{"id":"https://openalex.org/W2229196312","doi":"https://doi.org/10.1109/tac.2017.2677879","title":"Convergence Rate of Distributed ADMM Over Networks","display_name":"Convergence Rate of Distributed ADMM Over Networks","publication_year":2017,"publication_date":"2017-03-07","ids":{"openalex":"https://openalex.org/W2229196312","doi":"https://doi.org/10.1109/tac.2017.2677879","mag":"2229196312"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2017.2677879","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2017.2677879","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1601.00194","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006356937","display_name":"Ali Makhdoumi","orcid":"https://orcid.org/0000-0001-5422-0314"},"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":true,"raw_author_name":"Ali Makhdoumi","raw_affiliation_strings":["Massachusetts Institute of Technology, Cambridge, MA, USA","Massachusetts Institute Of Technology#TAB#"],"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Massachusetts Institute Of Technology#TAB#","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067307504","display_name":"Asuman Ozdaglar","orcid":"https://orcid.org/0000-0002-1827-1285"},"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":"Asuman Ozdaglar","raw_affiliation_strings":["Massachusetts Institute of Technology, Cambridge, MA, USA","Massachusetts Institute of Technology Cambridge, MA USA"],"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Massachusetts Institute of Technology Cambridge, MA USA","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5006356937"],"corresponding_institution_ids":["https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":1.8778932,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.78334252,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"62","issue":"10","first_page":"5082","last_page":"5095"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9948999881744385,"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"}},{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9933000206947327,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.7436738610267639},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.6988168358802795},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6834248304367065},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5883963108062744},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5873732566833496},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5764262676239014},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5681565403938293},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5182121396064758},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4914315938949585},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4899060130119324},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.45686715841293335},{"id":"https://openalex.org/keywords/distributed-algorithm","display_name":"Distributed algorithm","score":0.422895610332489},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37407100200653076},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36895066499710083},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3097277283668518},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.14981064200401306},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1338869333267212},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07009035348892212}],"concepts":[{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.7436738610267639},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.6988168358802795},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6834248304367065},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5883963108062744},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5873732566833496},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5764262676239014},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5681565403938293},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5182121396064758},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4914315938949585},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4899060130119324},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.45686715841293335},{"id":"https://openalex.org/C130120984","wikidata":"https://www.wikidata.org/wiki/Q2835898","display_name":"Distributed algorithm","level":2,"score":0.422895610332489},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37407100200653076},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36895066499710083},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3097277283668518},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.14981064200401306},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1338869333267212},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07009035348892212},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","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/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tac.2017.2677879","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2017.2677879","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1601.00194","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1601.00194","pdf_url":"https://arxiv.org/pdf/1601.00194","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:2229196312","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1601.00194","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1601.00194","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1601.00194","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1601.00194","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1601.00194","pdf_url":"https://arxiv.org/pdf/1601.00194","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":115,"referenced_works":["https://openalex.org/W130696423","https://openalex.org/W199271301","https://openalex.org/W1532777473","https://openalex.org/W1547358136","https://openalex.org/W1549918636","https://openalex.org/W1578099820","https://openalex.org/W1583497301","https://openalex.org/W1587744656","https://openalex.org/W1603765807","https://openalex.org/W1626317705","https://openalex.org/W1674574997","https://openalex.org/W1