{"id":"https://openalex.org/W4292064643","doi":"https://doi.org/10.1137/20m1381678","title":"Simple and Optimal Methods for Stochastic Variational Inequalities, I: Operator Extrapolation","display_name":"Simple and Optimal Methods for Stochastic Variational Inequalities, I: Operator Extrapolation","publication_year":2022,"publication_date":"2022-08-16","ids":{"openalex":"https://openalex.org/W4292064643","doi":"https://doi.org/10.1137/20m1381678"},"language":"en","primary_location":{"id":"doi:10.1137/20m1381678","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1381678","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/A5052705774","display_name":"Georgios Kotsalis","orcid":"https://orcid.org/0000-0001-8105-4251"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Georgios Kotsalis","raw_affiliation_strings":["H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, 30332 "],"affiliations":[{"raw_affiliation_string":"H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, 30332 ","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042544900","display_name":"Guanghui Lan","orcid":"https://orcid.org/0000-0002-2103-087X"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Guanghui Lan","raw_affiliation_strings":["School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, 30332 "],"affiliations":[{"raw_affiliation_string":"School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, 30332 ","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100736706","display_name":"Tianjiao Li","orcid":"https://orcid.org/0000-0001-6660-0883"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tianjiao Li","raw_affiliation_strings":["School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, 30332 "],"affiliations":[{"raw_affiliation_string":"School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, 30332 ","institution_ids":["https://openalex.org/I130701444"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5052705774"],"corresponding_institution_ids":["https://openalex.org/I130701444"],"apc_list":null,"apc_paid":null,"fwci":4.9783,"has_fulltext":false,"cited_by_count":36,"citation_normalized_percentile":{"value":0.95868189,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"32","issue":"3","first_page":"2041","last_page":"2073"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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":0.9879999756813049,"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":0.9836999773979187,"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":0.7643519639968872},{"id":"https://openalex.org/keywords/extrapolation","display_name":"Extrapolation","score":0.7543507814407349},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.7449707984924316},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.6798908710479736},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.6183304190635681},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.571138322353363},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5665621757507324},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.48513612151145935},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.4374057352542877},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4359338879585266},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3773665726184845},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.30307814478874207},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1861925721168518},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.09570148587226868},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08535730838775635}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7643519639968872},{"id":"https://openalex.org/C132459708","wikidata":"https://www.wikidata.org/wiki/Q744069","display_name":"Extrapolation","level":2,"score":0.7543507814407349},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.7449707984924316},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.6798908710479736},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.6183304190635681},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.571138322353363},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5665621757507324},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.48513612151145935},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4374057352542877},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4359338879585266},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3773665726184845},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30307814478874207},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1861925721168518},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.09570148587226868},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08535730838775635},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/20m1381678","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1381678","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/G1595064629","display_name":null,"funder_award_id":"W911NF-18-1-0223","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G1633690903","display_name":null,"funder_award_id":"00014-20","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"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/G2336166159","display_name":null,"funder_award_id":"4-20-","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G2435350416","display_name":null,"funder_award_id":"N00014-20-1-20","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G7034037648","display_name":null,"funder_award_id":"4-20-1-","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G7249327428","display_name":null,"funder_award_id":"N00014-20-1-2089","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"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/G8876996369","display_name":null,"funder_award_id":"N00014","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G8998121839","display_name":null,"funder_award_id":"911NF","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"},{"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":23,"referenced_works":["https://openalex.org/W605736217","https://openalex.org/W1487404723","https://openalex.org/W1822292100","https://openalex.org/W1966953121","https://openalex.org/W1992208280","https://openalex.org/W2005369372","https://openalex.org/W2006118023","https://openalex.org/W2020278060","https://openalex.org/W2038497950","https://openalex.org/W2049966847","https://openalex.org/W2081316950","https://openalex.org/W2089559088","https://openalex.org/W2110412969","https://openalex.org/W2124477018","https://openalex.org/W2125913552","https://openalex.org/W2593248927","https://openalex.org/W2950866122","https://openalex.org/W2962823973","https://openalex.org/W2963373496","https://openalex.org/W3025638325","https://openalex.org/W3101497372","https://openalex.org/W4242209908","https://openalex.org/W4251057111"],"related_works":["https://openalex.org/W1968270095","https://openalex.org/W4296478327","https://openalex.org/W1960072520","https://openalex.org/W2042397106","https://openalex.org/W4361730764","https://openalex.org/W1965029248","https://openalex.org/W2220129715","https://openalex.org/W2387596242","https://openalex.org/W2085771669","https://openalex.org/W2383497899"],"abstract_inverted_index":{"In":[0,88,157],"this":[1],"paper":[2],"we":[3],"first":[4,109],"present":[5,116],"a":[6,34,54,60,97,117,139,190],"novel":[7],"operator":[8,72,120,172],"extrapolation":[9,73,121],"(OE)":[10],"method":[11,75,122,132],"for":[12,52,82,95,107,129,186],"solving":[13,33,53,83,96],"deterministic":[14,136],"variational":[15,168],"inequality":[16,169],"(VI)":[17],"problems.":[18,87],"Similar":[19],"to":[20,123,134,148,164],"the":[21,47,70,92,108,112,126,130,150,154],"gradient":[22],"(operator)":[23],"projection":[24,36],"method,":[25],"OE":[26,44,131],"updates":[27],"one":[28],"single":[29,35],"search":[30],"sequence":[31],"by":[32],"subproblem":[37],"in":[38,59,111,189],"each":[39],"iteration.":[40],"We":[41,67,114,177],"show":[42],"that":[43],"can":[45],"achieve":[46],"optimal":[48,79,93,181],"rate":[49],"of":[50,56,153],"convergence":[51,80],"variety":[55],"VI":[57,86],"problems":[58,170],"much":[61],"simpler":[62],"way":[63],"than":[64],"existing":[65],"approaches.":[66],"then":[68],"introduce":[69],"stochastic":[71,85,101,118],"(SOE)":[74],"and":[76,103],"establish":[77],"its":[78],"behavior":[81],"various":[84],"particular,":[89],"SOE":[90],"achieves":[91],"complexity":[94],"fundamental":[98],"problem,":[99],"i.e.,":[100],"smooth":[102],"strongly":[104],"monotone":[105,167],"VI,":[106],"time":[110],"literature.":[113],"also":[115,179],"block":[119,141],"further":[124],"reduce":[125],"iteration":[127],"cost":[128],"applied":[133,163],"large-scale":[135],"VIs":[137],"with":[138],"certain":[140],"structure.":[142],"Numerical":[143],"experiments":[144],"have":[145],"been":[146],"conducted":[147],"demonstrate":[149],"potential":[151],"advantages":[152],"proposed":[155],"algorithms.":[156],"fact,":[158],"all":[159],"these":[160],"algorithms":[161],"are":[162],"solve":[165],"generalized":[166],"whose":[171],"is":[173],"not":[174],"necessarily":[175],"monotone.":[176],"will":[178],"discuss":[180],"OE-based":[182],"policy":[183],"evaluation":[184],"methods":[185],"reinforcement":[187],"learning":[188],"companion":[191],"paper.":[192]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":12},{"year":2024,"cited_by_count":13},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":3}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}