{"id":"https://openalex.org/W2571423792","doi":"https://doi.org/10.1109/tac.2012.2184199","title":"Zero-Gradient-Sum Algorithms for Distributed Convex Optimization: The Continuous-Time Case","display_name":"Zero-Gradient-Sum Algorithms for Distributed Convex Optimization: The Continuous-Time Case","publication_year":2012,"publication_date":"2012-01-12","ids":{"openalex":"https://openalex.org/W2571423792","doi":"https://doi.org/10.1109/tac.2012.2184199","mag":"2571423792"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2012.2184199","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2012.2184199","pdf_url":null,"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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100675573","display_name":"Jie Lu","orcid":"https://orcid.org/0000-0002-4362-6543"},"institutions":[{"id":"https://openalex.org/I8692664","display_name":"University of Oklahoma","ror":"https://ror.org/02aqsxs83","country_code":"US","type":"education","lineage":["https://openalex.org/I8692664"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jie Lu","raw_affiliation_strings":["School of Electrical and Computer Engineering, University of Oklahoma, Norman, OK, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Computer Engineering, University of Oklahoma, Norman, OK, USA","institution_ids":["https://openalex.org/I8692664"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101932271","display_name":"Choon Yik Tang","orcid":"https://orcid.org/0000-0001-6145-301X"},"institutions":[{"id":"https://openalex.org/I8692664","display_name":"University of Oklahoma","ror":"https://ror.org/02aqsxs83","country_code":"US","type":"education","lineage":["https://openalex.org/I8692664"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Choon Yik Tang","raw_affiliation_strings":["School of Electrical and Computer Engineering, University of Oklahoma, Norman, OK, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Computer Engineering, University of Oklahoma, Norman, OK, USA","institution_ids":["https://openalex.org/I8692664"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":10.0612,"has_fulltext":false,"cited_by_count":398,"citation_normalized_percentile":{"value":0.98432695,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"57","issue":"9","first_page":"2348","last_page":"2354"},"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9930999875068665,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.645039975643158},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5958513021469116},{"id":"https://openalex.org/keywords/algebraic-connectivity","display_name":"Algebraic connectivity","score":0.5581609606742859},{"id":"https://openalex.org/keywords/network-topology","display_name":"Network topology","score":0.5048161149024963},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5021779537200928},{"id":"https://openalex.org/keywords/consensus","display_name":"Consensus","score":0.49764707684516907},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.4823588728904724},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4660191535949707},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.4459449350833893},{"id":"https://openalex.org/keywords/distributed-algorithm","display_name":"Distributed algorithm","score":0.4240427613258362},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4178868234157562},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36921072006225586},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.30620884895324707},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.2669650912284851},{"id":"https://openalex.org/keywords/laplacian-matrix","display_name":"Laplacian matrix","score":0.2594016492366791},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.21519580483436584},{"id":"https://openalex.org/keywords/multi-agent-system","display_name":"Multi-agent system","score":0.18226996064186096},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.16438686847686768}],"concepts":[{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.645039975643158},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5958513021469116},{"id":"https://openalex.org/C7948225","wikidata":"https://www.wikidata.org/wiki/Q4723998","display_name":"Algebraic