922736325","https://openalex.org/W1966333543","https://openalex.org/W1966735762","https://openalex.org/W1969061574","https://openalex.org/W1986080131","https://openalex.org/W1992841740","https://openalex.org/W2019569173","https://openalex.org/W2029080014","https://openalex.org/W2029460515","https://openalex.org/W2037710455","https://openalex.org/W2042018868","https://openalex.org/W2045079045","https://openalex.org/W2046387702","https://openalex.org/W2049659086","https://openalex.org/W2056510226","https://openalex.org/W2057929279","https://openalex.org/W2061670230","https://openalex.org/W2066332749","https://openalex.org/W2070291355","https://openalex.org/W2074796812","https://openalex.org/W2093356327","https://openalex.org/W2095938605","https://openalex.org/W2096433175","https://openalex.org/W2104050041","https://openalex.org/W2106715795","https://openalex.org/W2106955134","https://openalex.org/W2108970807","https://openalex.org/W2111020053","https://openalex.org/W2114791779","https://openalex.org/W2117412539","https://openalex.org/W2119821739","https://openalex.org/W2123705108","https://openalex.org/W2127676223","https://openalex.org/W2127941149","https://openalex.org/W2129122308","https://openalex.org/W2130062883","https://openalex.org/W2132291180","https://openalex.org/W2134711723","https://openalex.org/W2138243089","https://openalex.org/W2143552821","https://openalex.org/W2148087609","https://openalex.org/W2150026392","https://openalex.org/W2151685478","https://openalex.org/W2154834860","https://openalex.org/W2157017541","https://openalex.org/W2157166636","https://openalex.org/W2162576315","https://openalex.org/W2162761269","https://openalex.org/W2164278908","https://openalex.org/W2164642931","https://openalex.org/W2165744313","https://openalex.org/W2170299295","https://openalex.org/W2185133926","https://openalex.org/W2216134724","https://openalex.org/W2238591594","https://openalex.org/W2244987555","https://openalex.org/W2519209343","https://openalex.org/W2571425027","https://openalex.org/W2951090613","https://openalex.org/W2951264764","https://openalex.org/W2951781666","https://openalex.org/W2952033860","https://openalex.org/W2953332881","https://openalex.org/W2962696932","https://openalex.org/W2963000588","https://openalex.org/W2963980562","https://openalex.org/W2964064266","https://openalex.org/W2964102336","https://openalex.org/W3101665129","https://openalex.org/W4229706427","https://openalex.org/W4239510810","https://openalex.org/W4250589301","https://openalex.org/W4292363360","https://openalex.org/W4300028551","https://openalex.org/W6605358575","https://openalex.org/W6608099645","https://openalex.org/W6629492864","https://openalex.org/W6633789451","https://openalex.org/W6634001224","https://openalex.org/W6636483370","https://openalex.org/W6637158000","https://openalex.org/W6637330293","https://openalex.org/W6640345655","https://openalex.org/W6657774730","https://openalex.org/W6662929504","https://openalex.org/W6667037994","https://openalex.org/W6674502225","https://openalex.org/W6675881135","https://openalex.org/W6676186549","https://openalex.org/W6679154944","https://openalex.org/W6679314259","https://openalex.org/W6680402377","https://openalex.org/W6681872947","https://openalex.org/W6684583874","https://openalex.org/W6684700714","https://openalex.org/W6686227884","https://openalex.org/W6688321278","https://openalex.org/W6688622646","https://openalex.org/W6689770638","https://openalex.org/W6723038927","https://openalex.org/W6726507875","https://openalex.org/W6729906699","https://openalex.org/W6766564463","https://openalex.org/W7061399666"],"related_works":["https://openalex.org/W2123705108","https://openalex.org/W3014624975","https://openalex.org/W3102634715","https://openalex.org/W2257097853","https://openalex.org/W2786632953","https://openalex.org/W2952023151","https://openalex.org/W3172556047","https://openalex.org/W2546267725","https://openalex.org/W2936287122","https://openalex.org/W2223328134","https://openalex.org/W2996559389","https://openalex.org/W3210195281","https://openalex.org/W2951713178","https://openalex.org/W2164278908","https://openalex.org/W2129122308","https://openalex.org/W2950833068","https://openalex.org/W3033819030","https://openalex.org/W2040424361","https://openalex.org/W2570138859","https://openalex.org/W41686486"],"abstract_inverted_index":{"We":[0,41,68],"propose":[1],"a":[2,25],"distributed":[3,35],"algorithm":[4,88],"based":[5],"on":[6,126],"Alternating":[7],"Direction":[8],"Method":[9],"of":[10,17,66,114,123,135,143],"Multipliers":[11],"(ADMM)":[12],"to":[13,91],"minimize":[14],"the":[15,49,54,64,73,83,92,111,115,121,127,140,144],"sum":[16],"locally":[18],"known":[19],"convex":[20,77],"functions":[21,45,74],"using":[22],"communication":[23],"over":[24],"network.":[26,145],"This":[27],"optimization":[28],"problem":[29],"emerges":[30],"in":[31,34],"many":[32],"applications":[33],"machine":[36],"learning":[37],"and":[38,53,78,132],"statistical":[39],"estimation.":[40],"show":[42,70],"that":[43,71],"when":[44],"are":[46,75],"convex,":[47],"both":[48],"objective":[50],"function":[51],"values":[52],"feasibility":[55],"violation":[56],"converge":[57],"with":[58,103],"rate":[59,129],"$O(\\frac{1}{T})$,":[60],"where":[61,108],"$T$":[62],"is":[63,110],"number":[65,113],"iterations.":[67],"then":[69],"if":[72],"strongly":[76],"have":[79],"Lipschitz":[80],"continuous":[81],"gradients,":[82],"sequence":[84],"generated":[85],"by":[86],"our":[87],"converges":[89],"linearly":[90],"optimal":[93],"solution.":[94],"In":[95],"particular,":[96],"an":[97],"$\u03b5$-optimal":[98],"solution":[99],"can":[100],"be":[101],"computed":[102],"$O(\\sqrt{\u03ba_f}":[104],"\\log":[105],"(1/\u03b5))$":[106],"iterations,":[107],"$\u03ba_f$":[109],"condition":[112],"problem.":[116],"Our":[117],"analysis":[118],"also":[119],"highlights":[120],"effect":[122],"network":[124],"structure":[125],"convergence":[128],"through":[130],"maximum":[131],"minimum":[133],"degree":[134],"nodes":[136],"as":[137,139],"well":[138],"algebraic":[141],"connectivity":[142]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1}],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}
