{"id":"https://openalex.org/W3105600443","doi":"https://doi.org/10.1109/tsp.2021.3097211","title":"Distributed Stochastic Consensus Optimization With Momentum for Nonconvex Nonsmooth Problems","display_name":"Distributed Stochastic Consensus Optimization With Momentum for Nonconvex Nonsmooth Problems","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3105600443","doi":"https://doi.org/10.1109/tsp.2021.3097211","mag":"3105600443"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2021.3097211","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2021.3097211","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Signal Processing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2011.05082","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100430098","display_name":"Zhiguo Wang","orcid":"https://orcid.org/0000-0003-2604-3597"},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]},{"id":"https://openalex.org/I4210116924","display_name":"Chinese University of Hong Kong, Shenzhen","ror":"https://ror.org/02d5ks197","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633","https://openalex.org/I180726961","https://openalex.org/I4210116924"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhiguo Wang","raw_affiliation_strings":["Chinese University of Hong Kong, Shenzhen, China","College of Mathematics, Sichuan University, Chengdu, Sichuan, China"],"raw_orcid":"https://orcid.org/0000-0003-2604-3597","affiliations":[{"raw_affiliation_string":"Chinese University of Hong Kong, Shenzhen, China","institution_ids":["https://openalex.org/I4210116924"]},{"raw_affiliation_string":"College of Mathematics, Sichuan University, Chengdu, Sichuan, China","institution_ids":["https://openalex.org/I24185976"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100462851","display_name":"Jiawei Zhang","orcid":"https://orcid.org/0000-0003-1377-7938"},"institutions":[{"id":"https://openalex.org/I4210099586","display_name":"Shenzhen Research Institute of Big Data","ror":"https://ror.org/00z1gwf89","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210099586"]},{"id":"https://openalex.org/I4210116924","display_name":"Chinese University of Hong Kong, Shenzhen","ror":"https://ror.org/02d5ks197","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633","https://openalex.org/I180726961","https://openalex.org/I4210116924"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiawei Zhang","raw_affiliation_strings":["Chinese University of Hong Kong, Shenzhen, China","Shenzhen Research Institute of Big Data, Shenzhen, Guangdong Province, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chinese University of Hong Kong, Shenzhen, China","institution_ids":["https://openalex.org/I4210116924"]},{"raw_affiliation_string":"Shenzhen Research Institute of Big Data, Shenzhen, Guangdong Province, China","institution_ids":["https://openalex.org/I4210099586"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064271996","display_name":"Tsung\u2010Hui Chang","orcid":"https://orcid.org/0000-0003-1349-2764"},"institutions":[{"id":"https://openalex.org/I4210099586","display_name":"Shenzhen Research Institute of Big Data","ror":"https://ror.org/00z1gwf89","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210099586"]},{"id":"https://openalex.org/I4210116924","display_name":"Chinese University of Hong Kong, Shenzhen","ror":"https://ror.org/02d5ks197","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633","https://openalex.org/I180726961","https://openalex.org/I4210116924"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tsung-Hui Chang","raw_affiliation_strings":["Chinese University of Hong Kong, Shenzhen, China","Shenzhen Research Institute of Big Data, Shenzhen, Guangdong Province, China"],"raw_orcid":"https://orcid.org/0000-0003-1349-2764","affiliations":[{"raw_affiliation_string":"Chinese University of Hong Kong, Shenzhen, China","institution_ids":["https://openalex.org/I4210116924"]},{"raw_affiliation_string":"Shenzhen Research Institute of Big Data, Shenzhen, Guangdong Province, China","institution_ids":["https://openalex.org/I4210099586"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100402458","display_name":"Jian Li","orcid":"https://orcid.org/0000-0002-0030-1423"},"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":"Jian Li","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Florida, Gainesville, FL, USA"],"raw_orcid":"https://orcid.org/0000-0002-0030-1423","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Florida, Gainesville, FL, USA","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101766226","display_name":"Zhi\u2010Quan Luo","orcid":"https://orcid.org/0000-0003-3995-914X"},"institutions":[{"id":"https://openalex.org/I4210099586","display_name":"Shenzhen Research Institute of Big Data","ror":"https://ror.org/00z1gwf89","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210099586"]},{"id":"https://openalex.org/I4210116924","display_name":"Chinese