{"id":"https://openalex.org/W4392744751","doi":"https://doi.org/10.1090/mcom/3965","title":"Stochastic nested primal-dual method for nonconvex constrained composition optimization","display_name":"Stochastic nested primal-dual method for nonconvex constrained composition optimization","publication_year":2024,"publication_date":"2024-03-13","ids":{"openalex":"https://openalex.org/W4392744751","doi":"https://doi.org/10.1090/mcom/3965"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3965","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3965","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","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/A5007152671","display_name":"Lingzi Jin","orcid":null},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":true,"raw_author_name":"Lingzi Jin","raw_affiliation_strings":["Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong, People\u00e2\u0080\u0099s Republic of China","Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong, People\u2019s Republic of China","Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong, People\u00e2\u0080\u0099s Republic of China","institution_ids":["https://openalex.org/I14243506"]},{"raw_affiliation_string":"Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong, People\u2019s Republic of China","institution_ids":["https://openalex.org/I14243506"]},{"raw_affiliation_string":"Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong, People's Republic of China","institution_ids":["https://openalex.org/I14243506"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101973357","display_name":"Xiao Wang","orcid":"https://orcid.org/0009-0008-4210-2896"},"institutions":[{"id":"https://openalex.org/I4210136793","display_name":"Peng Cheng Laboratory","ror":"https://ror.org/03qdqbt06","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210136793"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiao Wang","raw_affiliation_strings":["Peng Cheng Laboratory, Shenzhen, 518066, People\u00e2\u0080\u0099s Republic of China","Peng Cheng Laboratory, Shenzhen, 518066, People\u2019s Republic of China","Peng Cheng Laboratory, Shenzhen, 518066, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Peng Cheng Laboratory, Shenzhen, 518066, People\u00e2\u0080\u0099s Republic of China","institution_ids":["https://openalex.org/I4210136793"]},{"raw_affiliation_string":"Peng Cheng Laboratory, Shenzhen, 518066, People\u2019s Republic of China","institution_ids":["https://openalex.org/I4210136793"]},{"raw_affiliation_string":"Peng Cheng Laboratory, Shenzhen, 518066, People's Republic of China","institution_ids":["https://openalex.org/I4210136793"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5007152671"],"corresponding_institution_ids":["https://openalex.org/I14243506"],"apc_list":null,"apc_paid":null,"fwci":1.0911,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.79295848,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":"94","issue":"351","first_page":"305","last_page":"358"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9991000294685364,"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"}},"topics":[{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9991000294685364,"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":0.9934999942779541,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9890999794006348,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8606626391410828},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.6296625137329102},{"id":"https://openalex.org/keywords/composition","display_name":"Composition (language)","score":0.5480844378471375},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5045770406723022},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4136695861816406}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8606626391410828},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.6296625137329102},{"id":"https://openalex.org/C40231798","wikidata":"https://www.wikidata.org/wiki/Q1333743","display_name":"Composition (language)","level":2,"score":0.5480844378471375},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5045770406723022},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4136695861816406},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/mcom/3965","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3965","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W1494085563","https://openalex.org/W1503425191","https://openalex.org/W1970039276","https://openalex.org/W2015060724","https://openalex.org/W2043545458","https://openalex.org/W2095331394","https://openalex.org/W2125062699","https://openalex.org/W2145725490","https://openalex.org/W2157570139","https://openalex.org/W2512803856","https://openalex.org/W2751403060","https