{"id":"https://openalex.org/W4292961219","doi":"https://doi.org/10.1137/20m1375796","title":"Stochastic Approximation Methods for the Two-Stage Stochastic Linear Complementarity Problem","display_name":"Stochastic Approximation Methods for the Two-Stage Stochastic Linear Complementarity Problem","publication_year":2022,"publication_date":"2022-08-24","ids":{"openalex":"https://openalex.org/W4292961219","doi":"https://doi.org/10.1137/20m1375796"},"language":"en","primary_location":{"id":"doi:10.1137/20m1375796","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1375796","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/A5100443817","display_name":"Lin Chen","orcid":"https://orcid.org/0000-0003-4330-1519"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lin Chen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100617985","display_name":"Yongchao Liu","orcid":"https://orcid.org/0000-0001-9955-4414"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yongchao Liu","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-9955-4414","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047743962","display_name":"Xinmin Yang","orcid":"https://orcid.org/0000-0002-5185-5709"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xinmin Yang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5080552363","display_name":"Jin Zhang","orcid":"https://orcid.org/0000-0002-6691-5612"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jin Zhang","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-6691-5612","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3066,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.8162033,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"32","issue":"3","first_page":"2129","last_page":"2155"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10698","display_name":"Transportation Planning and Optimization","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/3313","display_name":"Transportation"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10328","display_name":"Supply Chain and Inventory Management","score":0.9936000108718872,"subfield":{"id":"https://openalex.org/subfields/1404","display_name":"Management Information Systems"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6951597929000854},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6795420050621033},{"id":"https://openalex.org/keywords/complementarity","display_name":"Complementarity (molecular biology)","score":0.6760132312774658},{"id":"https://openalex.org/keywords/stochastic-programming","display_name":"Stochastic programming","score":0.6260080337524414},{"id":"https://openalex.org/keywords/linear-complementarity-problem","display_name":"Linear complementarity problem","score":0.6055619120597839},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5479247570037842},{"id":"https://openalex.org/keywords/stochastic-optimization","display_name":"Stochastic optimization","score":0.45621293783187866},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.45031192898750305},{"id":"https://openalex.org/keywords/mixed-complementarity-problem","display_name":"Mixed complementarity problem","score":0.42577916383743286},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.42120304703712463},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35774391889572144},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.10768309235572815}],"concepts":[{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6951597929000854},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6795420050621033},{"id":"https://openalex.org/C202269582","wikidata":"https://www.wikidata.org/wiki/Q2644277","display_name":"Complementarity (molecular biology)","level":2,"score":0.6760132312774658},{"id":"https://openalex.org/C137631369","wikidata":"https://www.wikidata.org/wiki/Q7617831","display_name":"Stochastic programming","level":2,"score":0.6260080337524414},{"id":"https://openalex.org/C34320192","wikidata":"https://www.wikidata.org/wiki/Q783105","display_name":"Linear complementarity problem","level":3,"score":0.6055619120597839},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5479247570037842},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.45621293783187866},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.45031192898750305},{"id":"https://openalex.org/C77196050","wikidata":"https://www.wikidata.org/wiki/Q6883962","display_name":"Mixed complementarity problem","level":3,"score":0.42577916383743286},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.42120304703712463},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35774391889572144},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.10768309235572815},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/20m1375796","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1375796","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/G131378450","display_name":null,"funder_award_id":"cstc2021jcyj-msxmX0047","funder_id":"https://openalex.org/F4320323172","funder_display_name":"Natural Science Foundation of Chongqing"},{"id":"https://openalex.org/G1636070402","display_name":null,"funder_award_id":"11991023","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2130172530","display_name":null,"funder_award_id":"CXQT20014","funder_id":"https://openalex.org/F4320321135","funder_display_name":"Chongqing