{"id":"https://openalex.org/W4312437966","doi":"https://doi.org/10.1109/tac.2022.3230767","title":"On Centralized and Distributed Mirror Descent: Convergence Analysis Using Quadratic Constraints","display_name":"On Centralized and Distributed Mirror Descent: Convergence Analysis Using Quadratic Constraints","publication_year":2022,"publication_date":"2022-12-20","ids":{"openalex":"https://openalex.org/W4312437966","doi":"https://doi.org/10.1109/tac.2022.3230767"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2022.3230767","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2022.3230767","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/A5076743577","display_name":"Youbang Sun","orcid":"https://orcid.org/0000-0003-2494-8552"},"institutions":[{"id":"https://openalex.org/I12912129","display_name":"Northeastern University","ror":"https://ror.org/04t5xt781","country_code":"US","type":"education","lineage":["https://openalex.org/I12912129"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Youbang Sun","raw_affiliation_strings":["Department of Mechanical and Industrial Engineering, Northeastern University, Boston, MA, USA"],"raw_orcid":"https://orcid.org/0000-0003-2494-8552","affiliations":[{"raw_affiliation_string":"Department of Mechanical and Industrial Engineering, Northeastern University, Boston, MA, USA","institution_ids":["https://openalex.org/I12912129"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043154223","display_name":"Mahyar Fazlyab","orcid":"https://orcid.org/0000-0001-9695-6178"},"institutions":[{"id":"https://openalex.org/I145311948","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95","country_code":"US","type":"education","lineage":["https://openalex.org/I145311948"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mahyar Fazlyab","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, MD, USA"],"raw_orcid":"https://orcid.org/0000-0001-9695-6178","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, MD, USA","institution_ids":["https://openalex.org/I145311948"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040922600","display_name":"Shahin Shahrampour","orcid":"https://orcid.org/0000-0003-3093-8510"},"institutions":[{"id":"https://openalex.org/I12912129","display_name":"Northeastern University","ror":"https://ror.org/04t5xt781","country_code":"US","type":"education","lineage":["https://openalex.org/I12912129"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shahin Shahrampour","raw_affiliation_strings":["Department of Mechanical and Industrial Engineering, Northeastern University, Boston, MA, USA"],"raw_orcid":"https://orcid.org/0000-0003-3093-8510","affiliations":[{"raw_affiliation_string":"Department of Mechanical and Industrial Engineering, Northeastern University, Boston, MA, USA","institution_ids":["https://openalex.org/I12912129"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3638,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.80922475,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"68","issue":"5","first_page":"3139","last_page":"3146"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9987999796867371,"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":0.9972000122070312,"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/rate-of-convergence","display_name":"Rate of convergence","score":0.7367568016052246},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.6022418737411499},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5743537545204163},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.5583606362342834},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5338849425315857},{"id":"https://openalex.org/keywords/stochastic-gradient-descent","display_name":"Stochastic gradient descent","score":0.49806714057922363},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4708620607852936},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.45148593187332153},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.44500282406806946},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.431260883808136},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42902493476867676},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.40622326731681824},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3427302837371826},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3167848587036133},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10146218538284302},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09417501091957092}],"concepts":[{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.7367568016052246},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.6022418737411499},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5743537545204163},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.5583606362342834},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5338849425315857},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.49806714057922363},