{"id":"https://openalex.org/W3190424950","doi":"https://doi.org/10.1109/tsmc.2021.3098641","title":"Designing Zero-Gradient-Sum Protocols for Finite-Time Distributed Optimization Problem","display_name":"Designing Zero-Gradient-Sum Protocols for Finite-Time Distributed Optimization Problem","publication_year":2021,"publication_date":"2021-07-29","ids":{"openalex":"https://openalex.org/W3190424950","doi":"https://doi.org/10.1109/tsmc.2021.3098641","mag":"3190424950"},"language":"en","primary_location":{"id":"doi:10.1109/tsmc.2021.3098641","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmc.2021.3098641","pdf_url":null,"source":{"id":"https://openalex.org/S4210209078","display_name":"IEEE Transactions on Systems Man and Cybernetics Systems","issn_l":"2168-2216","issn":["2168-2216","2168-2232"],"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 Systems, Man, and Cybernetics: Systems","raw_type":"journal-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/A5086540629","display_name":"Zizhen Wu","orcid":"https://orcid.org/0000-0003-0741-9827"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]},{"id":"https://openalex.org/I4391767778","display_name":"State Key Laboratory of Turbulence and Complex Systems","ror":"https://ror.org/04km98768","country_code":null,"type":"facility","lineage":["https://openalex.org/I20231570","https://openalex.org/I4391767778"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zizhen Wu","raw_affiliation_strings":["Department of Mechanics and Engineering Science, State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0003-0741-9827","affiliations":[{"raw_affiliation_string":"Department of Mechanics and Engineering Science, State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing, China","institution_ids":["https://openalex.org/I20231570","https://openalex.org/I4391767778"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091694797","display_name":"Zhongkui Li","orcid":"https://orcid.org/0000-0002-9361-4305"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]},{"id":"https://openalex.org/I4391767778","display_name":"State Key Laboratory of Turbulence and Complex Systems","ror":"https://ror.org/04km98768","country_code":null,"type":"facility","lineage":["https://openalex.org/I20231570","https://openalex.org/I4391767778"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhongkui Li","raw_affiliation_strings":["Department of Mechanics and Engineering Science, State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-9361-4305","affiliations":[{"raw_affiliation_string":"Department of Mechanics and Engineering Science, State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing, China","institution_ids":["https://openalex.org/I20231570","https://openalex.org/I4391767778"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073958329","display_name":"Junzhi Yu","orcid":"https://orcid.org/0000-0002-6347-572X"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]},{"id":"https://openalex.org/I4391767778","display_name":"State Key Laboratory of Turbulence and Complex Systems","ror":"https://ror.org/04km98768","country_code":null,"type":"facility","lineage":["https://openalex.org/I20231570","https://openalex.org/I4391767778"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Junzhi Yu","raw_affiliation_strings":["Department of Mechanics and Engineering Science, State Key Laboratory for Turbulence and Complex Systems, BIC-ESAT, College of Engineering, Peking University, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanics and Engineering Science, State Key Laboratory for Turbulence and Complex Systems, BIC-ESAT, College of Engineering, Peking University, Beijing, China","institution_ids":["https://openalex.org/I20231570","https://openalex.org/I4391767778"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.1653,"has_fulltext":false,"cited_by_count":63,"citation_normalized_percentile":{"value":0.95651772,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"52","issue":"7","first_page":"4569","last_page":"4577"},"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":0.9873999953269958,"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"}},{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9854000210762024,"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/convergence","display_name":"Convergence (economics)","score":0.7128576636314392},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6299266815185547},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.6051256060600281},{"id":"https://openalex.org/keywords/settling-time","display_name":"Settling time","score":0.581182599067688},{"id":"https://openalex.org/keywords/network-topology","display_name":"Network topology","score":0.5262554883956909},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.49279287457466125},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.4877472519874573},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.48740485310554504},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.47486066818237305},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4345276355743408},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4338498115539551},{"id":"https://openalex.org/keywords/multi-agent-system","display_name":"Multi-agent system","score":0.4331350326538086},{"id":"https://openalex.org/keywords/protocol","display_name":"Protocol (science)","score":0.42417392134666443},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.41395366191864014},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4125317633152008},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.2995494604110718}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7128576636314392},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6299266815185547},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.6051256060600281},{"id":"https://openalex.org/C14781684","wikidata":"https://www.wikidata.org/wiki/Q3983320","display_name":"Settling