{"id":"https://openalex.org/W2889159892","doi":"https://doi.org/10.1109/tac.2018.2867257","title":"Linear Stochastic Approximation Algorithms and Group Consensus Over Random Signed Networks","display_name":"Linear Stochastic Approximation Algorithms and Group Consensus Over Random Signed Networks","publication_year":2018,"publication_date":"2018-08-27","ids":{"openalex":"https://openalex.org/W2889159892","doi":"https://doi.org/10.1109/tac.2018.2867257","mag":"2889159892"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2018.2867257","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tac.2018.2867257","pdf_url":"https://ieeexplore.ieee.org/ielx7/9/8698250/08447261.pdf","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":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://ieeexplore.ieee.org/ielx7/9/8698250/08447261.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100359782","display_name":"Ge Chen","orcid":"https://orcid.org/0000-0003-4308-1341"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210095018","display_name":"National Center for Mathematics and Interdisciplinary Sciences","ror":"https://ror.org/00s97k668","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210095018"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ge Chen","raw_affiliation_strings":["National Center for Mathematics and Interdisciplinary Sciences & Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China"],"affiliations":[{"raw_affiliation_string":"National Center for Mathematics and Interdisciplinary Sciences & Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210095018","https://openalex.org/I4210120485","https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035843542","display_name":"Xiaoming Duan","orcid":"https://orcid.org/0000-0002-2655-3987"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xiaoming Duan","raw_affiliation_strings":["Department of Mechanical Engineering and the Center of Control, Dynamical-Systems and Computation, University of California at Santa Barbara, Santa Barbara, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering and the Center of Control, Dynamical-Systems and Computation, University of California at Santa Barbara, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074966640","display_name":"Wenjun Mei","orcid":"https://orcid.org/0000-0001-9575-1496"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wenjun Mei","raw_affiliation_strings":["Department of Mechanical Engineering and the Center of Control, Dynamical-Systems and Computation, University of California at Santa Barbara, Santa Barbara, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering and the Center of Control, Dynamical-Systems and Computation, University of California at Santa Barbara, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068353454","display_name":"Francesco Bullo","orcid":"https://orcid.org/0000-0002-4785-2118"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Francesco Bullo","raw_affiliation_strings":["Department of Mechanical Engineering and the Center of Control, Dynamical-Systems and Computation, University of California at Santa Barbara, Santa Barbara, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering and the Center of Control, Dynamical-Systems and Computation, University of California at Santa Barbara, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100359782"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210095018","https://openalex.org/I4210120485"],"apc_list":null,"apc_paid":null,"fwci":1.1725,"has_fulltext":true,"cited_by_count":18,"citation_normalized_percentile":{"value":0.81620463,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"64","issue":"5","first_page":"1874","last_page":"1889"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9998999834060669,"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":0.9998999834060669,"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/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9979000091552734,"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/stochastic-approximation","display_name":"Stochastic approximation","score":0.6630373001098633},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6372743844985962},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5192399024963379},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4963429570198059},{"id":"https://openalex.org/keywords/convergence-of-random-variables","display_name":"Convergence of random variables","score":0.4747743308544159},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.4702526330947876},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4670715928077698},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.46185103058815},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44517219066619873},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.44207778573036194},{"id":"https://openalex.org/keywords/multivariate-random-variable","display_name":"Multivariate random