed-integer":[8,72],"nonlinear":[9,41],"programming":[10,73],"(MINLP)":[11],"problems":[12,198],"is":[13,36,89,127,149,228],"presented.":[14],"The":[15,34,63,169],"Supporting":[16],"Hyperplane":[17],"Optimization":[18],"Toolkit":[19],"(SHOT)":[20],"combines":[21],"a":[22,77,84,130,137],"dual":[23,64],"strategy":[24,65],"based":[25],"on":[26,186,194,235],"polyhedral":[27,93],"outer":[28],"approximations":[29],"(POA)":[30],"with":[31,48,51,70],"primal":[32],"heuristics.":[33],"POA":[35],"achieved":[37],"by":[38],"expressing":[39],"the":[40,45,52,71,92,103,108,113,187,200,206,222,236],"feasible":[42],"set":[43],"of":[44,205,225],"MINLP":[46,197],"problem":[47,88,202],"linearizations":[49,94],"obtained":[50],"extended":[53,58],"supporting":[54],"hyperplane":[55],"(ESH)":[56],"and":[57,134,146,154,161,172,183],"cutting":[59],"plane":[60],"(ECP)":[61],"algorithms.":[62],"can":[66,155,211],"be":[67,156,212],"tightly":[68],"integrated":[69],"(MIP)":[74],"subsolver":[75],"in":[76,102,116,119,152,158,176,180,209,214],"so-called":[78],"single-tree":[79],"manner,":[80],"i.e.":[81],",":[82],"only":[83],"single":[85],"MIP":[86,104,109],"optimization":[87],"solved,":[90],"where":[91],"are":[95,178,189],"added":[96],"as":[97,129,163,218],"lazy":[98],"constraints":[99],"through":[100,165,191],"callbacks":[101],"solver.":[105],"This":[106],"enables":[107],"to":[111,121,144,231],"reuse":[112],"branching":[114],"tree":[115],"each":[117],"iteration,":[118],"contrast":[120],"most":[122],"other":[123,215,232],"POA-based":[124,216],"methods.":[125],"SHOT":[126,177,210],"available":[128,151],"COIN-OR":[131],"project,":[133],"it":[135,142,227],"utilizes":[136],"flexible":[138],"task-based":[139],"structure":[140],"making":[141],"easy":[143],"extend":[145],"modify.":[147],"It":[148],"currently":[150],"GAMS,":[153],"utilized":[157,213],"AMPL,":[159],"Pyomo":[160],"JuMP":[162],"well":[164],"its":[166],"ASL":[167],"interface.":[168],"main":[170],"functionality":[171],"solution":[173],"strategies":[174],"implemented":[175],"described":[179],"their":[184],"impact":[185],"performance":[188],"illustrated":[190],"numerical":[192],"benchmarks":[193],"406":[195],"convex":[196],"from":[199],"MINLPLib":[201],"library.":[203],"Many":[204],"features":[207],"introduced":[208],"solvers":[217,234],"well.":[219],"To":[220],"show":[221],"overall":[223],"effectiveness":[224],"SHOT,":[226],"also":[229],"compared":[230],"state-of-the-art":[233],"same":[237],"benchmark":[238],"set.":[239]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}