://openalex.org/W2768546550","https://openalex.org/W2782777630","https://openalex.org/W2785315711","https://openalex.org/W2803106003","https://openalex.org/W2902742530","https://openalex.org/W2939629406","https://openalex.org/W2962890301","https://openalex.org/W2963313444","https://openalex.org/W2964158744","https://openalex.org/W2969215180","https://openalex.org/W2970657951","https://openalex.org/W2976677498","https://openalex.org/W3007099432","https://openalex.org/W3011766119","https://openalex.org/W3015822598","https://openalex.org/W3035804846","https://openalex.org/W3044298048","https://openalex.org/W3080245286","https://openalex.org/W3081147848","https://openalex.org/W3092013327","https://openalex.org/W3120534383","https://openalex.org/W3125796663","https://openalex.org/W3134825596","https://openalex.org/W3154049590","https://openalex.org/W3161641506","https://openalex.org/W3174976469","https://openalex.org/W3201952969","https://openalex.org/W4214809715","https://openalex.org/W4243837489","https://openalex.org/W4244393449","https://openalex.org/W4283397226","https://openalex.org/W4379646807","https://openalex.org/W4390616274"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793","https://openalex.org/W4238204885"],"abstract_inverted_index":{"In":[0,40],"this":[1],"paper":[2],"we":[3,55,75,114,204,230],"study":[4],"the":[5,12,50,60,81,88,96,107,111,121,130,134,137,193,196,201,224,227,260,263],"nonconvex":[6,73],"constrained":[7],"composition":[8,16],"optimization,":[9],"in":[10,99,200],"which":[11,91],"objective":[13],"contains":[14],"a":[15,31,64,77,100,116,206,210,216,242,248],"of":[17,59,110,123,195,226,262],"two":[18],"expected-value":[19],"functions":[20],"whose":[21],"accurate":[22],"information":[23],"is":[24],"normally":[25],"expensive":[26],"to":[27,48,80,86,94,104,150,214,222],"calculate.":[28],"We":[29,128],"propose":[30,205,231],"STochastic":[32],"nEsted":[33],"Primal-dual":[34],"(STEP)":[35],"method":[36,139],"for":[37],"such":[38],"problems.":[39],"each":[41],"iteration,":[42],"with":[43,140,241],"an":[44,152,232,254],"auxiliary":[45],"variable":[46,98],"introduced":[47],"track":[49],"inner":[51],"layer":[52],"function":[53,62,85],"values":[54],"compute":[56],"stochastic":[57,78],"gradients":[58],"nested":[61],"using":[63],"subsampling":[65],"strategy.":[66],"To":[67,191],"alleviate":[68],"difficulties":[69],"caused":[70],"by":[71,136,235],"possibly":[72],"constraints,":[74],"construct":[76],"approximation":[79],"linearized":[82],"augmented":[83],"Lagrangian":[84],"update":[87,95,112],"primal":[89],"variable,":[90],"further":[92],"motivates":[93],"dual":[97],"weighted-average":[101],"way.":[102],"Moreover,":[103,221],"better":[105],"understand":[106],"asymptotic":[108],"dynamics":[109],"schemes":[113],"consider":[115],"deterministic":[117],"continuous-time":[118],"system":[119],"from":[120],"perspective":[122],"ordinary":[124],"differential":[125],"equation":[126],"(ODE).":[127],"analyze":[129],"Karush-Kuhn-Tucker":[131],"measure":[132],"at":[133],"output":[135],"STEP":[138,202,228],"constant":[141],"parameters":[142],"and":[143,147,253],"establish":[144],"its":[145,238],"iteration":[146],"sample":[148],"complexities":[149],"find":[151],"<inline-formula":[153,179],"content-type=\"math/mathml\">":[154,180],"<mml:math":[155,181],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[156,182],"alttext=\"epsilon\">":[157,183],"<mml:semantics>":[158,184],"<mml:mi>\u03f5</mml:mi>":[159,185],"<mml:annotation":[160,186],"encoding=\"application/x-tex\">\\epsilon</mml:annotation>":[161,187],"</mml:semantics>":[162,188],"</mml:math>":[163,189],"</inline-formula>-stationary":[164],"point,":[165],"ensuring":[166],"that":[167],"expected":[168],"stationarity,":[169],"feasibility":[170,199],"as":[171,173],"well":[172],"complementary":[174],"slackness":[175],"are":[176],"below":[177],"accuracy":[178],"</inline-formula>.":[190],"leverage":[192],"benefit":[194],"(near)":[197],"initial":[198,219],"method,":[203],"two-stage":[207],"framework":[208],"incorporating":[209],"feasibility-seeking":[211],"phase,":[212],"aiming":[213],"locate":[215],"nearly":[217],"feasible":[218],"point.":[220],"enhance":[223],"adaptivity":[225],"algorithm,":[229],"adaptive":[233],"variant":[234],"adaptively":[236],"adjusting":[237],"parameters,":[239],"along":[240],"complexity":[243],"analysis.":[244],"Numerical":[245],"results":[246],"on":[247],"risk-averse":[249],"portfolio":[250],"optimization":[251],"problem":[252],"orthogonal":[255],"nonnegative":[256],"matrix":[257],"decomposition":[258],"reveal":[259],"effectiveness":[261],"proposed":[264],"algorithms.":[265]},"counts_by_year":[{"year":2025,"cited_by_count":3}],"updated_date":"2026-01-22T23:29:09.771500","created_date":"2025-10-10T00:00:00"}