University"},{"id":"https://openalex.org/G2482177623","display_name":null,"funder_award_id":"cstc2019jcyj-zdxmX0016","funder_id":"https://openalex.org/F4320323172","funder_display_name":"Natural Science Foundation of Chongqing"},{"id":"https://openalex.org/G2808773884","display_name":null,"funder_award_id":"12101097","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3049148066","display_name":"\u57fa\u4e8e\u53d8\u5206\u5206\u6790\u7684\u5206\u88c2\u7b97\u6cd5\u7ebf\u6027\u6536\u655b\u7387\u7814\u7a76","funder_award_id":"11971220","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4162409669","display_name":null,"funder_award_id":"CQYC20210302270","funder_id":"https://openalex.org/F4320321135","funder_display_name":"Chongqing University"},{"id":"https://openalex.org/G5391772797","display_name":null,"funder_award_id":"11991024","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6695554926","display_name":null,"funder_award_id":"2022B1515020082","funder_id":"https://openalex.org/F4320337111","funder_display_name":"Basic and Applied Basic Research Foundation of Guangdong Province"},{"id":"https://openalex.org/G6884296105","display_name":"\u57fa\u4e8e\u8bef\u5dee\u754c\u7684\u968f\u673a\u53d8\u5206\u4e0d\u7b49\u5f0f\u7f6e\u4fe1\u57df\u7814\u7a76\u53ca\u5e94\u7528","funder_award_id":"11971090","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7773084092","display_name":null,"funder_award_id":"RCYX20200714114700072","funder_id":"https://openalex.org/F4320335966","funder_display_name":"Science and Technology Planning Project of Shenzhen Municipality"},{"id":"https://openalex.org/G8242860656","display_name":null,"funder_award_id":"12171063","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321135","display_name":"Chongqing University","ror":"https://ror.org/023rhb549"},{"id":"https://openalex.org/F4320323172","display_name":"Natural Science Foundation of Chongqing","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335966","display_name":"Science and Technology Planning Project of Shenzhen Municipality","ror":null},{"id":"https://openalex.org/F4320337111","display_name":"Basic and Applied Basic Research Foundation of Guangdong Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1551360398","https://openalex.org/W1969007958","https://openalex.org/W1994616650","https://openalex.org/W2010659474","https://openalex.org/W2011775410","https://openalex.org/W2029463628","https://openalex.org/W2038038281","https://openalex.org/W2078816386","https://openalex.org/W2124181538","https://openalex.org/W2147977073","https://openalex.org/W2294586855","https://openalex.org/W2306243954","https://openalex.org/W2568744357","https://openalex.org/W2593248927","https://openalex.org/W2597644112","https://openalex.org/W2793390883","https://openalex.org/W2958970240","https://openalex.org/W2962823973","https://openalex.org/W2962930655","https://openalex.org/W2963155955","https://openalex.org/W2963622009","https://openalex.org/W4236218737","https://openalex.org/W4301791716"],"related_works":["https://openalex.org/W2128234186","https://openalex.org/W2276648117","https://openalex.org/W819098253","https://openalex.org/W2599483915","https://openalex.org/W15122084","https://openalex.org/W1548220668","https://openalex.org/W2765841216","https://openalex.org/W169948756","https://openalex.org/W2607337407","https://openalex.org/W1566966152"],"abstract_inverted_index":{"The":[0],"two-stage":[1,18],"stochastic":[2,19,29,81,84],"linear":[3,20,122],"complementarity":[4,123],"problem":[5],"(TSLCP),":[6],"which":[7,99],"can":[8],"be":[9],"regarded":[10],"as":[11,28,61],"a":[12,62,65],"special":[13],"and":[14,35,91,103,131,138,149],"important":[15],"reformulation":[16],"of":[17,80,98,106,110,135,155],"programming,":[21,30],"has":[22,40],"arisen":[23],"in":[24],"various":[25],"fields,":[26],"such":[27],"game":[31],"theory,":[32],"traffic":[33],"equilibrium,":[34],"theoretical":[36],"economics.":[37],"Considerable":[38],"effort":[39],"been":[41],"devoted":[42],"to":[43,54,72],"designing":[44],"numerical":[45,147],"methods":[46],"for":[47],"solving":[48],"TSLCPs.":[49],"A":[50],"popular":[51],"approach":[52],"is":[53,144],"integrate":[55],"the":[56,83,92,107,111,117,121,132,153],"progressive":[57],"hedging":[58],"algorithm":[59],"(PHA)":[60],"sub-algorithm":[63],"into":[64],"discretization":[66],"framework.":[67],"In":[68,119],"this":[69],"paper,":[70],"aiming":[71],"solve":[73],"large-scale":[74],"TSLCPs,":[75],"we":[76],"propose":[77],"two":[78],"kinds":[79],"methods:":[82],"approximation":[85],"method":[86],"based":[87],"on":[88],"projection":[89],"(SAP)":[90],"dynamic":[93],"sampling":[94],"SAP":[95,137],"(DS-SAP),":[96],"both":[97,136],"offering":[100],"more":[101],"direct":[102],"improved":[104],"control":[105],"computational":[108],"costs":[109],"involved":[112],"subproblems,":[113],"especially":[114],"compared":[115],"with":[116,140],"PHA.":[118],"particular,":[120],"subproblems":[124],"are":[125],"solved":[126],"inexactly":[127],"during":[128],"each":[129],"iteration,":[130],"convergence":[133],"analysis":[134],"DS-SAP":[139],"an":[141],"inexactness":[142],"criterion":[143],"presented.":[145],"Moreover,":[146],"implementations":[148],"practical":[150],"applications":[151],"demonstrate":[152],"efficiency":[154],"our":[156],"proposed":[157],"methods.":[158]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2020,"cited_by_count":1}],"updated_date":"2026-07-14T08:27:34.040176","created_date":"2025-10-10T00:00:00"}