{"id":"https://openalex.org/W2899194738","doi":"https://doi.org/10.1137/17m1118609","title":"Distributed Continuous-Time Algorithms for Nonsmooth Extended Monotropic Optimization Problems","display_name":"Distributed Continuous-Time Algorithms for Nonsmooth Extended Monotropic Optimization Problems","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2899194738","doi":"https://doi.org/10.1137/17m1118609","mag":"2899194738"},"language":"en","primary_location":{"id":"doi:10.1137/17m1118609","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1118609","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://dr.ntu.edu.sg/bitstream/10356/86220/1/DISTRIBUTED%20CONTINUOUS-TIME%20ALGORITHMS%20FOR.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015366869","display_name":"Xianlin Zeng","orcid":"https://orcid.org/0000-0002-6224-9974"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xianlin Zeng","raw_affiliation_strings":["Key Laboratory of Intelligent Control and Decision of Complex Systems, School of Automation, Beijing Institute of Technology, 100081, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Intelligent Control and Decision of Complex Systems, School of Automation, Beijing Institute of Technology, 100081, Beijing, China","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089663996","display_name":"Peng Yi","orcid":"https://orcid.org/0000-0002-2494-1505"},"institutions":[{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]},{"id":"https://openalex.org/I204465549","display_name":"Washington University in St. Louis","ror":"https://ror.org/01yc7t268","country_code":"US","type":"education","lineage":["https://openalex.org/I204465549"]}],"countries":["CN","US"],"is_corresponding":false,"raw_author_name":"Peng Yi","raw_affiliation_strings":["Department of Electrical and Systems Engineering, Washington University in St. Louis, St. Louis, MO 63130","Key Laboratory of Systems and Control, University of Chinese Academy of Sciences, Chinese Academy of Sciences, Beijing, 100190, China"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Systems Engineering, Washington University in St. Louis, St. Louis, MO 63130","institution_ids":["https://openalex.org/I204465549"]},{"raw_affiliation_string":"Key Laboratory of Systems and Control, University of Chinese Academy of Sciences, Chinese Academy of Sciences, Beijing, 100190, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100359415","display_name":"Yiguang Hong","orcid":"https://orcid.org/0000-0001-9505-8739"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Yiguang Hong","raw_affiliation_strings":["Nanyang Technological University, Singapore"],"affiliations":[{"raw_affiliation_string":"Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100365448","display_name":"Lihua Xie","orcid":"https://orcid.org/0000-0002-7137-4136"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Lihua Xie","raw_affiliation_strings":["School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798"],"affiliations":[{"raw_affiliation_string":"School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798","institution_ids":["https://openalex.org/I172675005"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5015366869"],"corresponding_institution_ids":["https://openalex.org/I125839683"],"apc_list":null,"apc_paid":null,"fwci":8.3856,"has_fulltext":true,"cited_by_count":87,"citation_normalized_percentile":{"value":0.97864874,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"56","issue":"6","first_page":"3973","last_page":"3993"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9998000264167786,"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":0.9998000264167786,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9900000095367432,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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":0.9873999953269958,"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/subgradient-method","display_name":"Subgradient method","score":0.8555102348327637},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6453401446342468},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5813961625099182},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5604608058929443},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.5236353874206543},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.48956021666526794},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.473458468914032},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.44597509503364563},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.4420733153820038},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.43730294704437256},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.43562692403793335},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37589216232299805},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.36340969800949097},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2836490273475647}],"concepts":[{"id":"https://openalex.org/C158968445","wikidata":"https://www.wikidata.org/wiki/Q7631150","display_name":"Subgradient method","level":2,"score":0.8555102348327637},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6453401446342468},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5813961625099182},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5604608058929443},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.5236353874206543},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.48956021666526794},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.473458468914032},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.44597509503364563},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.4420733153820038},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.43730294704437256},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.43562692403793335},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37589216232299805},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.36340969800949097},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2836490273475647},{"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/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/17m1118609","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1118609","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:dr.ntu.edu.sg:10356/86220","is_oa":true,"landing_page_url":"http://hdl.handle.net/10220/49275","pdf_url":"https://dr.ntu.edu.sg/bitstream/10356/86220/1/DISTRIBUTED%20CONTINUOUS-TIME%20ALGORITHMS%20FOR.pdf","source":{"id":"https://openalex.org/S4306402609","display_name":"DR-NTU (Nanyang Technological University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I172675005","host_organization_name":"Nanyang Technological University","host_organization_lineage":["https://openalex.org/I172675005"],"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":"Journal