University of Hong Kong, Shenzhen","ror":"https://ror.org/02d5ks197","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633","https://openalex.org/I180726961","https://openalex.org/I4210116924"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhi-Quan Luo","raw_affiliation_strings":["Chinese University of Hong Kong, Shenzhen, China","Shenzhen Research Institute of Big Data, Shenzhen, Guangdong Province, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chinese University of Hong Kong, Shenzhen, China","institution_ids":["https://openalex.org/I4210116924"]},{"raw_affiliation_string":"Shenzhen Research Institute of Big Data, Shenzhen, Guangdong Province, China","institution_ids":["https://openalex.org/I4210099586"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.798,"has_fulltext":false,"cited_by_count":36,"citation_normalized_percentile":{"value":0.93307574,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"69","issue":null,"first_page":"4486","last_page":"4501"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9994999766349792,"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":0.9994999766349792,"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/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"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9926000237464905,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5663771629333496},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5582811236381531},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.5462961792945862},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5424762964248657},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5111382603645325},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4782780110836029},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4768044650554657},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.47500455379486084},{"id":"https://openalex.org/keywords/distributed-algorithm","display_name":"Distributed algorithm","score":0.43337389826774597},{"id":"https://openalex.org/keywords/stochastic-optimization","display_name":"Stochastic optimization","score":0.4282338619232178},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40638473629951477},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33359798789024353}],"concepts":[{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5663771629333496},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5582811236381531},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.5462961792945862},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5424762964248657},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5111382603645325},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4782780110836029},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4768044650554657},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.47500455379486084},{"id":"https://openalex.org/C130120984","wikidata":"https://www.wikidata.org/wiki/Q2835898","display_name":"Distributed algorithm","level":2,"score":0.43337389826774597},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.4282338619232178},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40638473629951477},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33359798789024353},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tsp.2021.3097211","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2021.3097211","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Signal Processing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2011.05082","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2011.05082","pdf_url":"https://arxiv.org/pdf/2011.05082","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":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2011.05082","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2011.05082","pdf_url":"https://arxiv.org/pdf/2011.05082","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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4415435663","display_name":"\u6570\u636e\u4e0e\u6a21\u578b\u53cc\u9a71\u52a8\u7684\u5927\u89c4\u6a21MIMO\u9ad8\u901f\u4f20\u8f93\u5173\u952e\u6280\u672f\u7814\u7a76","funder_award_id":"62071409","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4577391995","display_name":null,"funder_award_id":"2018YFB1800800","funder_id":"https://openalex.org/F4320336026","funder_display_name":"National Key Research and Development Program of China Stem Cell and Translational Research"},{"id":"https://openalex.org/G5702201066","display_name":null,"funder_award_id":"JCYJ20190813171003723","funder_id":"https://openalex.org/F4320335803","funder_display_name":"Shenzhen Fundamental Research and Discipline Layout project"},{"id":"https://openalex.org/G940306304","display_name":null,"funder_award_id":"61731018","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335803","display_name":"Shenzhen Fundamental Research and Discipline Layout