variable","score":0.4318177103996277},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.421497642993927},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.380405992269516},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.2417585253715515}],"concepts":[{"id":"https://openalex.org/C55479107","wikidata":"https://www.wikidata.org/wiki/Q97663916","display_name":"Stochastic approximation","level":3,"score":0.6630373001098633},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6372743844985962},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5192399024963379},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4963429570198059},{"id":"https://openalex.org/C95763700","wikidata":"https://www.wikidata.org/wiki/Q578985","display_name":"Convergence of random variables","level":3,"score":0.4747743308544159},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.4702526330947876},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4670715928077698},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.46185103058815},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44517219066619873},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.44207778573036194},{"id":"https://openalex.org/C138405894","wikidata":"https://www.wikidata.org/wiki/Q3179949","display_name":"Multivariate random variable","level":3,"score":0.4318177103996277},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.421497642993927},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.380405992269516},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.2417585253715515},{"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2018.2867257","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tac.2018.2867257","pdf_url":"https://ieeexplore.ieee.org/ielx7/9/8698250/08447261.pdf","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"}],"best_oa_location":{"id":"doi:10.1109/tac.2018.2867257","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tac.2018.2867257","pdf_url":"https://ieeexplore.ieee.org/ielx7/9/8698250/08447261.pdf","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"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.44999998807907104,"id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G1023919524","display_name":null,"funder_award_id":", Grant","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1121271761","display_name":null,"funder_award_id":"Program","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1231421488","display_name":null,"funder_award_id":"under","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1468664469","display_name":null,"funder_award_id":"W911NF-15-1-0577","funder_id":"https://openalex.org/F4320338295","funder_display_name":"Army Research Laboratory"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2320943543","display_name":null,"funder_award_id":"2014CB845301","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2802266602","display_name":null,"funder_award_id":"2014CB845301","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3435950671","display_name":null,"funder_award_id":"and Gr","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G391238517","display_name":null,"funder_award_id":", and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3967839092","display_name":null,"funder_award_id":"2014CB845301/2/3","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G424839487","display_name":null,"funder_award_id":"61673373","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4388460390","display_name":null,"funder_award_id":"11688101","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G4852649143","display_name":null,"funder_award_id":"W911NF-15-1-0577","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G4903121842","display_name":null,"funder_award_id":"91427304","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G5171771356","display_name":null,"funder_award_id":"2014CB","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G5259331294","display_name":null,"funder_award_id":"W911NF","funder_id":"https://openalex.org/F4320338295","funder_display_name":"Army Research Laboratory"},{"id":"https://openalex.org/G5385673730","display_name":null,"funder_award_id":"W911NF-15-1-","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6258415954","display_name":null,"funder_award_id":"Chinese","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6967058303","display_name":null,"funder_award_id":"11688101","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7117679969","display_name":null,"funder_award_id":"91427304","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7218984639","display_name":null,"funder_award_id":"2014CB845301/2/3","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7452299184","display_name":null,"funder_award_id":"W911NF","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G7484467084","display_name":null,"funder_award_id":"QYZDJ-SSW-JSC003","funder_id":"https://openalex.org/F4320321133","funder_display_name":"Chinese