{"id":"https://openalex.org/W4385175567","doi":"https://doi.org/10.1007/s10957-023-02254-9","title":"A Successive Linear Relaxation Method for MINLPs with Multivariate Lipschitz Continuous Nonlinearities","display_name":"A Successive Linear Relaxation Method for MINLPs with Multivariate Lipschitz Continuous Nonlinearities","publication_year":2023,"publication_date":"2023-07-23","ids":{"openalex":"https://openalex.org/W4385175567","doi":"https://doi.org/10.1007/s10957-023-02254-9"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-023-02254-9","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s10957-023-02254-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-023-02254-9.pdf","source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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 Optimization Theory and Applications","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/s10957-023-02254-9.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012480793","display_name":"Julia Gr\u00fcbel","orcid":null},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Julia Gr\u00fcbel","raw_affiliation_strings":["Energie Campus N\u00fcrnberg, F\u00fcrther Str. 250, 90429, Nuremberg, Germany","Energie Campus N\u00fcrnberg, F\u00fcrther Str.\u00a0250, 90429, Nuremberg, Germany","Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg (FAU), Lange Gasse 20, 90403, Nuremberg, Germany","Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg (FAU), Lange Gasse\u00a020, 90403, Nuremberg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Energie Campus N\u00fcrnberg, F\u00fcrther Str. 250, 90429, Nuremberg, Germany","institution_ids":[]},{"raw_affiliation_string":"Energie Campus N\u00fcrnberg, F\u00fcrther Str.\u00a0250, 90429, Nuremberg, Germany","institution_ids":[]},{"raw_affiliation_string":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg (FAU), Lange Gasse 20, 90403, Nuremberg, Germany","institution_ids":["https://openalex.org/I181369854"]},{"raw_affiliation_string":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg (FAU), Lange Gasse\u00a020, 90403, Nuremberg, Germany","institution_ids":["https://openalex.org/I181369854"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026739880","display_name":"Richard Krug","orcid":null},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Richard Krug","raw_affiliation_strings":["Department of Data Science, Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg (FAU), Cauerstr. 11, 91058, Erlangen, Germany","Department of Data Science, Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg (FAU), Cauerstr.\u00a011, 91058, Erlangen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Data Science, Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg (FAU), Cauerstr. 11, 91058, Erlangen, Germany","institution_ids":["https://openalex.org/I181369854"]},{"raw_affiliation_string":"Department of Data Science, Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg (FAU), Cauerstr.\u00a011, 91058, Erlangen, Germany","institution_ids":["https://openalex.org/I181369854"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002857019","display_name":"Martin Schmidt","orcid":"https://orcid.org/0000-0001-6208-5677"},"institutions":[{"id":"https://openalex.org/I89864525","display_name":"Universit\u00e4t Trier","ror":"https://ror.org/02778hg05","country_code":"DE","type":"education","lineage":["https://openalex.org/I89864525"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Martin Schmidt","raw_affiliation_strings":["Department of Mathematics, Trier University, Universit\u00e4tsring 15, 54296, Trier, Germany","Department of Mathematics, Trier University, Universit\u00e4tsring\u00a015, 54296, Trier, Germany"],"raw_orcid":"https://orcid.org/0000-0001-6208-5677","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Trier University, Universit\u00e4tsring 15, 54296, Trier, Germany","institution_ids":["https://openalex.org/I89864525"]},{"raw_affiliation_string":"Department of Mathematics, Trier University, Universit\u00e4tsring\u00a015, 54296, Trier, Germany","institution_ids":["https://openalex.org/I89864525"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054920423","display_name":"Winnifried Wollner","orcid":"https://orcid.org/0000-0002-6571-8043"},"institutions":[{"id":"https://openalex.org/I159176309","display_name":"Universit\u00e4t Hamburg","ror":"https://ror.org/00g30e956","country_code":"DE","type":"education","lineage":["https://openalex.org/I159176309"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Winnifried Wollner","raw_affiliation_strings":["MIN Fakul\u00e4t, Fachbereich Mathematik, Universit\u00e4t Hamburg, Bundesstr. 