{"id":"https://openalex.org/W4381739722","doi":"https://doi.org/10.1137/21m1403837","title":"Iteration-Complexity of First-Order Augmented Lagrangian Methods for Convex Conic Programming","display_name":"Iteration-Complexity of First-Order Augmented Lagrangian Methods for Convex Conic Programming","publication_year":2023,"publication_date":"2023-06-23","ids":{"openalex":"https://openalex.org/W4381739722","doi":"https://doi.org/10.1137/21m1403837"},"language":"en","primary_location":{"id":"doi:10.1137/21m1403837","doi":"https://doi.org/10.1137/21m1403837","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1403837","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-a","jufo-3","ki-jl-1","norway-2","poland-140","russia-white-list-1"],"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 Optimization","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1803.09941","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000609407","display_name":"Zhaosong Lu","orcid":"https://orcid.org/0000-0003-3277-7853","observed_orcids":["https://orcid.org/0000-0003-3277-7853"]},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhaosong Lu","raw_affiliation_strings":["Department of Industrial and Systems Engineering, University of Minnesota, Minneapolis, MN 55455 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Industrial and Systems Engineering, University of Minnesota, Minneapolis, MN 55455 USA","institution_ids":["https://openalex.org/I130238516"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029816914","display_name":"Zirui Zhou","orcid":"https://orcid.org/0000-0003-1690-0161","observed_orcids":["https://orcid.org/0000-0003-1690-0161"]},"institutions":[{"id":"https://openalex.org/I4210115038","display_name":"Huawei Technologies (Canada)","ror":"https://ror.org/026venb53","country_code":"CA","type":"company","lineage":["https://openalex.org/I2250955327","https://openalex.org/I4210115038"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Zirui Zhou","raw_affiliation_strings":["Huawei Technologies Canada, Burnaby V5C 6S7, BC, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Huawei Technologies Canada, Burnaby V5C 6S7, BC, Canada","institution_ids":["https://openalex.org/I4210115038"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.3687,"has_fulltext":true,"cited_by_count":25,"citation_normalized_percentile":{"value":0.89274662,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":99},"biblio":{"volume":"33","issue":"2","first_page":"1159","last_page":"1190"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.7265999913215637,"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"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.7265999913215637,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.2442999929189682,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.011599999852478504,"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/augmented-lagrangian-method","display_name":"augmented Lagrangian method","score":0.8140000104904175},{"id":"https://openalex.org/keywords/iteration-complexity","display_name":"iteration complexity","score":0.8009999990463257},{"id":"https://openalex.org/keywords/adaptive-regularization","display_name":"adaptive regularization","score":0.8050000071525574},{"id":"https://openalex.org/keywords/first-order-methods","display_name":"first-order methods","score":0.5910000205039978},{"id":"https://openalex.org/keywords/complexity-bounds","display_name":"complexity bounds","score":0.44600000977516174}],"concepts":[{"id":"https://openalex.org/C50454189","wikidata":"https://www.wikidata.org/wiki/Q2075125","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","level":2,"score":0.8856207132339478},{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.8171790242195129},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7304763793945312},{"id":"https://openalex.org/C108598597","wikidata":"https://www.wikidata.org/wiki/Q124255","display_name":"Conic section","level":2,"score":0.7222313284873962},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5841361284255981},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4898523986339569},{"id":"https://openalex.org/C155253501","wikidata":"https://www.wikidata.org/wiki/Q461992","display_name":"Interior point method","level":2,"score":0.46324411034584045},{"id":"https://openalex.org/C79187972","wikidata":"https://www.wikidata.org/wiki/Q2654791","display_name":"Conic