{"id":"https://openalex.org/W1514810191","doi":"https://doi.org/10.1109/acc.2015.7170791","title":"On the convergence rate of a Distributed Augmented Lagrangian optimization algorithm","display_name":"On the convergence rate of a Distributed Augmented Lagrangian optimization algorithm","publication_year":2015,"publication_date":"2015-07-01","ids":{"openalex":"https://openalex.org/W1514810191","doi":"https://doi.org/10.1109/acc.2015.7170791","mag":"1514810191"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2015.7170791","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2015.7170791","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 American Control Conference (ACC)","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/A5086888501","display_name":"Nikolaos Chatzipanagiotis","orcid":"https://orcid.org/0000-0003-2326-5119"},"institutions":[{"id":"https://openalex.org/I170897317","display_name":"Duke University","ror":"https://ror.org/00py81415","country_code":"US","type":"education","lineage":["https://openalex.org/I170897317"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Nikolaos Chatzipanagiotis","raw_affiliation_strings":["Dept. of Mechanical Engineering and Materials Science, Duke University, Durham, NC, USA","Department of Mechanical Engineering and Materials Science, Duke University, Durham,#N#NC\u00a027708,#N#USA"],"affiliations":[{"raw_affiliation_string":"Dept. of Mechanical Engineering and Materials Science, Duke University, Durham, NC, USA","institution_ids":["https://openalex.org/I170897317"]},{"raw_affiliation_string":"Department of Mechanical Engineering and Materials Science, Duke University, Durham,#N#NC\u00a027708,#N#USA","institution_ids":["https://openalex.org/I170897317"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080808780","display_name":"Michael M. Zavlanos","orcid":"https://orcid.org/0000-0003-1748-8228"},"institutions":[{"id":"https://openalex.org/I170897317","display_name":"Duke University","ror":"https://ror.org/00py81415","country_code":"US","type":"education","lineage":["https://openalex.org/I170897317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Michael M. Zavlanos","raw_affiliation_strings":["Dept. of Mechanical Engineering and Materials Science, Duke University, Durham, NC, USA","Department of Mechanical Engineering and Materials Science, Duke University, Durham,#N#NC\u00a027708,#N#USA"],"affiliations":[{"raw_affiliation_string":"Dept. of Mechanical Engineering and Materials Science, Duke University, Durham, NC, USA","institution_ids":["https://openalex.org/I170897317"]},{"raw_affiliation_string":"Department of Mechanical Engineering and Materials Science, Duke University, Durham,#N#NC\u00a027708,#N#USA","institution_ids":["https://openalex.org/I170897317"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5086888501"],"corresponding_institution_ids":["https://openalex.org/I170897317"],"apc_list":null,"apc_paid":null,"fwci":2.3297,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.891425,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"541","last_page":"546"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9994000196456909,"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":0.9994000196456909,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9991999864578247,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9969000220298767,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/augmented-lagrangian-method","display_name":"Augmented Lagrangian method","score":0.8181407451629639},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.662899374961853},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6528829336166382},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.6104795336723328},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5938193202018738},{"id":"https://openalex.org/keywords/ergodic-theory","display_name":"Ergodic theory","score":0.5270999670028687},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5229681134223938},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4858340919017792},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4747474789619446},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43854543566703796},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.43710771203041077},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.42183324694633484},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3670673370361328}],"concepts":[{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.8181407451629639},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.662899374961853},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6528829336166382},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.6104795336723328},