{"id":"https://openalex.org/W3216451006","doi":"https://doi.org/10.1109/tnnls.2021.3127883","title":"A Second-Order Projected Primal-Dual Dynamical System for Distributed Optimization and Learning","display_name":"A Second-Order Projected Primal-Dual Dynamical System for Distributed Optimization and Learning","publication_year":2021,"publication_date":"2021-11-24","ids":{"openalex":"https://openalex.org/W3216451006","doi":"https://doi.org/10.1109/tnnls.2021.3127883","mag":"3216451006","pmid":"https://pubmed.ncbi.nlm.nih.gov/34818195"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2021.3127883","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2021.3127883","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 Neural Networks and Learning Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5100695917","display_name":"Xiaoxuan Wang","orcid":"https://orcid.org/0000-0002-0501-1521"},"institutions":[{"id":"https://openalex.org/I16609230","display_name":"Hunan University","ror":"https://ror.org/05htk5m33","country_code":"CN","type":"education","lineage":["https://openalex.org/I16609230"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoxuan Wang","raw_affiliation_strings":["School of Mathematics, and the Hunan Provincial Key Laboratory of Intelligent Information Processing and Applied Mathematics, Hunan University, Changsha, Hunan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, and the Hunan Provincial Key Laboratory of Intelligent Information Processing and Applied Mathematics, Hunan University, Changsha, Hunan, China","institution_ids":["https://openalex.org/I16609230"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012649202","display_name":"Shaofu Yang","orcid":"https://orcid.org/0000-0001-7727-9669"},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shaofu Yang","raw_affiliation_strings":["School of Computer Science and Engineering, Southeast University, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0001-7727-9669","affiliations":[{"raw_affiliation_string":"School of Computer Science and Engineering, Southeast University, Nanjing, China","institution_ids":["https://openalex.org/I76569877"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051086253","display_name":"Zhenyuan Guo","orcid":"https://orcid.org/0000-0003-2564-6433"},"institutions":[{"id":"https://openalex.org/I16609230","display_name":"Hunan University","ror":"https://ror.org/05htk5m33","country_code":"CN","type":"education","lineage":["https://openalex.org/I16609230"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhenyuan Guo","raw_affiliation_strings":["School of Mathematics, and the Hunan Provincial Key Laboratory of Intelligent Information Processing and Applied Mathematics, Hunan University, Changsha, Hunan, China"],"raw_orcid":"https://orcid.org/0000-0003-2564-6433","affiliations":[{"raw_affiliation_string":"School of Mathematics, and the Hunan Provincial Key Laboratory of Intelligent Information Processing and Applied Mathematics, Hunan University, Changsha, Hunan, China","institution_ids":["https://openalex.org/I16609230"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074290686","display_name":"Tingwen Huang","orcid":"https://orcid.org/0000-0001-9610-846X"},"institutions":[{"id":"https://openalex.org/I58152225","display_name":"Texas A&M University at Qatar","ror":"https://ror.org/03vb4dm14","country_code":"QA","type":"education","lineage":["https://openalex.org/I58152225","https://openalex.org/I91045830"]}],"countries":["QA"],"is_corresponding":false,"raw_author_name":"Tingwen Huang","raw_affiliation_strings":["Science Program, Texas A&#x0026;M University at Qatar, Doha, Qatar"],"raw_orcid":"https://orcid.org/0000-0001-9610-846X","affiliations":[{"raw_affiliation_string":"Science Program, Texas A&#x0026;M University at Qatar, Doha, Qatar","institution_ids":["https://openalex.org/I58152225"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.0384,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.91691779,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"34","issue":"9","first_page":"6568","last_page":"6577"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":1.0,"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":1.0,"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":0.9972000122070312,"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9871000051498413,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6195124387741089},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.5999622344970703},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.5932321548461914},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.5736485719680786},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5360285043716431},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5118359923362732},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4996004104614258},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.49773839116096497},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.47999900579452515},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.46954211592674255},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.44874072074890137},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.43896743655204773},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.424469530582428},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4023962616920471},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39673537015914917},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.29524025321006775}],"concepts":[{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6195124387741089},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.5999622344970703},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.5932321548461914},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.5736485719680786},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5360285043716431},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5118359923362732},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4996004104614258},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.49773839116096497},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.47999900579452515},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.46954211592674255},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.44874072074890137},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.43896743655204773},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.424469530582428},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4023962616920471},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39673537015914917},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.29524025321006775},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"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/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2021.3127883","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2021.3127883","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 