connectivity","level":4,"score":0.5581609606742859},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.5048161149024963},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5021779537200928},{"id":"https://openalex.org/C107107730","wikidata":"https://www.wikidata.org/wiki/Q2994424","display_name":"Consensus","level":3,"score":0.49764707684516907},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4823588728904724},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4660191535949707},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.4459449350833893},{"id":"https://openalex.org/C130120984","wikidata":"https://www.wikidata.org/wiki/Q2835898","display_name":"Distributed algorithm","level":2,"score":0.4240427613258362},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4178868234157562},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36921072006225586},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30620884895324707},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.2669650912284851},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.2594016492366791},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.21519580483436584},{"id":"https://openalex.org/C41550386","wikidata":"https://www.wikidata.org/wiki/Q529909","display_name":"Multi-agent system","level":2,"score":0.18226996064186096},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.16438686847686768},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2012.2184199","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2012.2184199","pdf_url":null,"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":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W87454703","https://openalex.org/W1864806140","https://openalex.org/W1973754217","https://openalex.org/W1988795359","https://openalex.org/W2044212084","https://openalex.org/W2054104996","https://openalex.org/W2066332749","https://openalex.org/W2085752001","https://openalex.org/W2099175737","https://openalex.org/W2107396783","https://openalex.org/W2115428923","https://openalex.org/W2117412539","https://openalex.org/W2124541940","https://openalex.org/W2126510988","https://openalex.org/W2142184324","https://openalex.org/W2150633835","https://openalex.org/W2160785244","https://openalex.org/W2562862721","https://openalex.org/W4247555059","https://openalex.org/W4250589301"],"related_works":["https://openalex.org/W2393350255","https://openalex.org/W257189624","https://openalex.org/W2356369451","https://openalex.org/W4297903463","https://openalex.org/W2157782185","https://openalex.org/W2537685543","https://openalex.org/W2592592723","https://openalex.org/W2123112061","https://openalex.org/W2888970658","https://openalex.org/W4313024142"],"abstract_inverted_index":{"This":[0],"technical":[1,116],"note":[2,117],"presents":[3],"a":[4,28,52,65,74,122],"set":[5],"of":[6,76,93,114,125],"continuous-time":[7],"distributed":[8,132,135],"algorithms":[9,24,40,128],"that":[10,32,48,73],"solve":[11],"unconstrained,":[12],"separable,":[13],"convex":[14,136],"optimization":[15],"problems":[16],"over":[17],"undirected":[18],"networks":[19],"with":[20],"fixed":[21],"topologies.":[22],"The":[23,112],"are":[25,36],"developed":[26],"using":[27],"Lyapunov":[29],"function":[30,110],"candidate":[31],"exploits":[33],"convexity,":[34],"and":[35,55,81,84,99,109,129],"called":[37],"Zero-Gradient-Sum":[38],"(ZGS)":[39],"as":[41,121],"they":[42],"yield":[43],"nonlinear":[44],"networked":[45],"dynamical":[46],"systems":[47],"evolve":[49],"invariantly":[50],"on":[51,87],"zero-gradient-sum":[53],"manifold":[54],"converge":[56,79],"asymptotically":[57],"to":[58,68,134],"the":[59,94,103],"unknown":[60],"optimizer.":[61],"We":[62],"also":[63],"describe":[64],"systematic":[66],"way":[67],"construct":[69],"ZGS":[70],"algorithms,":[71],"show":[72],"subset":[75],"them":[77],"actually":[78],"exponentially,":[80],"obtain":[82],"lower":[83],"upper":[85],"bounds":[86],"their":[88],"convergence":[89],"rates":[90],"in":[91],"terms":[92],"network":[95],"topologies,":[96],"problem":[97],"characteristics,":[98],"algorithm":[100],"parameters,":[101],"including":[102],"algebraic":[104],"connectivity,":[105],"Laplacian":[106],"spectral":[107],"radius,":[108],"curvatures.":[111],"findings":[113],"this":[115],"may":[118],"be":[119],"regarded":[120],"natural":[123],"generalization":[124],"several":[126],"well-known":[127],"results":[130],"for":[131],"consensus,":[133],"optimization.":[137]},"counts_by_year":[{"year":2026,"cited_by_count":15},{"year":2025,"cited_by_count":46},{"year":2024,"cited_by_count":40},{"year":2023,"cited_by_count":37},{"year":2022,"cited_by_count":32},{"year":2021,"cited_by_count":35},{"year":2020,"cited_by_count":36},{"year":2019,"cited_by_count":35},{"year":2018,"cited_by_count":41},{"year":2017,"cited_by_count":26},{"year":2016,"cited_by_count":28},{"year":2015,"cited_by_count":14},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
