{"id":"https://openalex.org/W2042170876","doi":"https://doi.org/10.1007/s10107-006-0022-3","title":"Dual multilevel optimization","display_name":"Dual multilevel optimization","publication_year":2006,"publication_date":"2006-09-18","ids":{"openalex":"https://openalex.org/W2042170876","doi":"https://doi.org/10.1007/s10107-006-0022-3","mag":"2042170876"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-006-0022-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-006-0022-3","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","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/A5069178025","display_name":"Timothy A. Davis","orcid":"https://orcid.org/0000-0001-7614-6899"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Timothy A. Davis","raw_affiliation_strings":["Department of Computer and Information Science and Engineering, University of Florida, PO Box 116120, Gainesville, FL, 32611-6120, USA","University of Florida, Department of Computer and Information Science and Engineering, PO Box 116120, 32611-6120, Gainesville, FL, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer and Information Science and Engineering, University of Florida, PO Box 116120, Gainesville, FL, 32611-6120, USA","institution_ids":["https://openalex.org/I33213144"]},{"raw_affiliation_string":"University of Florida, Department of Computer and Information Science and Engineering, PO Box 116120, 32611-6120, Gainesville, FL, USA#TAB#","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002362913","display_name":"William W. Hager","orcid":"https://orcid.org/0000-0003-3132-7017"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"William W. Hager","raw_affiliation_strings":["Department of Mathematics, University of Florida, Gainesville, PO Box 118105, FL, 32611-8105, USA","University of Florida, Department of Mathematics, PO Box 118105, 32611-8105, Gainesville, FL, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Florida, Gainesville, PO Box 118105, FL, 32611-8105, USA","institution_ids":["https://openalex.org/I33213144"]},{"raw_affiliation_string":"University of Florida, Department of Mathematics, PO Box 118105, 32611-8105, Gainesville, FL, USA#TAB#","institution_ids":["https://openalex.org/I33213144"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5002362913"],"corresponding_institution_ids":["https://openalex.org/I33213144"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":1.0159,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.78556616,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"112","issue":"2","first_page":"403","last_page":"425"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9976999759674072,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9975000023841858,"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/simplex-algorithm","display_name":"Simplex algorithm","score":0.7498838305473328},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.7173532843589783},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.664476752281189},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6537925004959106},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.5941431522369385},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.5927740931510925},{"id":"https://openalex.org/keywords/simplex","display_name":"Simplex","score":0.4705671966075897},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.44278544187545776},{"id":"https://openalex.org/keywords/graph-partition","display_name":"Graph partition","score":0.41990625858306885},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3998599350452423},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3566223680973053},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.16605573892593384}],"concepts":[{"id":"https://openalex.org/C144521790","wikidata":"https://www.wikidata.org/wiki/Q134164","display_name":"Simplex algorithm","level":3,"score":0.7498838305473328},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.7173532843589783},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.664476752281189},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6537925004959106},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.5941431522369385},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.5927740931510925},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.4705671966075897},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.44278544187545776},{"id":"https://openalex.org/C48903430","wikidata":"https://www.wikidata.org/wiki/Q491370","display_name":"Graph partition","level":3,"score":0.41990625858306885},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3998599350452423},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3566223680973053},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.16605573892593384},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10107-006-0022-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-006-0022-3","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W570845671","https://openalex.org/W1494838936","https://openalex.org/W1603646489","https://openalex.org/W1995875735","https://openalex.org/W2002257715","https://openalex.org/W2004951603","https://openalex.org/W2016990965","https://openalex.org/W2017466123","https://openalex.org/W2036438040","https://openalex.org/W2036555554","https://openalex.org/W2043839703","https://openalex.org/W2044559999","https://openalex.org/W2049064539","https://openalex.org/W2050448951","https://openalex.org/W2063558363","https://openalex.org/W2063597636","https://openalex.org/W2068683191","https://openalex.org/W2069245506","https://openalex.org/W2070232376","https://openalex.org/W2072197890","https://openalex.org/W2102812372","https://openalex.org/W2118953734","https://openalex.org/W2132250012","https://openalex.org/W2167797964","https://openalex.org/W2170739273","https://openalex.org/W2266946488","https://openalex.org/W2978725006","https://openalex.org/W2993383518","https://openalex.org/W4230055019","https://openalex.org/W4235266393","https://openalex.org/W4285719527","https://openalex.org/W4291236916"],"related_works":["https://openalex.org/W3125083766","https://openalex.org/W2384679317","https://openalex.org/W3143155029","https://openalex.org/W2353454564","https://openalex.org/W2385197181","https://openalex.org/W2027241495","https://openalex.org/W2379462157","https://openalex.org/W165108556","https://openalex.org/W2977677980","https://openalex.org/W1595212828"],"abstract_inverted_index":null,"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}