optimization","level":5,"score":0.44242310523986816},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.4316200017929077},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.41959965229034424},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.406514048576355},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32879817485809326},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.304546594619751},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.24103236198425293},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2376796007156372},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/21m1403837","doi":"https://doi.org/10.1137/21m1403837","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1403837","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-a","jufo-3","ki-jl-1","norway-2","poland-140","russia-white-list-1"],"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 Optimization","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1803.09941","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1803.09941","pdf_url":"https://arxiv.org/pdf/1803.09941","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"doi:10.48550/arxiv.1803.09941","doi":"https://doi.org/10.48550/arxiv.1803.09941","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1803.09941","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1803.09941","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1803.09941","pdf_url":"https://arxiv.org/pdf/1803.09941","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1695691088","display_name":null,"funder_award_id":"IIS-2211491","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G18439693","display_name":"Collaborative Research: III: Medium: New Machine Learning Empowered Nanoinformatics System for Advancing Nanomaterial Design","funder_award_id":"2211491","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4381739722.pdf","grobid_xml":"https://content.openalex.org/works/W4381739722.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W269693995","https://openalex.org/W1550611075","https://openalex.org/W1669104078","https://openalex.org/W1699262394","https://openalex.org/W1996287810","https://openalex.org/W1999915705","https://openalex.org/W2038497950","https://openalex.org/W2042261731","https://openalex.org/W2042335549","https://openalex.org/W2042860556","https://openalex.org/W2044774602","https://openalex.org/W2057624533","https://openalex.org/W2107465205","https://openalex.org/W2124541940","https://openalex.org/W2124768887","https://openalex.org/W2135779729","https://openalex.org/W2143075842","https://openalex.org/W2163786124","https://openalex.org/W2167732364","https://openalex.org/W2169899245","https://openalex.org/W2605995072","https://openalex.org/W2611293703","https://openalex.org/W2770716722","https://openalex.org/W2798766386","https://openalex.org/W2962956186","https://openalex.org/W2969771825","https://openalex.org/W3012080241","https://openalex.org/W3125796663","https://openalex.org/W3141595720","https://openalex.org/W4242209908","https://openalex.org/W4245189002","https://openalex.org/W4299439662","https://openalex.org/W4301014524"],"related_works":["https://openalex.org/W2044774602","https://openalex.org/W269693995","https://openalex.org/W3011456202","https://openalex.org/W2951072042","https://openalex.org/W3153954249","https://openalex.org/W3206860823","https://openalex.org/W1502987098","https://openalex.org/W2969771825","https://openalex.org/W2955184355","https://openalex.org/W2951136802"],"abstract_inverted_index":{"Abstract.":[0],"In":[1,12],"this":[2,31],"paper":[3],"we":[4,14],"consider":[5],"a":[6,43,90,125],"class":[7],"of":[8,45,56,59,118,128,153],"convex":[9],"conic":[10],"programming.":[11],"particular,":[13],"first":[15],"propose":[16,79],"an":[17,66,80,110,168],"inexact":[18,130,143,169],"augmented":[19,36],"Lagrangian":[20,37],"(I-AL)":[21],"method":[22,28,63,84],"that":[23,52,87],"resembles":[24],"the":[25,35,53,60,119,129,136,139,154,159,164],"classical":[26],"I-AL":[27,62,83,106,120,140,156,165],"for":[29,64,108],"solving":[30],"problem,":[32],"in":[33,158],"which":[34,97,161],"subproblems":[38],"are":[39],"solved":[40],"approximately":[41],"by":[42,104],"variant":[44],"Nesterov\u2019s":[46],"optimal":[47],"first-order":[48,57,91,105,155],"method.":[49,172],"We":[50,77],"show":[51,86],"total":[54],"number":[55],"iterations":[58],"proposed":[61],"finding":[65,109],"[Formula:":[67,74,94,111],"see":[68,75,95,112],"text]-KKT":[69,113],"solution":[70],"is":[71,122,146],"at":[72],"most":[73],"text].":[76],"then":[78],"adaptively":[81],"regularized":[82],"and":[85,135,142],"it":[88],"achieves":[89],"iteration":[92],"complexity":[93,101,116,151],"text],":[96],"significantly":[98],"improves":[99],"existing":[100,150],"bounds":[102],"achieved":[103],"methods":[107,121,141,157,166],"solution.":[114],"Our":[115],"analysis":[117,127],"based":[123],"on":[124],"sharp":[126],"proximal":[131],"point":[132],"algorithm":[133],"(PPA)":[134],"connection":[137],"between":[138],"PPA.":[144],"It":[145],"vastly":[147],"different":[148],"from":[149],"analyses":[152],"literature,":[160],"typically":[162],"regard":[163],"as":[167],"dual":[170],"gradient":[171]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2023-06-24T00:00:00"}