{"id":"https://openalex.org/W1987225287","doi":"https://doi.org/10.1007/s10898-012-9961-9","title":"Geometric branch-and-bound methods for constrained global optimization problems","display_name":"Geometric branch-and-bound methods for constrained global optimization problems","publication_year":2012,"publication_date":"2012-08-03","ids":{"openalex":"https://openalex.org/W1987225287","doi":"https://doi.org/10.1007/s10898-012-9961-9","mag":"1987225287"},"language":"en","primary_location":{"id":"doi:10.1007/s10898-012-9961-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10898-012-9961-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10898-012-9961-9.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/s10898-012-9961-9.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050034758","display_name":"Daniel Scholz","orcid":"https://orcid.org/0000-0002-9310-0101"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Daniel Scholz","raw_affiliation_strings":["G\u00f6ttingen, Germany"],"affiliations":[{"raw_affiliation_string":"G\u00f6ttingen, Germany","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5050034758"],"corresponding_institution_ids":[],"apc_list":{"value":2190,"currency":"EUR","value_usd":2780},"apc_paid":{"value":2190,"currency":"EUR","value_usd":2780},"fwci":0.4543,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.61518494,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"57","issue":"3","first_page":"771","last_page":"782"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998999834060669,"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":0.9998999834060669,"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/T12158","display_name":"Guidance and Control Systems","score":0.9896000027656555,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9857000112533569,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/branch-and-bound","display_name":"Branch and bound","score":0.8494349718093872},{"id":"https://openalex.org/keywords/bounding-overwatch","display_name":"Bounding overwatch","score":0.7872785329818726},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7787796258926392},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6994445323944092},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6344765424728394},{"id":"https://openalex.org/keywords/global-optimization","display_name":"Global optimization","score":0.6227403283119202},{"id":"https://openalex.org/keywords/branch-and-cut","display_name":"Branch and cut","score":0.5323002338409424},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5143064260482788},{"id":"https://openalex.org/keywords/branch-and-price","display_name":"Branch and price","score":0.4859555959701538},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4811331331729889},{"id":"https://openalex.org/keywords/geometric-programming","display_name":"Geometric programming","score":0.4547615945339203},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.18799340724945068},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18755373358726501}],"concepts":[{"id":"https://openalex.org/C93693863","wikidata":"https://www.wikidata.org/wiki/Q897659","display_name":"Branch and bound","level":2,"score":0.8494349718093872},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.7872785329818726},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7787796258926392},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6994445323944092},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6344765424728394},{"id":"https://openalex.org/C164752517","wikidata":"https://www.wikidata.org/wiki/Q5570875","display_name":"Global optimization","level":2,"score":0.6227403283119202},{"id":"https://openalex.org/C50797617","wikidata":"https://www.wikidata.org/wiki/Q498566","display_name":"Branch and cut","level":3,"score":0.5323002338409424},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5143064260482788},{"id":"https://openalex.org/C123558587","wikidata":"https://www.wikidata.org/wiki/Q4956382","display_name":"Branch and price","level":3,"score":0.4859555959701538},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4811331331729889},{"id":"https://openalex.org/C20729856","wikidata":"https://www.wikidata.org/wiki/Q2078279","display_name":"Geometric programming","level":2,"score":0.4547615945339203},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.18799340724945068},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18755373358726501},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10898-012-9961-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10898-012-9961-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10898-012-9961-9.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:57:y:2013:i:3:p:771-782","is_oa":false,"landing_page_url":"http://hdl.handle.net/10.1007/s10898-012-9961-9","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"},{"id":"pmh:oai:publications.goettingen-research-online.de:2/144368","is_oa":true,"landing_page_url":"https://resolver.sub.uni-goettingen.de/purl?gro-2/144368","pdf_url":null,"source":{"id":"https://openalex.org/S4306401634","display_name":"GoeScholar  The Publication Server of the Georg-August-Universit\u00e4t G\u00f6ttingen (Georg-August-Universit\u00e4t G\u00f6ttingen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210122495","host_organization_name":"Asklepios Klinik St. Georg","host_organization_lineage":["https://openalex.org/I4210122495"],"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":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s10898-012-9961-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10898-012-9961-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10898-012-9961-9.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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1987225287.pdf","grobid_xml":"https://content.openalex.org/works/W1987225287.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W402691944","https://openalex.org/W607845112","https://openalex.org/W1483874187","https://openalex.org/W1499399028","https://openalex.org/W1964993547","https://openalex.org/W1969761511","https://openalex.org/W1984425167","https://openalex.org/W2011687300","https://openalex.org/W2022071508","https://openalex.org/W2032938471","https://openalex.org/W2034721242","https://openalex.org/W2056371558","https://openalex.org/W2067648572","https://openalex.org/W2074660787","https://openalex.org/W2124990434","https://openalex.org/W2125642377","https://openalex.org/W2272795305","https://openalex.org/W2301746362","https://openalex.org/W2313401481","https://openalex.org/W2483998465","https://openalex.org/W2499108855","https://openalex.org/W2787523326","https://openalex.org/W3146520007","https://openalex.org/W4205131240","https://openalex.org/W4210916633","https://openalex.org/W4212864101","https://openalex.org/W4300549156"],"related_works":["https://openalex.org/W2009796757","https://openalex.org/W1971357083","https://openalex.org/W2084616826","https://openalex.org/W2024753861","https://openalex.org/W1997215277","https://openalex.org/W2008600006","https://openalex.org/W1983294952","https://openalex.org/W1968202374","https://openalex.org/W2889871839","https://openalex.org/W1974138128"],"abstract_inverted_index":{"Geometric":[0],"branch-and-bound":[1,27,66],"methods":[2,67],"are":[3,85],"popular":[4],"solution":[5],"algorithms":[6],"in":[7,14,64,70],"deterministic":[8],"global":[9,31],"optimization":[10,32],"to":[11,23,48],"solve":[12],"problems":[13,33],"small":[15],"dimensions.":[16],"The":[17],"aim":[18],"of":[19,38,52,59,62],"this":[20],"paper":[21],"is":[22,47],"formulate":[24],"a":[25],"geometric":[26,65],"method":[28,55],"for":[29,83],"constrained":[30],"which":[34],"allows":[35],"the":[36,50,53,57,60],"use":[37],"arbitrary":[39],"bounding":[40],"operations.":[41],"In":[42],"particular,":[43],"our":[44],"main":[45],"goal":[46],"prove":[49],"convergence":[51,63],"suggested":[54],"using":[56,80],"concept":[58],"rate":[61],"as":[68],"introduced":[69],"some":[71,75],"recent":[72],"publications.":[73],"Furthermore,":[74],"efficient":[76],"further":[77],"discarding":[78],"tests":[79],"necessary":[81],"conditions":[82],"optimality":[84],"derived":[86],"and":[87],"illustrated":[88],"numerically":[89],"on":[90],"an":[91],"obnoxious":[92],"facility":[93],"location":[94],"problem.":[95]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
