{"id":"https://openalex.org/W2914113355","doi":"https://doi.org/10.1109/cdc.2018.8619119","title":"Consensus-based Distributed Optimization in Multi-agent Systems: Convergence and Differential Privacy","display_name":"Consensus-based Distributed Optimization in Multi-agent Systems: Convergence and Differential Privacy","publication_year":2018,"publication_date":"2018-12-01","ids":{"openalex":"https://openalex.org/W2914113355","doi":"https://doi.org/10.1109/cdc.2018.8619119","mag":"2914113355"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2018.8619119","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2018.8619119","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-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/A5082206880","display_name":"Tie Ding","orcid":"https://orcid.org/0000-0002-2169-8861"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210110792","display_name":"Centre de Recherche en Automatique de Nancy","ror":"https://ror.org/022r5hc56","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210099203","https://openalex.org/I4210100260","https://openalex.org/I4210110792","https://openalex.org/I4210159245","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Tie Ding","raw_affiliation_strings":["CNRS, CRAN, Universit\u00e9 de Lorraine, Nancy, France"],"affiliations":[{"raw_affiliation_string":"CNRS, CRAN, Universit\u00e9 de Lorraine, Nancy, France","institution_ids":["https://openalex.org/I90183372","https://openalex.org/I1294671590","https://openalex.org/I4210110792"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007013035","display_name":"Shanying Zhu","orcid":"https://orcid.org/0000-0003-4860-4519"},"institutions":[{"id":"https://openalex.org/I1283613182","display_name":"Universidade Tecnol\u00f3gica Federal do Paran\u00e1","ror":"https://ror.org/002v2kq79","country_code":"BR","type":"education","lineage":["https://openalex.org/I1283613182"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Shanying Zhu","raw_affiliation_strings":["Department of Computer Science, Federal University of Technology\u2014Paran\u00e1, Curitiba, Brazil"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Federal University of Technology\u2014Paran\u00e1, Curitiba, Brazil","institution_ids":["https://openalex.org/I1283613182"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004668792","display_name":"Jianping He","orcid":"https://orcid.org/0000-0002-6253-7802"},"institutions":[{"id":"https://openalex.org/I111088046","display_name":"Boston University","ror":"https://ror.org/05qwgg493","country_code":"US","type":"education","lineage":["https://openalex.org/I111088046"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jianping He","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Boston University, Boston, MA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Boston University, Boston, MA, USA","institution_ids":["https://openalex.org/I111088046"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038267080","display_name":"Cailian Chen","orcid":"https://orcid.org/0000-0001-6533-8713"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Cailian Chen","raw_affiliation_strings":["Centre for Intelligent and Networked Systems, Beijing National Research Centre for Information Science and Technology Tsinghua University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Centre for Intelligent and Networked Systems, Beijing National Research Centre for Information Science and Technology Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100690710","display_name":"Xinping Guan","orcid":"https://orcid.org/0009-0006-6233-8762"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xinping Guan","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5082206880"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210110792","https://openalex.org/I90183372"],"apc_list":null,"apc_paid":null,"fwci":1.8564,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.89432362,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"3409","last_page":"3414"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10764","display_name":"Privacy-Preserving Technologies in Data","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T10764","display_name":"Privacy-Preserving Technologies in Data","score":0.9994999766349792,"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":0.9987999796867371,"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/T10246","display_name":"Mobile Ad Hoc Networks","score":0.9922999739646912,"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/differential-privacy","display_name":"Differential privacy","score":0.9341782927513123},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.7933302521705627},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6376153826713562},{"id":"https://openalex.org/keywords/laplace-transform","display_name":"Laplace transform","score":0.5753454566001892},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.550553560256958},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5504504442214966},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5372085571289062},{"id":"https://openalex.org/keywords/multi-agent-system","display_name":"Multi-agent