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4708620607852936},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45148593187332153},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.44500282406806946},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.431260883808136},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42902493476867676},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.40622326731681824},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3427302837371826},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3167848587036133},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10146218538284302},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09417501091957092},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"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/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2022.3230767","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2022.3230767","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W1503425191","https://openalex.org/W1571416372","https://openalex.org/W1962121538","https://openalex.org/W2016384870","https://openalex.org/W2018493294","https://openalex.org/W2039867272","https://openalex.org/W2044212084","https://openalex.org/W2057929279","https://openalex.org/W2097460613","https://openalex.org/W2097944741","https://openalex.org/W2114791779","https://openalex.org/W2164642931","https://openalex.org/W2243169878","https://openalex.org/W2251632681","https://openalex.org/W2513180554","https://openalex.org/W2521320587","https://openalex.org/W2532703171","https://openalex.org/W2763533254","https://openalex.org/W2783742282","https://openalex.org/W2901838001","https://openalex.org/W2963007855","https://openalex.org/W2963732316","https://openalex.org/W2963910188","https://openalex.org/W2964102336","https://openalex.org/W2964191394","https://openalex.org/W2964211247","https://openalex.org/W2993403400","https://openalex.org/W3005717566","https://openalex.org/W3008463948","https://openalex.org/W3011252985","https://openalex.org/W3016889113","https://openalex.org/W3016890209","https://openalex.org/W3087338967","https://openalex.org/W3092262213","https://openalex.org/W3100513551","https://openalex.org/W3104429825","https://openalex.org/W3108866329","https://openalex.org/W4206526750","https://openalex.org/W4226207560","https://openalex.org/W4301435544","https://openalex.org/W4312437966","https://openalex.org/W6684579695","https://openalex.org/W6739792718","https://openalex.org/W6783047790"],"related_works":["https://openalex.org/W3002546633","https://openalex.org/W4312206320","https://openalex.org/W2964170259","https://openalex.org/W2160052563","https://openalex.org/W2765682467","https://openalex.org/W4206119629","https://openalex.org/W2115832833","https://openalex.org/W2803118069","https://openalex.org/W2126408684","https://openalex.org/W4382937879"],"abstract_inverted_index":{"Mirror":[0],"descent":[1,16],"(MD)":[2],"is":[3],"a":[4,81,96],"powerful":[5],"first-order":[6],"optimization":[7,12],"technique":[8],"that":[9,74,88,175],"subsumes":[10],"several":[11],"algorithms":[13],"including":[14],"gradient":[15],"(GD).":[17],"In":[18],"this":[19],"work,":[20],"we":[21,54,70,112],"leverage":[22],"quadratic":[23],"constraints":[24],"and":[25,32,59,66,79,119],"Lyapunov":[26],"functions":[27],"to":[28,85,183],"analyze":[29,113],"the":[30,34,38,86,90,114,121,132,136,141,153,164,184],"stability":[31],"characterize":[33,120],"convergence":[35,77,115,180],"rate":[36,92,107,122,143,159],"of":[37,93,116,131,138,144],"MD":[39,65,118,146,162],"algorithm":[40],"as":[41,43,95],"well":[42],"its":[44],"distributed":[45,117,145,161,188],"variant":[46],"using":[47,124],"semidefinite":[48],"programming":[49],"(SDP).":[50],"For":[51,63],"both":[52,56],"algorithms,":[53],"consider":[55],"strongly":[57,67,171],"convex":[58,61,68,109,165,172],"nonstrongly":[60],"assumptions.":[62],"centralized":[64],"problems,":[69],"construct":[71],"an":[72,105,125],"SDP":[73,87,126],"certifies":[75,178],"exponential":[76],"rates":[78,181,186],"derive":[80],"closed-form":[82],"feasible":[83],"solution":[84],"recovers":[89],"optimal":[91],"GD":[94],"special":[97],"case.":[98],"We":[99,155],"complement":[100],"our":[101,139,176],"analysis":[102],"by":[103],"providing":[104],"explicit$O(1/k)$convergence":[106],"for":[108,160,187],"problems.":[110],"Next,":[111],"numerically":[123],"whose":[127],"dimensions":[128],"are":[129],"independent":[130],"network":[133],"size.":[134],"To":[135],"best":[137],"knowledge,":[140],"numerical":[142,168],"has":[147],"not":[148],"been":[149],"previously":[150],"reported":[151],"in":[152,163],"literature.":[154],"further":[156],"prove":[157],"an$O(1/k)$convergence":[158],"setting.":[166],"Our":[167],"experiments":[169],"on":[170],"problems":[173],"indicate":[174],"framework":[177],"superior":[179],"compared":[182],"existing":[185],"GD.":[189]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}