project","ror":null},{"id":"https://openalex.org/F4320336026","display_name":"National Key Research and Development Program of China Stem Cell and Translational Research","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":66,"referenced_works":["https://openalex.org/W1571416372","https://openalex.org/W1627780903","https://openalex.org/W1969073096","https://openalex.org/W2044212084","https://openalex.org/W2092620240","https://openalex.org/W2105693192","https://openalex.org/W2123705108","https://openalex.org/W2129122308","https://openalex.org/W2164278908","https://openalex.org/W2266148951","https://openalex.org/W2541884796","https://openalex.org/W2594560857","https://openalex.org/W2733300693","https://openalex.org/W2785628099","https://openalex.org/W2789243870","https://openalex.org/W2795577721","https://openalex.org/W2798766386","https://openalex.org/W2803565980","https://openalex.org/W2804540002","https://openalex.org/W2808402975","https://openalex.org/W2892002891","https://openalex.org/W2895070114","https://openalex.org/W2914328083","https://openalex.org/W2944542720","https://openalex.org/W2949934631","https://openalex.org/W2954270931","https://openalex.org/W2963228337","https://openalex.org/W2963748878","https://openalex.org/W2963755123","https://openalex.org/W2964026281","https://openalex.org/W2965281821","https://openalex.org/W3006555759","https://openalex.org/W3007093918","https://openalex.org/W3012206388","https://openalex.org/W3021435406","https://openalex.org/W3034666238","https://openalex.org/W3038022836","https://openalex.org/W3040421305","https://openalex.org/W3043309535","https://openalex.org/W3048490699","https://openalex.org/W3081144209","https://openalex.org/W3086080324","https://openalex.org/W3099104659","https://openalex.org/W3105600443","https://openalex.org/W3106445841","https://openalex.org/W3120430922","https://openalex.org/W3141595720","https://openalex.org/W4244633107","https://openalex.org/W4292363360","https://openalex.org/W4308706819","https://openalex.org/W4318619660","https://openalex.org/W6728757088","https://openalex.org/W6740710678","https://openalex.org/W6748071933","https://openalex.org/W6748632073","https://openalex.org/W6751658988","https://openalex.org/W6754707222","https://openalex.org/W6759238902","https://openalex.org/W6762930437","https://openalex.org/W6773817997","https://openalex.org/W6773844993","https://openalex.org/W6774831228","https://openalex.org/W6774934054","https://openalex.org/W6780564044","https://openalex.org/W6785732086","https://openalex.org/W6792289226"],"related_works":["https://openalex.org/W2922314686","https://openalex.org/W3004192664","https://openalex.org/W2371283136","https://openalex.org/W1789848037","https://openalex.org/W2107924917","https://openalex.org/W2985979428","https://openalex.org/W2510140549","https://openalex.org/W2187449906","https://openalex.org/W2962818859","https://openalex.org/W2154682027"],"abstract_inverted_index":{"While":[0],"many":[1],"distributed":[2,38,153],"optimization":[3,45],"algorithms":[4],"have":[5],"been":[6],"proposed":[7,56,107,173],"for":[8,43,144,151],"solving":[9],"smooth":[10],"or":[11],"convex":[12],"problems":[13],"over":[14],"the":[15,55,87,90,100,106,110,123,128,132,137,169,172],"networks,":[16],"few":[17],"of":[18,46,89,113,119,125,171],"them":[19],"can":[20,58],"handle":[21],"non-convex":[22,47,145,154],"and":[23,48,79,146,157],"non-smooth":[24,49,91,147],"problems.":[25,50,148],"Based":[26],"on":[27],"a":[28,35,64,94,152,158],"proximal":[29],"primal-dual":[30],"approach,":[31],"this":[32],"paper":[33],"presents":[34],"new":[36],"(stochastic)":[37],"algorithm":[39,57,108,135],"with":[40,68,136],"Nesterov":[41],"momentum":[42],"accelerated":[44],"Theoretically,":[51],"we":[52],"show":[53],"that":[54],"achieve":[59],"an":[60],"\u03f5-stationary":[61],"solution":[62],"under":[63],"constant":[65],"step":[66],"size":[67],"<i":[69,80,138],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[70,74,81,139],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">O</i>":[71,82,140],"(1/\u03f5":[72],"<sup":[73],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[75],")":[76],"computation":[77,114],"complexity":[78,85,115,143],"(1/\u03f5)":[83,141],"communication":[84,120,142],"when":[86],"epigraph":[88],"term":[92],"is":[93,131],"polyhedral":[95],"set.":[96],"When":[97],"compared":[98],"to":[99,167],"existing":[101],"gradient":[102],"tracking":[103],"based":[104,162],"methods,":[105],"has":[109],"same":[111],"order":[112,118],"but":[116],"lower":[117],"complexity.":[121],"To":[122],"best":[124],"our":[126],"knowledge,":[127],"presented":[129,166],"result":[130],"first":[133],"stochastic":[134],"Numerical":[149],"experiments":[150],"regression":[155],"problem":[156,164],"deep":[159],"neural":[160],"network":[161],"classification":[163],"are":[165],"illustrate":[168],"effectiveness":[170],"algorithms.":[174]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