55, 20146, Hamburg, Germany","MIN Fakul\u00e4t, Fachbereich Mathematik, Universit\u00e4t Hamburg, Bundesstr.\u00a055, 20146, Hamburg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MIN Fakul\u00e4t, Fachbereich Mathematik, Universit\u00e4t Hamburg, Bundesstr. 55, 20146, Hamburg, Germany","institution_ids":["https://openalex.org/I159176309"]},{"raw_affiliation_string":"MIN Fakul\u00e4t, Fachbereich Mathematik, Universit\u00e4t Hamburg, Bundesstr.\u00a055, 20146, Hamburg, Germany","institution_ids":["https://openalex.org/I159176309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5002857019"],"corresponding_institution_ids":["https://openalex.org/I89864525"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":1.1444,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.73956511,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"198","issue":"3","first_page":"1077","last_page":"1117"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9973999857902527,"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":0.9973999857902527,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.987500011920929,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9592999815940857,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.8379867076873779},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.6965857744216919},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6785597801208496},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5601407885551453},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.5534489750862122},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.5289347767829895},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.49949169158935547},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4971652328968048},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49115416407585144},{"id":"https://openalex.org/keywords/linear-programming-relaxation","display_name":"Linear programming relaxation","score":0.46016523241996765},{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.4505409300327301},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.4193033277988434},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.23912250995635986},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21704712510108948},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09634938836097717}],"concepts":[{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.8379867076873779},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.6965857744216919},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6785597801208496},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5601407885551453},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.5534489750862122},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.5289347767829895},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.49949169158935547},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4971652328968048},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49115416407585144},{"id":"https://openalex.org/C25360446","wikidata":"https://www.wikidata.org/wiki/Q1512771","display_name":"Linear programming relaxation","level":3,"score":0.46016523241996765},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.4505409300327301},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.4193033277988434},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.23912250995635986},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21704712510108948},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09634938836097717},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10957-023-02254-9","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s10957-023-02254-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-023-02254-9.pdf","source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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 Optimization Theory and Applications","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:joptap:v:198:y:2023:i:3:d:10.1007_s10957-023-02254-9","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10957-023-02254-9","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/s10957-023-02254-9","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s10957-023-02254-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-023-02254-9.pdf","source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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 Optimization Theory and Applications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2862657677","display_name":null,"funder_award_id":"CRC TRR 154","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G7491996025","display_name":null,"funder_award_id":"TRR 