{"id":"https://openalex.org/W2963264932","doi":"https://doi.org/10.1137/140983938","title":"Block Stochastic Gradient Iteration for Convex and Nonconvex Optimization","display_name":"Block Stochastic Gradient Iteration for Convex and Nonconvex Optimization","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2963264932","doi":"https://doi.org/10.1137/140983938","mag":"2963264932"},"language":"en","primary_location":{"id":"doi:10.1137/140983938","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140983938","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,"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"},"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/A5055895298","display_name":"Yangyang Xu","orcid":"https://orcid.org/0000-0002-4163-3723"},"institutions":[{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Yangyang Xu","raw_affiliation_strings":["Computational and Applied Mathematics, Rice University, Houston, TX","Department of Mathematics, UCLA, Los Angeles, CA"],"affiliations":[{"raw_affiliation_string":"Computational and Applied Mathematics, Rice University, Houston, TX","institution_ids":["https://openalex.org/I74775410"]},{"raw_affiliation_string":"Department of Mathematics, UCLA, Los Angeles, CA","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085908411","display_name":"Wotao Yin","orcid":"https://orcid.org/0000-0001-6697-9731"},"institutions":[{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wotao Yin","raw_affiliation_strings":["Department of Mathematics, UCLA, Los Angeles, CA","Computational and Applied Mathematics, Rice University, Houston, TX"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, UCLA, Los Angeles, CA","institution_ids":[]},{"raw_affiliation_string":"Computational and Applied Mathematics, Rice University, Houston, TX","institution_ids":["https://openalex.org/I74775410"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5055895298"],"corresponding_institution_ids":["https://openalex.org/I74775410"],"apc_list":null,"apc_paid":null,"fwci":13.7362,"has_fulltext":false,"cited_by_count":135,"citation_normalized_percentile":{"value":0.99428333,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"25","issue":"3","first_page":"1686","last_page":"1716"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"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":0.9995999932289124,"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/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9886999726295471,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/mathematics","display_name":"Mathematics","score":0.8270246982574463},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.5958483219146729},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.5778636932373047},{"id":"https://openalex.org/keywords/coordinate-descent","display_name":"Coordinate descent","score":0.5692108273506165},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5189128518104553},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.505374014377594},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5020215511322021},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.498889684677124},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4645855724811554},{"id":"https://openalex.org/keywords/gauss\u2013seidel-method","display_name":"Gauss\u2013Seidel method","score":0.45463886857032776},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3576461970806122},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.22097811102867126},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.20410862565040588},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12109693884849548}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8270246982574463},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.5958483219146729},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.5778636932373047},{"id":"https://openalex.org/C157553263","wikidata":"https://www.wikidata.org/wiki/Q5168004","display_name":"Coordinate descent","level":2,"score":0.5692108273506165},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5189128518104553},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.505374014377594},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5020215511322021},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.498889684677124},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4645855724811554},{"id":"https://openalex.org/C3828260","wikidata":"https://www.wikidata.org/wiki/Q1069090","display_name":"Gauss\u2013Seidel method","level":3,"score":0.45463886857032776},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3576461970806122},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.22097811102867126},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.20410862565040588},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12109693884849548},{"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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":1,"locations":[{"id":"doi:10.1137/140983938","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140983938","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,"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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7452299184","display_name":null,"funder_award_id":"W911NF","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G8319276993","display_name":null,"funder_award_id":"1317602","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8998121839","display_name":null,"funder_award_id":"911NF","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G934873480","display_name":null,"funder_award_id":"W911NF-09-1-0383","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320333591","display_name":"Multidisciplinary University Research