time","level":3,"score":0.581182599067688},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.5262554883956909},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.49279287457466125},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4877472519874573},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.48740485310554504},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.47486066818237305},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4345276355743408},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4338498115539551},{"id":"https://openalex.org/C41550386","wikidata":"https://www.wikidata.org/wiki/Q529909","display_name":"Multi-agent system","level":2,"score":0.4331350326538086},{"id":"https://openalex.org/C2780385302","wikidata":"https://www.wikidata.org/wiki/Q367158","display_name":"Protocol (science)","level":3,"score":0.42417392134666443},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.41395366191864014},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4125317633152008},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.2995494604110718},{"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C142724271","wikidata":"https://www.wikidata.org/wiki/Q7208","display_name":"Pathology","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C160030872","wikidata":"https://www.wikidata.org/wiki/Q2142864","display_name":"Step response","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/C204787440","wikidata":"https://www.wikidata.org/wiki/Q188504","display_name":"Alternative medicine","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/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsmc.2021.3098641","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmc.2021.3098641","pdf_url":null,"source":{"id":"https://openalex.org/S4210209078","display_name":"IEEE Transactions on Systems Man and Cybernetics Systems","issn_l":"2168-2216","issn":["2168-2216","2168-2232"],"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 Systems, Man, and Cybernetics: Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5047483927","display_name":"\u57fa\u4e8e\u4e8b\u4ef6\u9a71\u52a8\u7684\u5b8c\u5168\u5206\u5e03\u5f0f\u534f\u540c\u63a7\u5236\u7814\u7a76","funder_award_id":"61973006","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7222494787","display_name":null,"funder_award_id":"U1713223","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7603313047","display_name":null,"funder_award_id":"U1909206","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"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W2040711492","https://openalex.org/W2057929279","https://openalex.org/W2062551655","https://openalex.org/W2070291355","https://openalex.org/W2114791779","https://openalex.org/W2124541940","https://openalex.org/W2154414031","https://openalex.org/W2191781618","https://openalex.org/W2245872406","https://openalex.org/W2268437176","https://openalex.org/W2327232412","https://openalex.org/W2517192452","https://openalex.org/W2571423792","https://openalex.org/W2752175744","https://openalex.org/W2763317297","https://openalex.org/W2767760906","https://openalex.org/W2768388593","https://openalex.org/W2774390121","https://openalex.org/W2800598982","https://openalex.org/W2807335901","https://openalex.org/W2807424650","https://openalex.org/W2889141596","https://openalex.org/W2905101123","https://openalex.org/W2943555865","https://openalex.org/W2946038967","https://openalex.org/W2970372812","https://openalex.org/W2972042470","https://openalex.org/W2982377397","https://openalex.org/W2983045961","https://openalex.org/W3016897523","https://openalex.org/W3081028519","https://openalex.org/W3089797543","https://openalex.org/W3114478348","https://openalex.org/W3115264163","https://openalex.org/W3155662393","https://openalex.org/W3158998839","https://openalex.org/W4241879758","https://openalex.org/W4293078920"],"related_works":["https://openalex.org/W1598820299","https://openalex.org/W2079049982","https://openalex.org/W1490949538","https://openalex.org/W2751205960","https://openalex.org/W2180200293","https://openalex.org/W2292721517","https://openalex.org/W2033417366","https://openalex.org/W2985979428","https://openalex.org/W2510140549","https://openalex.org/W2187449906"],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"the":[3,14,23,42,48,52,55,66,76,82,85,97,116,120,123],"distributed":[4],"finite-time":[5,38],"and":[6,91],"fixed-time":[7,94],"optimization":[8,31],"problems":[9],"are":[10,27],"investigated":[11],"by":[12,104],"adopting":[13],"zero-gradient-sum":[15],"(ZGS)":[16],"framework":[17],"in":[18,60,81],"multiagent":[19],"systems.":[20],"Specifically,":[21],"when":[22],"local":[24,58],"convex":[25],"functions":[26],"nonquadratic,":[28],"a":[29,37,61,71,93,106],"basic":[30],"protocol":[32],"is":[33,102,125],"proposed":[34],"to":[35,114],"obtain":[36],"convergence,":[39],"such":[40],"that":[41],"networked":[43],"system":[44],"can":[45,74],"cooperatively":[46],"seek":[47],"optimal":[49],"solution":[50],"of":[51,57,68,78,84,88,122],"global":[53],"objective,":[54,59],"sum":[56],"limited":[62],"time.":[63],"By":[64],"utilizing":[65],"property":[67],"quadratic":[69],"functions,":[70],"reduced":[72],"algorithm":[73,108],"remove":[75],"dependence":[77],"initial":[79],"conditions":[80],"estimation":[83],"upper":[86],"bound":[87],"settling":[89],"time":[90],"achieve":[92],"result.":[95],"Besides,":[96],"problem":[98],"with":[99,109],"time-varying":[100],"topologies":[101],"studied":[103],"introducing":[105],"modified":[107],"an":[110],"artificial":[111],"potential":[112],"function":[113],"preserve":[115],"network":[117],"connectivity.":[118],"Finally,":[119],"validity":[121],"protocols":[124],"demonstrated":[126],"via":[127],"some":[128],"example":[129],"simulations.":[130]},"counts_by_year":[{"year":2026,"cited_by_count":7},{"year":2025,"cited_by_count":22},{"year":2024,"cited_by_count":16},{"year":2023,"cited_by_count":13},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
