{"id":"https://openalex.org/W2988725654","doi":"https://doi.org/10.1137/18m1192536","title":"Accelerated Stochastic Algorithms for Nonconvex Finite-Sum and Multiblock Optimization","display_name":"Accelerated Stochastic Algorithms for Nonconvex Finite-Sum and Multiblock Optimization","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2988725654","doi":"https://doi.org/10.1137/18m1192536","mag":"2988725654"},"language":"en","primary_location":{"id":"doi:10.1137/18m1192536","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1192536","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/A5042544900","display_name":"Guanghui Lan","orcid":"https://orcid.org/0000-0002-2103-087X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Guanghui Lan","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5101670097","display_name":"Yu Yang","orcid":"https://orcid.org/0000-0002-0502-7603"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yu Yang","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5042544900"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.9163,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.91654612,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"29","issue":"4","first_page":"2753","last_page":"2784"},"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":0.9998999834060669,"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/T10136","display_name":"Statistical Methods and Inference","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7585530281066895},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.6729658246040344},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5416179299354553},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5321570634841919},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4629121422767639},{"id":"https://openalex.org/keywords/gradient-method","display_name":"Gradient method","score":0.42024242877960205},{"id":"https://openalex.org/keywords/condition-number","display_name":"Condition number","score":0.4152938723564148},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37170952558517456},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3305169939994812},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20675936341285706},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09384596347808838}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7585530281066895},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.6729658246040344},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5416179299354553},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5321570634841919},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4629121422767639},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.42024242877960205},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.4152938723564148},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37170952558517456},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3305169939994812},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20675936341285706},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09384596347808838},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/18m1192536","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1192536","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/G2278043753","display_name":null,"funder_award_id":"W911NF-18-1-0223","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G3173796844","display_name":null,"funder_award_id":"CMMI-1637474","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5961652494","display_name":null,"funder_award_id":"CMMI-1637473","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/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1965125844","https://openalex.org/W1975768153","https://openalex.org/W1987083649","https://openalex.org/W1992841740","https://openalex.org/W2029463628","https://openalex.org/W2074682976","https://openalex.org/W2295652899","https://openalex.org/W2914393402","https://openalex.org/W2963470657","https://openalex.org/W2964037929","https://openalex.org/W3098306969"],"related_works":["https://openalex.org/W3185235544","https://openalex.org/W2911623553","https://openalex.org/W4297791327","https://openalex.org/W2897842840","https://openalex.org/W2397777611","https://openalex.org/W1502031429","https://openalex.org/W2417585376","https://openalex.org/W1994157709","https://openalex.org/W4294336468","https://openalex.org/W2797811993"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,130],"present":[4],"new":[5,134,205],"stochastic":[6],"methods":[7,122],"for":[8,27,141],"solving":[9,28,142],"two":[10],"important":[11],"classes":[12],"of":[13,31,39,42,54,97,145,170,185,190,214],"nonconvex":[14,32,90,120,147],"optimization":[15,33,148],"problems.":[16],"We":[17,159,209],"first":[18],"introduce":[19],"a":[20,29,133,143,168],"randomized":[21,119,135],"accelerated":[22,91,136],"proximal":[23,137],"gradient":[24,55,84,92,98,121],"(RapGrad)":[25],"method":[26,140],"class":[30,144],"problems":[34,149],"whose":[35],"objective":[36],"function":[37],"consists":[38],"the":[40,52,59,64,67,95,117,183,188,207],"summation":[41],"$m$":[43,181],"components":[44],"and":[45,70,154,200],"show":[46],"that":[47,161],"it":[48],"can":[49,78,103,163],"significantly":[50],"reduce":[51],"number":[53,61,96,184],"computations":[56,85,99],"especially":[57],"when":[58,123],"condition":[60],"$L/\\mu$":[62],"(i.e.,":[63],"ratio":[65],"between":[66],"Lipschitz":[68],"constant":[69],"negative":[71],"curvature)":[72],"is":[73],"large.":[74],"More":[75],"specifically,":[76],"RapGrad":[77,102,199],"save":[79,165],"up":[80,166],"to":[81,167,203],"${\\cal":[82,105,112,171],"O}(\\sqrt{m})$":[83,172],"more":[86,175],"than":[87,116,176],"existing":[88],"batch":[89,178],"methods.":[93],"Moreover,":[94],"required":[100],"by":[101,128],"be":[104,204],"O}(m^\\frac{1}{6}":[106],"L^\\frac{1}{2}":[107],"/":[108],"\\mu^\\frac{1}{2})$":[109],"(at":[110],"least":[111],"O}(m^\\frac{2}{3})$)":[113],"times":[114],"smaller":[115],"best-known":[118],"$L/\\mu":[124],"\\ge":[125],"m$.":[126],"Inspired":[127],"RapGrad,":[129],"also":[131,164,210],"develop":[132],"dual":[138],"(RapDual)":[139],"multiblock":[146],"coupled":[150],"with":[151,198],"linear":[152],"constraints":[153],"some":[155],"special":[156],"structural":[157],"properties.":[158],"demonstrate":[160],"RapDual":[162,201],"factor":[169],"block":[173],"updates":[174],"its":[177],"counterpart,":[179],"where":[180],"denotes":[182],"blocks.":[186],"To":[187],"best":[189],"our":[191,218],"knowledge,":[192],"all":[193],"these":[194,215],"complexity":[195],"results":[196],"associated":[197],"seem":[202],"in":[206],"literature.":[208],"illustrate":[211],"potential":[212],"advantages":[213],"algorithms":[216],"through":[217],"preliminary":[219],"numerical":[220],"experiments.":[221]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2}],"updated_date":"2026-04-03T22:45:19.894376","created_date":"2025-10-10T00:00:00"}