Academy of Sciences"},{"id":"https://openalex.org/G7733782986","display_name":null,"funder_award_id":"QYZDJ","funder_id":"https://openalex.org/F4320321133","funder_display_name":"Chinese Academy of Sciences"},{"id":"https://openalex.org/G7757904293","display_name":null,"funder_award_id":"-SSW-","funder_id":"https://openalex.org/F4320321133","funder_display_name":"Chinese Academy of Sciences"},{"id":"https://openalex.org/G8003868975","display_name":null,"funder_award_id":"11688101","funder_id":"https://openalex.org/F4320321133","funder_display_name":"Chinese Academy of Sciences"},{"id":"https://openalex.org/G8153243514","display_name":null,"funder_award_id":"2014CB845301","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G8388070046","display_name":null,"funder_award_id":"61673373","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G8998121839","display_name":null,"funder_award_id":"911NF","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321133","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"},{"id":"https://openalex.org/F4320338295","display_name":"Army Research Laboratory","ror":"https://ror.org/011hc8f90"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2889159892.pdf","grobid_xml":"https://content.openalex.org/works/W2889159892.grobid-xml"},"referenced_works_count":47,"referenced_works":["https://openalex.org/W618263208","https://openalex.org/W1020659046","https://openalex.org/W1488435683","https://openalex.org/W1499021337","https://openalex.org/W1630241696","https://openalex.org/W1660184077","https://openalex.org/W1840794734","https://openalex.org/W1967509640","https://openalex.org/W1967931536","https://openalex.org/W1975286263","https://openalex.org/W1992412916","https://openalex.org/W1998692453","https://openalex.org/W2008711923","https://openalex.org/W2009497213","https://openalex.org/W2015410655","https://openalex.org/W2018800107","https://openalex.org/W2026656492","https://openalex.org/W2063642824","https://openalex.org/W2065831027","https://openalex.org/W2071983464","https://openalex.org/W2073859315","https://openalex.org/W2085768049","https://openalex.org/W2088103590","https://openalex.org/W2096913736","https://openalex.org/W2099175737","https://openalex.org/W2111709059","https://openalex.org/W2114403255","https://openalex.org/W2116863403","https://openalex.org/W2120339885","https://openalex.org/W2122512809","https://openalex.org/W2125668987","https://openalex.org/W2134252677","https://openalex.org/W2145554346","https://openalex.org/W2146890818","https://openalex.org/W2150312211","https://openalex.org/W2150843948","https://openalex.org/W2154834860","https://openalex.org/W2176039430","https://openalex.org/W2493687459","https://openalex.org/W2534090929","https://openalex.org/W2726287119","https://openalex.org/W2962700363","https://openalex.org/W3083024126","https://openalex.org/W3104530023","https://openalex.org/W4234406933","https://openalex.org/W4250134109","https://openalex.org/W4302033506"],"related_works":["https://openalex.org/W1556690683","https://openalex.org/W2134007003","https://openalex.org/W2019875157","https://openalex.org/W2250503047","https://openalex.org/W4310831616","https://openalex.org/W1489978714","https://openalex.org/W2951888513","https://openalex.org/W4301954754","https://openalex.org/W1572979401","https://openalex.org/W2782292024"],"abstract_inverted_index":{"This":[0],"paper":[1,63],"studies":[2],"linear":[3,30,118],"stochastic":[4],"approximation":[5],"(SA)":[6],"algorithms":[7,32,120],"and":[8,16,24,86,92,104,121],"their":[9],"application":[10],"to":[11,33,74,89,113],"multiagent":[12,98],"systems":[13],"in":[14,58],"engineering":[15],"sociology.":[17],"As":[18],"main":[19],"contribution,":[20],"we":[21,83,109],"provide":[22,84],"necessary":[23,85],"sufficient":[25,87],"conditions":[26,88],"for":[27,95],"convergence":[28,45],"of":[29,116,125],"SA":[31,60,119],"a":[34],"deterministic":[35],"or":[36],"random":[37,101,131],"final":[38],"vector.":[39],"We":[40],"also":[41,65],"characterize":[42,122],"the":[43,48,66,69,114,123,126],"system":[44,49,99],"rate,":[46],"when":[47,68],"is":[50],"convergent.":[51],"Moreover,":[52],"differing":[53],"from":[54],"non-negative":[55],"gain":[56,70],"functions":[57,71],"traditional":[59],"algorithms,":[61],"this":[62],"considers":[64],"case":[67],"are":[72],"allowed":[73],"take":[75],"arbitrary":[76],"real":[77],"numbers.":[78],"Using":[79],"our":[80,111],"general":[81],"treatment,":[82],"reach":[90],"consensus":[91,94],"group":[93],"first-order":[96],"discrete-time":[97],"over":[100,130],"signed":[102],"networks":[103],"with":[105],"state-dependent":[106],"noise.":[107],"Finally,":[108],"extend":[110],"results":[112],"setting":[115],"multidimensional":[117,127],"behavior":[124],"Friedkin-Johnsen":[128],"model":[129],"interaction":[132],"networks.":[133]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1}],"updated_date":"2026-04-13T07:58:08.660418","created_date":"2025-10-10T00:00:00"}