Neural Networks and Learning Systems","raw_type":"journal-article"},{"id":"pmid:34818195","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/34818195","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on neural networks and learning systems","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Partnerships for the goals","id":"https://metadata.un.org/sdg/17","score":0.4300000071525574}],"awards":[{"id":"https://openalex.org/G1887701658","display_name":null,"funder_award_id":"61573003","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6273817310","display_name":null,"funder_award_id":"62176056","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6346257250","display_name":null,"funder_award_id":"NPRP 8-274-2-107","funder_id":"https://openalex.org/F4320332753","funder_display_name":"Qatar National Research Fund"},{"id":"https://openalex.org/G6785507419","display_name":null,"funder_award_id":"2019JJ40022","funder_id":"https://openalex.org/F4320322843","funder_display_name":"Natural Science Foundation of\u00a0Hunan Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322843","display_name":"Natural Science Foundation of\u00a0Hunan Province","ror":null},{"id":"https://openalex.org/F4320332753","display_name":"Qatar National Research Fund","ror":"https://ror.org/01svaqq28"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":50,"referenced_works":["https://openalex.org/W206682702","https://openalex.org/W1857382374","https://openalex.org/W1970033879","https://openalex.org/W1988901237","https://openalex.org/W2011474549","https://openalex.org/W2029080014","https://openalex.org/W2114791779","https://openalex.org/W2146846916","https://openalex.org/W2164642931","https://openalex.org/W2216483973","https://openalex.org/W2302721240","https://openalex.org/W2341544006","https://openalex.org/W2521320587","https://openalex.org/W2584604366","https://openalex.org/W2790284998","https://openalex.org/W2790612450","https://openalex.org/W2807548807","https://openalex.org/W2886195789","https://openalex.org/W2898406129","https://openalex.org/W2898640938","https://openalex.org/W2901162217","https://openalex.org/W2904569464","https://openalex.org/W2917189468","https://openalex.org/W2917796591","https://openalex.org/W2921757699","https://openalex.org/W2936995161","https://openalex.org/W2944513470","https://openalex.org/W2963022670","https://openalex.org/W2964165783","https://openalex.org/W2969454470","https://openalex.org/W2978477998","https://openalex.org/W2995581462","https://openalex.org/W3024967635","https://openalex.org/W3026936419","https://openalex.org/W3043520642","https://openalex.org/W3045105032","https://openalex.org/W3046881313","https://openalex.org/W3082650005","https://openalex.org/W3083895600","https://openalex.org/W3101614605","https://openalex.org/W4240790602","https://openalex.org/W4243449554","https://openalex.org/W4292363360","https://openalex.org/W4299439662","https://openalex.org/W4300549156","https://openalex.org/W4366604739","https://openalex.org/W6688698367","https://openalex.org/W6752422486","https://openalex.org/W6761030284","https://openalex.org/W6851955609"],"related_works":["https://openalex.org/W4318347891","https://openalex.org/W4372267246","https://openalex.org/W2883143458","https://openalex.org/W2589063463","https://openalex.org/W4314947455","https://openalex.org/W1556545893","https://openalex.org/W4225392794","https://openalex.org/W3106270855","https://openalex.org/W2949938480","https://openalex.org/W2964561292"],"abstract_inverted_index":{"This":[0],"article":[1],"focuses":[2],"on":[3],"developing":[4],"distributed":[5],"optimization":[6],"strategies":[7],"for":[8],"a":[9,16],"class":[10],"of":[11,19,36,93,105,133],"machine":[12,150],"learning":[13],"problems":[14],"over":[15],"directed":[17],"network":[18],"computing":[20,52],"agents.":[21],"In":[22,128],"these":[23],"problems,":[24,78],"the":[25,50,74,77,79,87,94,103,106,115,120,129,131,134,140,145],"global":[26],"objective":[27,38,42],"function":[28],"is":[29,34,64,83,100,137],"an":[30],"addition":[31],"function,":[32],"which":[33],"composed":[35],"local":[37,41],"functions.":[39],"Such":[40],"functions":[43],"are":[44],"convex":[45],"and":[46,123,144],"only":[47],"endowed":[48],"by":[49,139],"corresponding":[51],"agent.":[53],"A":[54],"second-order":[55],"Nesterov":[56,88,107],"accelerated":[57,89,108],"dynamical":[58,109],"system":[59,110],"with":[60,73],"time-varying":[61],"damping":[62,121],"coefficient":[63,122],"developed":[65],"to":[66],"address":[67],"such":[68],"problems.":[69],"To":[70],"effectively":[71],"deal":[72],"constraints":[75],"in":[76,86,149],"projected":[80],"primal-dual":[81],"method":[82],"carried":[84],"out":[85],"system.":[90],"By":[91],"means":[92],"cocoercive":[95],"maximal":[96],"monotone":[97],"operator,":[98],"it":[99],"shown":[101],"that":[102,119],"trajectories":[104],"can":[111],"reach":[112],"consensus":[113],"at":[114],"optimal":[116],"solution,":[117],"provided":[118],"gains":[124],"meet":[125],"technical":[126],"conditions.":[127],"end,":[130],"validation":[132],"theoretical":[135],"results":[136],"demonstrated":[138],"email":[141],"classification":[142],"problem":[143,148],"logistic":[146],"regression":[147],"learning.":[151]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":3}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
