{"id":"https://openalex.org/W2049847730","doi":"https://doi.org/10.1007/s10479-005-3451-0","title":"Logic-Based Modeling and Solution of Nonlinear Discrete/Continuous Optimization Problems","display_name":"Logic-Based Modeling and Solution of Nonlinear Discrete/Continuous Optimization Problems","publication_year":2005,"publication_date":"2005-09-15","ids":{"openalex":"https://openalex.org/W2049847730","doi":"https://doi.org/10.1007/s10479-005-3451-0","mag":"2049847730"},"language":"en","primary_location":{"id":"doi:10.1007/s10479-005-3451-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10479-005-3451-0","pdf_url":null,"source":{"id":"https://openalex.org/S57667410","display_name":"Annals of Operations Research","issn_l":"0254-5330","issn":["0254-5330","1572-9338"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of 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/A5079268986","display_name":"Sang-Bum Lee","orcid":"https://orcid.org/0000-0001-5761-8483"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sangbum Lee","raw_affiliation_strings":["Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA15213","Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA15213","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh,","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056017028","display_name":"Ignacio E. Grossmann","orcid":"https://orcid.org/0000-0002-7210-084X"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ignacio E. Grossmann","raw_affiliation_strings":["Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA15213","Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA15213","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh,","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5056017028"],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":1.6443,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.83110835,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"139","issue":"1","first_page":"267","last_page":"288"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9991999864578247,"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":0.9991999864578247,"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":0.9987000226974487,"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/T11053","display_name":"Process Optimization and Integration","score":0.9976000189781189,"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/nonlinear-programming","display_name":"Nonlinear programming","score":0.6835353970527649},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.627490758895874},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6225534677505493},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5759187936782837},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.536176323890686},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5120304226875305},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4913577139377594},{"id":"https://openalex.org/keywords/continuous-optimization","display_name":"Continuous optimization","score":0.4683009684085846},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.46356117725372314},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4307805299758911},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.3875955045223236},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.18662390112876892}],"concepts":[{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.6835353970527649},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.627490758895874},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6225534677505493},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5759187936782837},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.536176323890686},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5120304226875305},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4913577139377594},{"id":"https://openalex.org/C92995354","wikidata":"https://www.wikidata.org/wiki/Q5165499","display_name":"Continuous optimization","level":4,"score":0.4683009684085846},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.46356117725372314},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4307805299758911},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.3875955045223236},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.18662390112876892},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"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/C122357587","wikidata":"https://www.wikidata.org/wiki/Q6934508","display_name":"Multi-swarm optimization","level":3,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"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/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s10479-005-3451-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10479-005-3451-0","pdf_url":null,"source":{"id":"https://openalex.org/S57667410","display_name":"Annals of Operations Research","issn_l":"0254-5330","issn":["0254-5330","1572-9338"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.18.5845","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.18.5845","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://egon.cheme.cmu.edu/Group/Papers/GrossmannAnnals.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.294.7042","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.294.7042","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://egon.cheme.cmu.edu/Papers/LeeLogicBased.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.325.4398","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.325.4398","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://cepac.cheme.cmu.edu/pasi2008/slides/vecchietti/library/reading/SangbumAnnals.pdf","raw_type":"text"},{"id":"pmh:oai:RePEc:spr:annopr:v:139:y:2005:i:1:p:267-288:10.1007/s10479-005-3451-0","is_oa":false,"landing_page_url":"http://hdl.handle.net/10.1007/s10479-005-3451-0","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":null,"sustainable_development_goals":[{"display_name":"Decent work and economic growth","id":"https://metadata.un.org/sdg/8","score":0.7099999785423279}],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320310207","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":65,"referenced_works":["https://openalex.org/W1499399028","https://openalex.org/W1524967768","https://openalex.org/W1538999574","https://openalex.org/W1541170979","https://openalex.org/W1542918674","https://openalex.org/W1553702074","https://openalex.org/W1563600186","https://openalex.org/W1965970856","https://openalex.org/W1966523142","https://openalex.org/W1968143987","https://openalex.org/W1968258027","https://openalex.org/W1970193303","https://openalex.org/W1972997295","https://openalex.org/W1973987247","https://openalex.org/W1975387421","https://openalex.org/W1987924891","https://openalex.org/W1988095917","https://openalex.org/W1988622494","https://openalex.org/W1997215277","https://openalex.org/W2007231110","https://openalex.org/W2009683816","https://openalex.org/W2016690114","https://openalex.org/W2019974854","https://openalex.org/W2021947147","https://openalex.org/W2022540256","https://openalex.org/W2023059010","https://openalex.org/W2030958139","https://openalex.org/W2033735555","https://openalex.org/W2044121814","https://openalex.org/W2048230499","https://openalex.org/W2048454955","https://openalex.org/W2049143039","https://openalex.org/W2049505431","https://openalex.org/W2051668769","https://openalex.org/W2053236872","https://openalex.org/W2054168093","https://openalex.org/W2057338659","https://openalex.org/W2057586259","https://openalex.org/W2057797261","https://openalex.org/W2061962896","https://openalex.org/W2066875914","https://openalex.org/W2069808690","https://openalex.org/W2071334094","https://openalex.org/W2078037398","https://openalex.org/W2090633148","https://openalex.org/W2091364465","https://openalex.org/W2093022060","https://openalex.org/W2100890245","https://openalex.org/W2104840146","https://openalex.org/W2105887395","https://openalex.org/W2106264302","https://openalex.org/W2130183935","https://openalex.org/W2134094348","https://openalex.org/W2137972592","https://openalex.org/W2166797227","https://openalex.org/W2167539320","https://openalex.org/W2295940297","https://openalex.org/W2378213882","https://openalex.org/W2505968561","https://openalex.org/W4212864101","https://openalex.org/W4240374930","https://openalex.org/W4248948761","https://openalex.org/W4251711537","https://openalex.org/W4253214256","https://openalex.org/W4253741566"],"related_works":["https://openalex.org/W2353523849","https://openalex.org/W2088344732","https://openalex.org/W2478592842","https://openalex.org/W2047956094","https://openalex.org/W4309490307","https://openalex.org/W1980522505","https://openalex.org/W4375949242","https://openalex.org/W2003270086","https://openalex.org/W2332119567","https://openalex.org/W4253768562"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}