{"id":"https://openalex.org/W2963649943","doi":"https://doi.org/10.1137/16m1084316","title":"Achieving Geometric Convergence for Distributed Optimization Over Time-Varying Graphs","display_name":"Achieving Geometric Convergence for Distributed Optimization Over Time-Varying Graphs","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2963649943","doi":"https://doi.org/10.1137/16m1084316","mag":"2963649943"},"language":"en","primary_location":{"id":"doi:10.1137/16m1084316","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1084316","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/A5110629459","display_name":"Angelia Nedi\u0107","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Angelia Nedi\u0107","raw_affiliation_strings":["Electrical, Computer, and Energy Engineering, School of (ECEE)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical, Computer, and Energy Engineering, School of (ECEE)","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005863931","display_name":"Alex Olshevsky","orcid":"https://orcid.org/0000-0002-5852-9789"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alex Olshevsky","raw_affiliation_strings":["Boston Univ"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Boston Univ","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102745656","display_name":"Wei Shi","orcid":"https://orcid.org/0000-0002-9511-3838"},"institutions":[{"id":"https://openalex.org/I55732556","display_name":"Arizona State University","ror":"https://ror.org/03efmqc40","country_code":"US","type":"education","lineage":["https://openalex.org/I55732556"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wei Shi","raw_affiliation_strings":["Arizona State University**"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Arizona State University**","institution_ids":["https://openalex.org/I55732556"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":83.9188,"has_fulltext":false,"cited_by_count":1034,"citation_normalized_percentile":{"value":0.99967662,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"27","issue":"4","first_page":"2597","last_page":"2633"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9997000098228455,"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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9997000098228455,"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/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9865000247955322,"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.967199981212616,"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/iterated-function","display_name":"Iterated function","score":0.7069224119186401},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.682806134223938},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6525755524635315},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5623185038566589},{"id":"https://openalex.org/keywords/directed-graph","display_name":"Directed graph","score":0.4951576292514801},{"id":"https://openalex.org/keywords/undirected-graph","display_name":"Undirected graph","score":0.4864906668663025},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.46275612711906433},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.436212956905365},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3665943741798401},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32977020740509033},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.22346875071525574}],"concepts":[{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.7069224119186401},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.682806134223938},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6525755524635315},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5623185038566589},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.4951576292514801},{"id":"https://openalex.org/C3018234147","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Undirected graph","level":3,"score":0.4864906668663025},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.46275612711906433},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.436212956905365},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3665943741798401},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32977020740509033},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.22346875071525574},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","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},{"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":1,"locations":[{"id":"doi:10.1137/16m1084316","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1084316","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":[{"id":"https://openalex.org/G2527926460","display_name":null,"funder_award_id":"AF