{"id":"https://openalex.org/W1993161326","doi":"https://doi.org/10.1137/0804004","title":"Fast Approximation Schemes for Convex Programs with Many Blocks and Coupling Constraints","display_name":"Fast Approximation Schemes for Convex Programs with Many Blocks and Coupling Constraints","publication_year":1994,"publication_date":"1994-02-01","ids":{"openalex":"https://openalex.org/W1993161326","doi":"https://doi.org/10.1137/0804004","mag":"1993161326"},"language":"en","primary_location":{"id":"doi:10.1137/0804004","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0804004","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/A5084098678","display_name":"Michael D. Grigoriadis","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michael D. Grigoriadis","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5110103498","display_name":"Leonid G. Khachiyan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Leonid G. Khachiyan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.4456,"has_fulltext":false,"cited_by_count":140,"citation_normalized_percentile":{"value":0.9694351,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"4","issue":"1","first_page":"86","last_page":"107"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9983999729156494,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/mathematics","display_name":"Mathematics","score":0.7341905832290649},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.5687596797943115},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.5465249419212341},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5181054472923279},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.5164492130279541},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.513279914855957},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5098258852958679},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.41914311051368713},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.41710686683654785},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.34023576974868774},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.320620596408844}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7341905832290649},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.5687596797943115},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.5465249419212341},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5181054472923279},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.5164492130279541},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.513279914855957},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5098258852958679},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.41914311051368713},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.41710686683654785},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34023576974868774},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.320620596408844},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0804004","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0804004","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":[{"display_name":"Decent work and economic growth","score":0.5099999904632568,"id":"https://metadata.un.org/sdg/8"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1978119584","https://openalex.org/W1983743030","https://openalex.org/W1997231674","https://openalex.org/W2005859793","https://openalex.org/W2013469283","https://openalex.org/W2015560695","https://openalex.org/W2021136283","https://openalex.org/W2035652501","https://openalex.org/W2069277547","https://openalex.org/W2077122251","https://openalex.org/W2104103056","https://openalex.org/W2118152326","https://openalex.org/W2136885855","https://openalex.org/W2149254401","https://openalex.org/W4249667877"],"related_works":["https://openalex.org/W4256429076","https://openalex.org/W2036012028","https://openalex.org/W4386395423","https://openalex.org/W3044475370","https://openalex.org/W4366562581","https://openalex.org/W4387870386","https://openalex.org/W3153752017","https://openalex.org/W4387635768","https://openalex.org/W2187449906","https://openalex.org/W2962818859"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"block-coordinate":[3],"descent":[4],"algorithms":[5,44],"for":[6,65,110,154,193],"the":[7,111,121,198],"approximate":[8,199],"solution":[9,200],"of":[10,18,22,91,114,116,120,141,157,181,188,201],"large":[11],"structured":[12],"convex":[13,25,35],"programming":[14],"problems.":[15],"The":[16,43,106,147],"constraints":[17,67],"such":[19,66,159],"problems":[20,64,96,161],"consist":[21],"K":[23,86,94],"disjoint":[24],"compact":[26],"sets":[27],"$B^k":[28],"$":[29],"called":[30,38],"blocks,":[31],"and":[32,138,173,178],"M":[33,79],"nonnegative-valued":[34],"block-separable":[36],"inequalities":[37],"coupling":[39],"or":[40,103],"resource":[41],"constraints.":[42],"are":[45],"based":[46],"on":[47],"an":[48],"exponential":[49],"potential":[50],"function":[51],"reduction":[52],"technique.":[53],"It":[54],"is":[55,144,191,204],"shown":[56],"that":[57],"feasibility":[58],"as":[59,61,160],"well":[60],"min-mix":[62],"resource-sharing":[63],"can":[68],"be":[69],"solved":[70],"to":[71,97,129,136],"a":[72,98,117,126,155,194],"relative":[73,196],"accuracy":[74],"$\\varepsilon$":[75],"in":[76,104,205],"$O(":[77],"K\\ln":[78],"(":[80],"\\varepsilon^{":[81],"-":[82],"2}":[83],"+":[84],"\\ln":[85],")":[87],")$":[88],"iterations,":[89],"each":[90,132],"which":[92,123],"solves":[93],"block":[95,128],"comparable":[99],"accuracy,":[100,197],"either":[101],"sequentially":[102],"parallel.":[105],"same":[107],"bound":[108],"holds":[109],"expected":[112],"number":[113,156],"iterations":[115],"randomized":[118],"variant":[119],"algorithm":[122],"uniformly":[124],"selects":[125],"random":[127],"process":[130],"at":[131],"iteration.":[133],"An":[134],"extension":[135],"objective":[137],"constraint":[139],"functions":[140],"arbitrary":[142],"sign":[143],"also":[145],"presented.":[146],"above":[148],"results":[149],"yield":[150],"fast":[151],"approximation":[152],"schemes":[153],"applications":[158],"with":[162,169],"additively":[163],"separable":[164],"functions,":[165],"generalized":[166],"concurrent":[167],"flows":[168],"side":[170],"constraints,":[171],"linear":[172],"nonlinear":[174],"supply-sharing":[175],"transportation":[176],"networks,":[177],"deterministic":[179],"equivalents":[180],"certain":[182],"two-stage":[183],"stochastic":[184],"programs.":[185],"Another":[186],"consequence":[187],"this":[189],"analysis":[190],"that,":[192],"fixed":[195],"matrix":[202],"games":[203],"$NC$.":[206]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":16},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":2}],"updated_date":"2026-07-31T08:31:51.225901","created_date":"2025-10-10T00:00:00"}