Initiative","ror":null},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":55,"referenced_works":["https://openalex.org/W17407774","https://openalex.org/W1499137793","https://openalex.org/W1505731132","https://openalex.org/W1540764732","https://openalex.org/W1751687266","https://openalex.org/W1775859518","https://openalex.org/W1968154520","https://openalex.org/W1969048569","https://openalex.org/W1972711404","https://openalex.org/W1974524469","https://openalex.org/W1975768153","https://openalex.org/W1980147176","https://openalex.org/W1983094140","https://openalex.org/W1983916623","https://openalex.org/W1987083649","https://openalex.org/W1992208280","https://openalex.org/W1994616650","https://openalex.org/W2005876975","https://openalex.org/W2008164266","https://openalex.org/W2013850411","https://openalex.org/W2022393739","https://openalex.org/W2023901033","https://openalex.org/W2024484010","https://openalex.org/W2029463628","https://openalex.org/W2038497950","https://openalex.org/W2039050532","https://openalex.org/W2050968963","https://openalex.org/W2058532290","https://openalex.org/W2062770263","https://openalex.org/W2075660001","https://openalex.org/W2082639035","https://openalex.org/W2091825929","https://openalex.org/W2095984592","https://openalex.org/W2100556411","https://openalex.org/W2105767123","https://openalex.org/W2111200589","https://openalex.org/W2117686388","https://openalex.org/W2118585731","https://openalex.org/W2120420045","https://openalex.org/W2124541940","https://openalex.org/W2125993116","https://openalex.org/W2128529555","https://openalex.org/W2135046866","https://openalex.org/W2144829365","https://openalex.org/W2152734820","https://openalex.org/W2153631186","https://openalex.org/W2154152198","https://openalex.org/W2156163061","https://openalex.org/W2162746441","https://openalex.org/W2168909589","https://openalex.org/W2169713291","https://openalex.org/W2604272474","https://openalex.org/W2611328865","https://openalex.org/W2963470657","https://openalex.org/W3103657382"],"related_works":["https://openalex.org/W4361762909","https://openalex.org/W2370324520","https://openalex.org/W2996186043","https://openalex.org/W2182726851","https://openalex.org/W2312248459","https://openalex.org/W1971339393","https://openalex.org/W1494446635","https://openalex.org/W2992376929","https://openalex.org/W2951674121","https://openalex.org/W4312206320"],"abstract_inverted_index":{"The":[0,28,155],"stochastic":[1,21,223],"gradient":[2],"(SG)":[3],"method":[4,51,82,263],"can":[5,38],"quickly":[6,39],"solve":[7,40],"a":[8,11,20,25,50,78,115,196],"problem":[9],"with":[10,42,63,70],"large":[12],"number":[13],"of":[14,57,97,135,145,157,176,191,195,279],"components":[15,65],"in":[16,66,99,113,189],"the":[17,35,54,67,95,100,104,109,143,150,168,173,182,192,208,220,244,254,260,265,277],"objective,":[18],"or":[19,117],"optimization":[22],"problem,":[23],"to":[24,268],"moderate":[26],"accuracy.":[27],"block":[29,79,106,284],"coordinate":[30,285],"descent/update":[31],"(BCD)":[32],"method,":[33],"on":[34,108,219],"other":[36],"hand,":[37],"problems":[41,62],"multiple":[43,71],"(blocks":[44,72],"of)":[45,73],"variables.":[46,74],"This":[47,75],"paper":[48,76],"introduces":[49],"that":[52],"combines":[53],"great":[55],"features":[56],"SG":[58,80,91,133,281],"and":[59,69,86,139,164,226,232,236,283,287],"BCD":[60,262],"for":[61,83,161,291],"many":[64],"objective":[68],"proposes":[77],"(BSG)":[81],"both":[84,162,201,280],"convex":[85,163,169,245],"nonconvex":[87,165,183,255,294],"programs.":[88],"BSG":[89,122,158,171,215,247,257,275],"generalizes":[90],"by":[92,149],"updating":[93],"all":[94],"blocks":[96],"variables":[98],"Gauss--Seidel":[101,137],"type":[102],"(updating":[103],"current":[105],"depends":[107],"previously":[110],"updated":[111],"block),":[112],"either":[114],"fixed":[116],"randomly":[118],"shuffled":[119],"order.":[120],"Although":[121],"has":[123,172],"slightly":[124],"more":[125],"work":[126],"at":[127],"each":[128],"iteration,":[129],"it":[130],"typically":[131],"outperforms":[132],"because":[134,264],"BSG's":[136],"updates":[138,286],"larger":[140],"step":[141],"sizes,":[142],"latter":[144,266],"which":[146,229,240],"are":[147,230,241],"determined":[148],"smaller":[151],"per-block":[152],"Lipschitz":[153],"constants.":[154],"convergence":[156,177,186],"is":[159,187,205,216,288],"established":[160,188],"cases.":[166],"In":[167,181,200],"case,":[170,184],"same":[174],"order":[175],"rate":[178],"as":[179],"SG.":[180,252],"its":[185],"terms":[190],"expected":[193],"violation":[194],"first-order":[197],"optimality":[198],"condition.":[199],"cases":[202],"our":[203],"analysis":[204],"nontrivial":[206],"since":[207],"typical":[209],"unbiasedness":[210],"assumption":[211],"no":[212],"longer":[213],"holds.":[214],"numerically":[217],"evaluated":[218],"following":[221],"problems:":[222],"least":[224],"squares":[225],"logistic":[227,238],"regression,":[228,239],"convex,":[231],"low-rank":[233],"tensor":[234],"recovery":[235],"bilinear":[237],"nonconvex.":[242],"On":[243,253],"problems,":[246,256],"performed":[248],"significantly":[249,258],"better":[250],"than":[251],"outperformed":[259],"deterministic":[261],"tends":[267],"stagnate":[269],"early":[270],"near":[271],"local":[272],"minimizers.":[273],"Overall,":[274],"inherits":[276],"benefits":[278],"approximation":[282],"especially":[289],"useful":[290],"solving":[292],"large-scale":[293],"problems.":[295]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":13},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":15},{"year":2020,"cited_by_count":23},{"year":2019,"cited_by_count":21},{"year":2018,"cited_by_count":15},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":6}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