FA95501510394","funder_id":"https://openalex.org/F4320332467","funder_display_name":"U.S. Air Force"},{"id":"https://openalex.org/G8824011968","display_name":null,"funder_award_id":"N00014-12-1-0998","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G8925639116","display_name":null,"funder_award_id":"CNS 15-44953","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320332467","display_name":"U.S. Air Force","ror":"https://ror.org/006gmme17"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W1506295250","https://openalex.org/W1571416372","https://openalex.org/W1627780903","https://openalex.org/W1973754217","https://openalex.org/W1987917074","https://openalex.org/W1994860969","https://openalex.org/W2022948311","https://openalex.org/W2044212084","https://openalex.org/W2048572907","https://openalex.org/W2066332749","https://openalex.org/W2073750241","https://openalex.org/W2074796812","https://openalex.org/W2076428552","https://openalex.org/W2091147489","https://openalex.org/W2093777540","https://openalex.org/W2101385798","https://openalex.org/W2108924122","https://openalex.org/W2115594466","https://openalex.org/W2123705108","https://openalex.org/W2124351843","https://openalex.org/W2129122308","https://openalex.org/W2130263842","https://openalex.org/W2137435346","https://openalex.org/W2140655807","https://openalex.org/W2148087609","https://openalex.org/W2151565294","https://openalex.org/W2151685478","https://openalex.org/W2154834860","https://openalex.org/W2155143729","https://openalex.org/W2266148951","https://openalex.org/W2295489065","https://openalex.org/W2345998142","https://openalex.org/W2528940545","https://openalex.org/W2596989490","https://openalex.org/W2963940890","https://openalex.org/W3123607434","https://openalex.org/W4292363360"],"related_works":["https://openalex.org/W2043128958","https://openalex.org/W1994341438","https://openalex.org/W2075073335","https://openalex.org/W3196191381","https://openalex.org/W2346528079","https://openalex.org/W2023059211","https://openalex.org/W2370572809","https://openalex.org/W2798936174","https://openalex.org/W2764127424","https://openalex.org/W4322810890"],"abstract_inverted_index":{"This":[0],"paper":[1],"considers":[2],"the":[3,12,57,67,74,89,93,98,120,127,137,150,154,165,177,180],"problem":[4],"of":[5,14,30,76,167,179],"distributed":[6,20,32],"optimization":[7],"over":[8],"time-varying":[9],"graphs.":[10],"For":[11],"case":[13,73],"undirected":[15,157],"graphs,":[16],"we":[17,83,124],"introduce":[18],"a":[19,28,31,37,61,114],"algorithm,":[21],"referred":[22],"to":[23,60,113,175,184],"as":[24,134,136],"DIGing,":[25],"based":[26],"on":[27],"combination":[29],"inexact":[33],"gradient":[34,38],"method":[35],"and":[36,49,63,106,116,183],"tracking":[39],"technique.":[40],"The":[41],"DIGing":[42,94,161],"algorithm":[43,86],"uses":[44,102],"doubly":[45,77],"stochastic":[46,78,104],"mixing":[47,79],"matrices":[48,80,105],"employs":[50],"fixed":[51,107],"step-sizes":[52,138],"and,":[53],"yet,":[54],"drives":[55],"all":[56],"agents'":[58],"iterates":[59],"global":[62,115],"consensual":[64,117],"minimizer.":[65,118],"When":[66,153],"graphs":[68],"are":[69],"directed,":[70],"in":[71,164],"which":[72],"implementation":[75],"is":[81,156],"unrealistic,":[82],"construct":[84],"an":[85],"that":[87,126,160],"incorporates":[88],"push-sum":[90],"protocol":[91],"into":[92],"structure,":[95],"thus":[96],"obtaining":[97],"Push-DIGing":[99,101],"algorithm.":[100],"column":[103],"step-sizes,":[108],"but":[109],"it":[110,158],"still":[111],"converges":[112],"Under":[119],"strong":[121],"convexity":[122],"assumption,":[123],"prove":[125],"algorithms":[128,182],"converge":[129],"at":[130],"R-linear":[131],"(geometric)":[132],"rates":[133],"long":[135],"do":[139],"not":[140],"exceed":[141],"some":[142,172],"upper":[143],"bounds.":[144],"We":[145,169],"establish":[146],"explicit":[147],"estimates":[148],"for":[149],"convergence":[151],"rates.":[152],"graph":[155],"shows":[159],"scales":[162],"polynomially":[163],"number":[166],"agents.":[168],"also":[170],"provide":[171],"numerical":[173],"experiments":[174],"demonstrate":[176],"efficacy":[178],"proposed":[181],"validate":[185],"our":[186],"theoretical":[187],"findings.":[188]},"counts_by_year":[{"year":2026,"cited_by_count":20},{"year":2025,"cited_by_count":128},{"year":2024,"cited_by_count":128},{"year":2023,"cited_by_count":117},{"year":2022,"cited_by_count":119},{"year":2021,"cited_by_count":131},{"year":2020,"cited_by_count":154},{"year":2019,"cited_by_count":128},{"year":2018,"cited_by_count":73},{"year":2017,"cited_by_count":27},{"year":2016,"cited_by_count":9}],"updated_date":"2026-06-17T08:01:34.144755","created_date":"2025-10-10T00:00:00"}