154","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4385175567.pdf"},"referenced_works_count":47,"referenced_works":["https://openalex.org/W10227180","https://openalex.org/W128066468","https://openalex.org/W181733065","https://openalex.org/W1521386166","https://openalex.org/W1588628884","https://openalex.org/W1600371943","https://openalex.org/W1820125862","https://openalex.org/W1970101292","https://openalex.org/W1978837378","https://openalex.org/W1982658920","https://openalex.org/W1984516801","https://openalex.org/W1986778884","https://openalex.org/W2009932764","https://openalex.org/W2011039300","https://openalex.org/W2047341913","https://openalex.org/W2048312720","https://openalex.org/W2052763589","https://openalex.org/W2053427412","https://openalex.org/W2057338659","https://openalex.org/W2071334094","https://openalex.org/W2104840146","https://openalex.org/W2110964083","https://openalex.org/W2133304166","https://openalex.org/W2170213261","https://openalex.org/W2291780936","https://openalex.org/W2334285086","https://openalex.org/W2403192619","https://openalex.org/W2417992597","https://openalex.org/W2499145065","https://openalex.org/W2521656710","https://openalex.org/W2790264739","https://openalex.org/W2791332936","https://openalex.org/W2811067097","https://openalex.org/W2811083908","https://openalex.org/W2902723719","https://openalex.org/W2968452945","https://openalex.org/W2980369525","https://openalex.org/W3107118572","https://openalex.org/W3126901467","https://openalex.org/W3157498319","https://openalex.org/W3171216778","https://openalex.org/W4212864101","https://openalex.org/W4293177929","https://openalex.org/W4300184951","https://openalex.org/W4318942333","https://openalex.org/W4378619654","https://openalex.org/W4393895844"],"related_works":["https://openalex.org/W2066305403","https://openalex.org/W2033140592","https://openalex.org/W2107689258","https://openalex.org/W4205854323","https://openalex.org/W2004417381","https://openalex.org/W2115855742","https://openalex.org/W2059496069","https://openalex.org/W3149578574","https://openalex.org/W4387578030","https://openalex.org/W132850461"],"abstract_inverted_index":{"Abstract":[0],"We":[1,143,200],"present":[2],"a":[3,47,58,63,72,153],"novel":[4],"method":[5,51,149,170,216],"for":[6,205],"mixed-integer":[7,64,189],"optimization":[8,176],"problems":[9,177],"with":[10,178],"multivariate":[11,122,125],"and":[12,36,71,106,112,117,150,167,180,188,208],"Lipschitz":[13,42,90],"continuous":[14],"nonlinearities.":[15],"In":[16],"particular,":[17],"we":[18,31,38,54,99,158],"do":[19],"not":[20],"assume":[21],"that":[22,30,37,173],"the":[23,68,79,83,89,93,101,119,136,140,145,160,163,168,202,211,214],"nonlinear":[24,187],"constraints":[25],"are":[26],"explicitly":[27],"given":[28],"but":[29],"can":[32,194],"only":[33],"evaluate":[34],"them":[35],"know":[39],"their":[40,131],"global":[41],"constants.":[43],"The":[44],"algorithm":[45],"is":[46,62,75],"successive":[48],"linear":[49,65,80],"relaxation":[50,66,81],"in":[52],"which":[53,61,74],"alternate":[55],"between":[56],"solving":[57],"master":[59,85],"problem,":[60,70],"of":[67,82,103,121,139,147,162,191,213],"original":[69],"subproblem,":[73],"designed":[76],"to":[77,219],"tighten":[78],"next":[84],"problem":[86,165],"by":[87,171,197],"using":[88],"information":[91],"about":[92],"respective":[94],"functions.":[95],"By":[96],"doing":[97],"so,":[98],"follow":[100],"ideas":[102],"Schmidt,":[104],"Sirvent,":[105],"Wollner":[107],"(Math":[108],"Program":[109],"178(1):449\u2013483":[110],"(2019)":[111],"Optim":[113],"Lett":[114],"16(5):1355-1372":[115],"(2022))":[116],"improve":[118],"tackling":[120],"constraints.":[123],"Although":[124],"nonlinearities":[126],"obviously":[127],"increase":[128],"modeling":[129],"capabilities,":[130],"incorporation":[132],"also":[133,151],"significantly":[134],"increases":[135],"computational":[137],"burden":[138],"proposed":[141,169],"algorithm.":[142],"prove":[144],"correctness":[146],"our":[148,198],"derive":[152],"worst-case":[154],"iteration":[155],"bound.":[156],"Finally,":[157],"show":[159],"generality":[161],"addressed":[164],"class":[166],"illustrating":[172],"both":[174,206],"bilevel":[175],"nonconvex":[179],"quadratic":[181],"lower":[182],"levels":[183],"as":[184,186],"well":[185],"models":[190],"gas":[192],"transport":[193],"be":[195],"tackled":[196],"method.":[199],"provide":[201],"necessary":[203],"theory":[204],"applications":[207],"briefly":[209],"illustrate":[210],"outcomes":[212],"new":[215],"when":[217],"applied":[218],"these":[220],"two":[221],"problems.":[222]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-06-13T06:13:01.061226","created_date":"2025-10-10T00:00:00"}