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5938193202018738},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.5270999670028687},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5229681134223938},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4858340919017792},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4747474789619446},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43854543566703796},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.43710771203041077},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42183324694633484},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3670673370361328},{"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/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","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/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/acc.2015.7170791","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2015.7170791","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 American Control Conference (ACC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1524324710","https://openalex.org/W1549918636","https://openalex.org/W1603765807","https://openalex.org/W1973615364","https://openalex.org/W1973889396","https://openalex.org/W1980236292","https://openalex.org/W1986080131","https://openalex.org/W1989659922","https://openalex.org/W1990615478","https://openalex.org/W1991482609","https://openalex.org/W2026342258","https://openalex.org/W2037091587","https://openalex.org/W2040179528","https://openalex.org/W2046387702","https://openalex.org/W2057873962","https://openalex.org/W2058532290","https://openalex.org/W2061117407","https://openalex.org/W2079261074","https://openalex.org/W2094631364","https://openalex.org/W2105693192","https://openalex.org/W2111076441","https://openalex.org/W2123705108","https://openalex.org/W2139596861","https://openalex.org/W2152637881","https://openalex.org/W2164278908","https://openalex.org/W2537861223","https://openalex.org/W2611293703","https://openalex.org/W3141222251","https://openalex.org/W4249512175","https://openalex.org/W4292363360","https://openalex.org/W4299439662","https://openalex.org/W4300028551","https://openalex.org/W6632668981","https://openalex.org/W6643754938","https://openalex.org/W6675881135","https://openalex.org/W6677012920"],"related_works":["https://openalex.org/W50969306","https://openalex.org/W2390585021","https://openalex.org/W412641959","https://openalex.org/W2779828239","https://openalex.org/W2131718214","https://openalex.org/W2008452439","https://openalex.org/W4387870386","https://openalex.org/W3159039452","https://openalex.org/W2187449906","https://openalex.org/W2962818859"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,18,57,62,91,100,138,155,159],"Accelerated":[3],"Distributed":[4],"Augmented":[5],"Lagrangians":[6,45],"(ADAL)":[7],"algorithm,":[8],"a":[9,28,77,83,95,112,130],"distributed":[10],"optimization":[11],"algorithm":[12],"that":[13,23,67,114,127],"was":[14],"recently":[15],"developed":[16],"by":[17],"authors":[19],"to":[20,34,56,117,154,166],"address":[21],"problems":[22],"involve":[24],"multiple":[25],"agents":[26,92],"optimizing":[27],"separable":[29,97],"convex":[30,35],"objective":[31],"function":[32],"subject":[33],"local":[36],"constraints":[37],"and":[38,102,108],"linear":[39],"coupling":[40],"constraints.":[41],"Optimization":[42],"using":[43],"augmented":[44],"(AL)":[46],"combines":[47],"low":[48],"computational":[49],"complexity":[50],"with":[51],"fast":[52],"convergence":[53,116,133,143],"speeds":[54],"due":[55],"regularization":[58],"terms":[59],"included":[60],"in":[61,111,147],"AL.":[63],"However,":[64],"decentralized":[65],"methods":[66],"employ":[68],"ALs":[69,75],"are":[70],"few,":[71],"as":[72],"decomposition":[73],"of":[74,99,140,158,162],"is":[76,82,145],"particularly":[78],"challenging":[79],"task.":[80],"ADAL":[81,128],"primal-dual":[84],"iterative":[85],"scheme":[86],"where":[87,135],"at":[88],"every":[89],"iteration":[90,167],"locally":[93],"optimize":[94],"novel":[96],"approximation":[98],"AL":[101],"then":[103],"appropriately":[104],"update":[105],"their":[106,118],"primal":[107,163],"dual":[109],"variables,":[110],"way":[113],"ensures":[115],"respective":[119],"optimal":[120],"sets.":[121],"In":[122],"this":[123],"paper,":[124],"we":[125],"prove":[126],"has":[129],"worst-case":[131],"O(1/k)":[132],"rate,":[134],"k":[136],"denotes":[137],"number":[139],"iterations.":[141],"The":[142],"rate":[144],"established":[146],"an":[148],"ergodic":[149,156],"sense,":[150],"i.e.,":[151],"it":[152],"refers":[153],"average":[157],"generated":[160],"sequences":[161],"variables":[164],"up":[165],"k.":[168]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}