{"id":"https://openalex.org/W1985236000","doi":"https://doi.org/10.1137/s1052623495285886","title":"An $\\epsilon$-Relaxation Method for Separable Convex Cost Network Flow Problems","display_name":"An $\\epsilon$-Relaxation Method for Separable Convex Cost Network Flow Problems","publication_year":1997,"publication_date":"1997-08-01","ids":{"openalex":"https://openalex.org/W1985236000","doi":"https://doi.org/10.1137/s1052623495285886","mag":"1985236000"},"language":"en","primary_location":{"id":"doi:10.1137/s1052623495285886","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1052623495285886","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","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/A5039911471","display_name":"Dimitri P. Bertsekas","orcid":"https://orcid.org/0000-0001-6909-7208"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Dimitri P. Bertsekas","raw_affiliation_strings":["Massachusetts Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091341927","display_name":"Lazaros Polymenakos","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lazaros C. Polymenakos","raw_affiliation_strings":["Massachusetts Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110258450","display_name":"Paul Tseng","orcid":null},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Paul Tseng","raw_affiliation_strings":["University of Washington"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Washington","institution_ids":["https://openalex.org/I201448701"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.7076,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.9309946,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"7","issue":"3","first_page":"853","last_page":"870"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11502","display_name":"Facility Location and Emergency Management","score":0.984000027179718,"subfield":{"id":"https://openalex.org/subfields/1407","display_name":"Organizational Behavior and Human Resource Management"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11502","display_name":"Facility Location and Emergency Management","score":0.984000027179718,"subfield":{"id":"https://openalex.org/subfields/1407","display_name":"Organizational Behavior and Human Resource Management"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9369999766349792,"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/T11770","display_name":"Fiscal Policy and Economic Growth","score":0.9218000173568726,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.792365312576294},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7369679808616638},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.7340378165245056},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6545051336288452},{"id":"https://openalex.org/keywords/flow-network","display_name":"Flow network","score":0.5692608952522278},{"id":"https://openalex.org/keywords/minimum-cost-flow-problem","display_name":"Minimum-cost flow problem","score":0.5624997019767761},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.553541362285614},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.5449215173721313},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.49155840277671814},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35810792446136475},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12134552001953125},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07087686657905579}],"concepts":[{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.792365312576294},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7369679808616638},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.7340378165245056},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6545051336288452},{"id":"https://openalex.org/C114809511","wikidata":"https://www.wikidata.org/wiki/Q1412924","display_name":"Flow network","level":2,"score":0.5692608952522278},{"id":"https://openalex.org/C99545648","wikidata":"https://www.wikidata.org/wiki/Q2897180","display_name":"Minimum-cost flow problem","level":3,"score":0.5624997019767761},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.553541362285614},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.5449215173721313},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.49155840277671814},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35810792446136475},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12134552001953125},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07087686657905579},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s1052623495285886","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1052623495285886","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W115980880","https://openalex.org/W1488595466","https://openalex.org/W1493391054","https://openalex.org/W1538875977","https://openalex.org/W1603765807","https://openalex.org/W1964119857","https://openalex.org/W1964160573","https://openalex.org/W1964540128","https://openalex.org/W1970403725","https://openalex.org/W1983853123","https://openalex.org/W1993305973","https://openalex.org/W2001274023","https://openalex.org/W2017466123","https://openalex.org/W2032545668","https://openalex.org/W2033976741","https://openalex.org/W2033982221","https://openalex.org/W2034306657","https://openalex.org/W2035934281","https://openalex.org/W2037823059","https://openalex.org/W2044973895","https://openalex.org/W2046715803","https://openalex.org/W2057750651","https://openalex.org/W2059616758","https://openalex.org/W2061670230","https://openalex.org/W2061872629","https://openalex.org/W2069958114","https://openalex.org/W2149342630","https://openalex.org/W2159046795","https://openalex.org/W2403039657","https://openalex.org/W2692373750","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2035934281","https://openalex.org/W1497106612","https://openalex.org/W2044973895","https://openalex.org/W1582098563","https://openalex.org/W1559582792","https://openalex.org/W2149342630","https://openalex.org/W2048441979","https://openalex.org/W2046715803","https://openalex.org/W1977545325","https://openalex.org/W1603765807","https://openalex.org/W2338905098","https://openalex.org/W2155370486","https://openalex.org/W2039651888","https://openalex.org/W2007313851","https://openalex.org/W1542339055","https://openalex.org/W2952526662","https://openalex.org/W1968143987","https://openalex.org/W1573199930","https://openalex.org/W1515029502","https://openalex.org/W115980880"],"abstract_inverted_index":{"We":[0,40,58],"propose":[1],"a":[2,47],"new":[3],"method":[4,19,23,33,44,66],"for":[5,25,75],"the":[6,9,21,43,65],"solution":[7],"of":[8],"single":[10],"commodity,":[11],"separable":[12],"convex":[13],"cost":[14,27,38],"network":[15],"flow":[16],"problem.":[17],"The":[18],"generalizes":[20],"$\\epsilon$-relaxation":[22],"developed":[24],"linear":[26,37],"problems":[28],"and":[29,51],"reduces":[30],"to":[31,36],"that":[32,42,64],"when":[34],"applied":[35],"problems.":[39,77],"show":[41],"terminates":[45],"with":[46],"near":[48],"optimal":[49],"solution,":[50],"we":[52],"provide":[53],"an":[54],"associated":[55],"complexity":[56],"analysis.":[57],"also":[59],"present":[60],"computational":[61],"results":[62],"showing":[63],"is":[67],"much":[68],"faster":[69],"than":[70],"earlier":[71],"relaxation":[72],"methods,":[73],"particularly":[74],"ill-conditioned":[76]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