system","score":0.4806877076625824},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4617147445678711},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.44693291187286377},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.43968555331230164},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.41016343235969543},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2656802535057068},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.19524651765823364},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1285858154296875},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.09172111749649048},{"id":"https://openalex.org/keywords/computer-security","display_name":"Computer security","score":0.08967536687850952}],"concepts":[{"id":"https://openalex.org/C23130292","wikidata":"https://www.wikidata.org/wiki/Q5275358","display_name":"Differential privacy","level":2,"score":0.9341782927513123},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7933302521705627},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6376153826713562},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.5753454566001892},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.550553560256958},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5504504442214966},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5372085571289062},{"id":"https://openalex.org/C41550386","wikidata":"https://www.wikidata.org/wiki/Q529909","display_name":"Multi-agent system","level":2,"score":0.4806877076625824},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4617147445678711},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.44693291187286377},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.43968555331230164},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.41016343235969543},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2656802535057068},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.19524651765823364},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1285858154296875},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.09172111749649048},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.08967536687850952},{"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/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"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/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2018.8619119","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2018.8619119","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7900000214576721,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1159423507","https://openalex.org/W1571416372","https://openalex.org/W1920382817","https://openalex.org/W2092845654","https://openalex.org/W2174932653","https://openalex.org/W2313103852","https://openalex.org/W2320793336","https://openalex.org/W2341190528","https://openalex.org/W2343466252","https://openalex.org/W2406813000","https://openalex.org/W2527559122","https://openalex.org/W2605026797","https://openalex.org/W2734500670","https://openalex.org/W2737743075","https://openalex.org/W2782092820","https://openalex.org/W2802328008","https://openalex.org/W2963112534","https://openalex.org/W2963649943","https://openalex.org/W2963822726","https://openalex.org/W3098954913","https://openalex.org/W6686869262","https://openalex.org/W6751581729"],"related_works":["https://openalex.org/W3038283795","https://openalex.org/W2604501336","https://openalex.org/W2734500670","https://openalex.org/W2558166297","https://openalex.org/W2315671126","https://openalex.org/W798507144","https://openalex.org/W2964481303","https://openalex.org/W1751413323","https://openalex.org/W2571704763","https://openalex.org/W3206394311"],"abstract_inverted_index":{"This":[0],"paper":[1],"studies":[2],"the":[3,16,28,77,81,101,108,114,120,124,143,146],"problem":[4],"of":[5,18,30,33,84,119,145],"optimization":[6],"in":[7],"multi-agent":[8],"systems":[9],"where":[10],"each":[11,32],"agent":[12,86],"seeks":[13],"to":[14,36,99,123,141],"minimize":[15],"sum":[17],"all":[19,91],"agents'":[20],"objective":[21,39,82],"functions":[22],"without":[23],"knowing":[24],"others'":[25],"functions.":[26],"Under":[27],"requirement":[29],"privacy,":[31],"them":[34],"needs":[35],"keep":[37],"its":[38],"function":[40,83],"private":[41],"from":[42],"other":[43,92],"agents":[44],"and":[45,61,113,131],"potential":[46],"attackers.":[47],"We":[48],"design":[49],"a":[50],"completely":[51],"distributed":[52],"algorithm,":[53],"which":[54],"achieves":[55],"differential":[56,129],"privacy":[57,130],"by":[58],"perturbing":[59],"states":[60],"adjusting":[62],"directions":[63],"with":[64],"decaying":[65],"Laplace":[66],"noise.":[67],"The":[68,126],"proposed":[69,147],"algorithm":[70,109],"ensures":[71],"that":[72,107],"an":[73],"attacker":[74],"who":[75],"intercepts":[76],"messages":[78],"cannot":[79],"obtain":[80],"any":[85],"even":[87],"if":[88],"it":[89],"bribes":[90],"agents.":[93],"A":[94],"constant":[95],"stepsize":[96],"is":[97,105,117,134],"adopted":[98],"improve":[100],"convergence":[102,115,132],"rate.":[103],"It":[104],"shown":[106],"converges":[110],"almost":[111],"surely":[112],"point":[116],"independent":[118],"noise":[121],"added":[122],"states.":[125],"trade-off":[127],"between":[128],"accuracy":[133],"also":[135],"characterized.":[136],"Finally,":[137],"simulations":[138],"are":[139],"conducted":[140],"validate":[142],"efficiency":[144],"algorithm.":[148]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1}],"updated_date":"2026-03-13T16:22:10.518609","created_date":"2025-10-10T00:00:00"}