Article"}],"best_oa_location":{"id":"pmh:oai:dr.ntu.edu.sg:10356/86220","is_oa":true,"landing_page_url":"http://hdl.handle.net/10220/49275","pdf_url":"https://dr.ntu.edu.sg/bitstream/10356/86220/1/DISTRIBUTED%20CONTINUOUS-TIME%20ALGORITHMS%20FOR.pdf","source":{"id":"https://openalex.org/S4306402609","display_name":"DR-NTU (Nanyang Technological University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I172675005","host_organization_name":"Nanyang Technological University","host_organization_lineage":["https://openalex.org/I172675005"],"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":"Journal Article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1004037678","display_name":null,"funder_award_id":"61733018","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program 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/G198884366","display_name":null,"funder_award_id":"61603378","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2082826544","display_name":null,"funder_award_id":"Postdoctoral","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"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/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/G3334912206","display_name":null,"funder_award_id":"2017M620020","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G3463386786","display_name":null,"funder_award_id":"2017M620","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G364181133","display_name":null,"funder_award_id":"2016YFB0901900","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation 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/G5223055782","display_name":null,"funder_award_id":"B0901","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5319174282","display_name":null,"funder_award_id":"61733018","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5612697103","display_name":null,"funder_award_id":"2017M","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G5947242638","display_name":null,"funder_award_id":"4152057","funder_id":"https://openalex.org/F4320322919","funder_display_name":"Natural Science Foundation of Beijing Municipality"},{"id":"https://openalex.org/G5983507987","display_name":null,"funder_award_id":"2016YFB0901900","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G6321201599","display_name":null,"funder_award_id":"6157334","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7059539623","display_name":null,"funder_award_id":"2016YFB090190","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G788007168","display_name":null,"funder_award_id":"6160337","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7893519798","display_name":null,"funder_award_id":"61573344","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8114646031","display_name":null,"funder_award_id":"2016Y","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G8121213928","display_name":null,"funder_award_id":"61573344","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program 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/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"},{"id":"https://openalex.org/F4320322919","display_name":"Natural Science Foundation of Beijing Municipality","ror":null},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2899194738.pdf"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W1966554507","https://openalex.org/W1968094122","https://openalex.org/W1973889396","https://openalex.org/W1982993533","https://openalex.org/W1983627730","https://openalex.org/W1988901237","https://openalex.org/W2027741263","https://openalex.org/W2029184861","https://openalex.org/W2042860072","https://openalex.org/W2056014954","https://openalex.org/W2089580321","https://openalex.org/W2114791779","https://openalex.org/W2139638005","https://openalex.org/W2145072018","https://openalex.org/W2154414031","https://openalex.org/W2163916252","https://openalex.org/W2164642931","https://openalex.org/W2215067230","https://openalex.org/W2248806424","https://openalex.org/W2266214069","https://openalex.org/W2273484141","https://openalex.org/W2277723519","https://openalex.org/W2341544006","https://openalex.org/W2402358239","https://openalex.org/W2521320587","https://openalex.org/W2567931453","https://openalex.org/W2592202249","https://openalex.org/W2963125098","https://openalex.org/W2964211247","https://openalex.org/W2964255343","https://openalex.org/W4246463991","https://openalex.org/W4292363360"],"related_works":["https://openalex.org/W4297153560","https://openalex.org/W2465405765","https://openalex.org/W2964186284","https://openalex.org/W2804400349","https://openalex.org/W2140018151","https://openalex.org/W3084689723","https://openalex.org/W3161275408","https://openalex.org/W2811183536","https://openalex.org/W3088056528","https://openalex.org/W4387870386"],"abstract_inverted_index":{"This":[0],"paper":[1],"studies":[2],"distributed":[3,79],"algorithms":[4,98],"for":[5],"the":[6,30,63,70,94,100,112,115,132,135],"nonsmooth":[7,26],"extended":[8],"monotropic":[9],"optimization":[10,17,73],"problem,":[11,74],"which":[12],"is":[13,29],"a":[14,20,40],"general":[15],"convex":[16,72],"problem":[18],"with":[19,43,83,111],"certain":[21],"separable":[22],"structure.":[23],"The":[24],"considered":[25],"objective":[27,34,57],"function":[28],"sum":[31],"of":[32,96,114,117,134],"local":[33,44,56,59],"functions":[35],"assigned":[36],"to":[37,99,130],"agents":[38],"in":[39],"multiagent":[41],"network,":[42],"set":[45,60],"constraints":[46],"and":[47,62,87,107,122],"affine":[48],"equality":[49],"constraints.":[50],"Each":[51],"agent":[52],"only":[53],"knows":[54],"its":[55],"function,":[58],"constraint,":[61],"information":[64],"exchanged":[65],"between":[66],"neighbors.":[67],"To":[68],"solve":[69],"constrained":[71],"we":[75,92,126],"propose":[76],"two":[77],"novel":[78],"continuous-time":[80],"subgradient-based":[81],"algorithms,":[82],"projected":[84],"output":[85],"feedback":[86],"derivative":[88],"feedback,":[89],"respectively.":[90],"Moreover,":[91],"prove":[93],"convergence":[95,109],"proposed":[97,136],"optimal":[101],"solutions":[102],"under":[103],"some":[104],"mild":[105],"conditions":[106],"analyze":[108],"rates,":[110],"help":[113],"techniques":[116],"variational":[118],"inequalities,":[119],"decomposition":[120],"methods,":[121],"differential":[123],"inclusions.":[124],"Finally,":[125],"give":[127],"an":[128],"example":[129],"illustrate":[131],"efficacy":[133],"algorithms.":[137]},"counts_by_year":[{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":14},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":16},{"year":2020,"cited_by_count":13},{"year":2019,"cited_by_count":13},{"year":2018,"cited_by_count":1}],"updated_date":"2026-03-18T14:38:29.013473","created_date":"2025-10-10T00:00:00"}