{"id":"https://openalex.org/W2295489065","doi":"https://doi.org/10.1137/130931278","title":"Stochastic First-Order Methods with Random Constraint Projection","display_name":"Stochastic First-Order Methods with Random Constraint Projection","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2295489065","doi":"https://doi.org/10.1137/130931278","mag":"2295489065"},"language":"en","primary_location":{"id":"doi:10.1137/130931278","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130931278","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/A5100707460","display_name":"Mengdi Wang","orcid":"https://orcid.org/0000-0002-2101-9507"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mengdi Wang","raw_affiliation_strings":["Princeton University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Princeton University","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039911471","display_name":"Dimitri P. Bertsekas","orcid":"https://orcid.org/0000-0001-6909-7208"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Dimitri P. Bertsekas","raw_affiliation_strings":["Massachusetts Institute Of Technology#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Massachusetts Institute Of Technology#TAB#","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.2706,"has_fulltext":false,"cited_by_count":47,"citation_normalized_percentile":{"value":0.96800818,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"26","issue":"1","first_page":"681","last_page":"717"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9986000061035156,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9904999732971191,"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":0.6514124870300293},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5140934586524963},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5091313719749451},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.4987366199493408},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.48624148964881897},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.4845825433731079},{"id":"https://openalex.org/keywords/convergence-of-random-variables","display_name":"Convergence of random variables","score":0.4440147280693054},{"id":"https://openalex.org/keywords/stochastic-optimization","display_name":"Stochastic optimization","score":0.4435860514640808},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.430691659450531},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.42353278398513794},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3475300073623657},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.3224230408668518},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.265656441450119}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6514124870300293},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5140934586524963},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5091313719749451},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4987366199493408},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.48624148964881897},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.4845825433731079},{"id":"https://openalex.org/C95763700","wikidata":"https://www.wikidata.org/wiki/Q578985","display_name":"Convergence of random variables","level":3,"score":0.4440147280693054},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.4435860514640808},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.430691659450531},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.42353278398513794},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3475300073623657},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.3224230408668518},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.265656441450119},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/130931278","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130931278","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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1506295250","https://openalex.org/W1975567493","https://openalex.org/W2002110362","https://openalex.org/W2012180727","https://openalex.org/W2033511209","https://openalex.org/W2039696315","https://openalex.org/W2050916497","https://openalex.org/W2073750241","https://openalex.org/W2076428552","https://openalex.org/W2079361630","https://openalex.org/W2085440994","https://openalex.org/W2096840748","https://openalex.org/W2100885264","https://openalex.org/W2167820643","https://openalex.org/W4254573171"],"related_works":["https://openalex.org/W1599334945","https://openalex.org/W2767307537","https://openalex.org/W2511372611","https://openalex.org/W3109443022","https://openalex.org/W3140489489","https://openalex.org/W2482464444","https://openalex.org/W1984538277","https://openalex.org/W1981090302","https://openalex.org/W2072615990","https://openalex.org/W1513489752"],"abstract_inverted_index":{"We":[0,44,141],"consider":[1,143],"convex":[2],"optimization":[3],"problems":[4,21],"with":[5],"structures":[6],"that":[7,95,120,189],"are":[8,159,180],"suitable":[9,115],"for":[10,49,150],"sequential":[11],"treatment":[12],"or":[13],"online":[14,164],"sampling.":[15],"In":[16],"particular,":[17],"we":[18,86,118,179],"focus":[19],"on":[20],"where":[22],"the":[23,31,35,77,96,121,131,171,184],"objective":[24],"function":[25],"is":[26,34,98],"an":[27,46,101],"expected":[28],"value,":[29],"and":[30,57,110,130,155,166],"constraint":[32,59],"set":[33],"intersection":[36],"of":[37,41,79,128,138,146,186,193],"a":[38,83,88,126,136,144,176],"large":[39],"number":[40,145],"simpler":[42],"sets.":[43],"propose":[45],"algorithmic":[47],"framework":[48],"stochastic":[50,152,187],"first-order":[51,153],"methods":[52],"using":[53,170],"random":[54,58,156],"projection/proximal":[55],"updates":[56],"updates,":[60],"which":[61,158],"contain":[62],"as":[63,69,71,175],"special":[64],"cases":[65],"several":[66],"known":[67],"algorithms":[68,81,188],"well":[70],"many":[72],"new":[73],"algorithms.":[74],"To":[75],"analyze":[76,183],"convergence":[78,91,97,173,185],"these":[80,194],"in":[82,161],"unified":[84],"manner,":[85],"prove":[87],"general":[89],"coupled":[90,105,172],"theorem.":[92],"It":[93],"states":[94],"obtained":[99],"from":[100],"interplay":[102],"between":[103],"two":[104],"processes:":[106],"progress":[107,111],"toward":[108,112],"feasibility":[109,132],"optimality.":[113],"Under":[114],"stepsize":[116],"assumptions,":[117],"show":[119],"optimality":[122],"error":[123,133],"decreases":[124,134],"at":[125,135],"rate":[127,137],"$\\mathcal{O}(1/\\sqrt{k})$":[129],"$\\mathcal{O}(\\log":[139],"k/k)$.":[140],"also":[142],"typical":[147],"sampling":[148,195],"processes":[149],"generating":[151],"information":[154],"constraints,":[157],"common":[160],"data-intensive":[162],"applications,":[163],"learning,":[165],"simulation":[167],"optimization.":[168],"By":[169],"theorem":[174],"modular":[177],"architecture,":[178],"able":[181],"to":[182],"use":[190],"arbitrary":[191],"combinations":[192],"processes.":[196]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}