{"id":"https://openalex.org/W4250547152","doi":"https://doi.org/10.1109/wsc.2013.6721484","title":"A regularized smoothing stochastic approximation (RSSA) algorithm for stochastic variational inequality problems","display_name":"A regularized smoothing stochastic approximation (RSSA) algorithm for stochastic variational inequality problems","publication_year":2013,"publication_date":"2013-12-01","ids":{"openalex":"https://openalex.org/W4250547152","doi":"https://doi.org/10.1109/wsc.2013.6721484"},"language":"en","primary_location":{"id":"doi:10.1109/wsc.2013.6721484","is_oa":false,"landing_page_url":"https://doi.org/10.1109/wsc.2013.6721484","pdf_url":null,"source":{"id":"https://openalex.org/S4363607809","display_name":"2013 Winter Simulations Conference (WSC)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 Winter Simulations Conference (WSC)","raw_type":"proceedings-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/A5003164670","display_name":"Farzad Yousefian","orcid":"https://orcid.org/0000-0003-2628-741X"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Farzad Yousefian","raw_affiliation_strings":["Industrial & Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, USA"],"affiliations":[{"raw_affiliation_string":"Industrial & Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110629459","display_name":"Angelia Nedi\u0107","orcid":null},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Angelia Nedic","raw_affiliation_strings":["Industrial & Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, USA"],"affiliations":[{"raw_affiliation_string":"Industrial & Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047034022","display_name":"Uday V. Shanbhag","orcid":"https://orcid.org/0000-0001-5869-9561"},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Uday V. Shanbhag","raw_affiliation_strings":["Industrial & Manufacturing Engineering, Pennsylvania State University, University Park, PA, USA"],"affiliations":[{"raw_affiliation_string":"Industrial & Manufacturing Engineering, Pennsylvania State University, University Park, PA, USA","institution_ids":["https://openalex.org/I130769515"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5003164670"],"corresponding_institution_ids":["https://openalex.org/I157725225"],"apc_list":null,"apc_paid":null,"fwci":1.2635,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.81895911,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"933","last_page":"944"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9984999895095825,"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":0.9984999895095825,"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/T11413","display_name":"Risk and Portfolio Optimization","score":0.9973999857902527,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9952999949455261,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.6796448230743408},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.6391052007675171},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6348601579666138},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.6159718632698059},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.6054937839508057},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.5989954471588135},{"id":"https://openalex.org/keywords/stochastic-approximation","display_name":"Stochastic approximation","score":0.5945613384246826},{"id":"https://openalex.org/keywords/tikhonov-regularization","display_name":"Tikhonov regularization","score":0.5724305510520935},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5298228859901428},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4852771461009979},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.4745020568370819},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.42208027839660645},{"id":"https://openalex.org/keywords/stochastic-optimization","display_name":"Stochastic optimization","score":0.4121403098106384},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.34307539463043213},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.260394811630249},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.2288193702697754},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14821094274520874}],"concepts":[{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.6796448230743408},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.6391052007675171},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6348601579666138},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.6159718632698059},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.6054937839508057},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.5989954471588135},{"id":"https://openalex.org/C55479107","wikidata":"https://www.wikidata.org/wiki/Q97663916","display_name":"Stochastic approximation","level":3,"score":0.5945613384246826},{"id":"https://openalex.org/C152442038","wikidata":"https://www.wikidata.org/wiki/Q2778212","display_name":"Tikhonov regularization","level":3,"score":0.5724305510520935},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5298228859901428},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4852771461009979},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.4745020568370819},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.42208027839660645},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.4121403098106384},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34307539463043213},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.260394811630249},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.2288193702697754},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14821094274520874},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/wsc.2013.6721484","is_oa":false,"landing_page_url":"https://doi.org/10.1109/wsc.2013.6721484","pdf_url":null,"source":{"id":"https://openalex.org/S4363607809","display_name":"2013 Winter Simulations Conference (WSC)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 Winter Simulations Conference (WSC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.44999998807907104,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1490324987","https://openalex.org/W1499021337","https://openalex.org/W1543439990","https://openalex.org/W1994616650","https://openalex.org/W1995033525","https://openalex.org/W2014837638","https://openalex.org/W2022255443","https://openalex.org/W2080335539","https://openalex.org/W2087771945","https://openalex.org/W2100911008","https://openalex.org/W2112383528","https://openalex.org/W2124181538","https://openalex.org/W2167732364","https://openalex.org/W2346269011","https://openalex.org/W2476569890","https://openalex.org/W2962720772","https://openalex.org/W2964121860","https://openalex.org/W4249513058","https://openalex.org/W4293376691","https://openalex.org/W6705043448"],"related_works":["https://openalex.org/W2071936224","https://openalex.org/W1973082942","https://openalex.org/W2977407579","https://openalex.org/W2124181538","https://openalex.org/W3207830353","https://openalex.org/W4286899070","https://openalex.org/W4323366756","https://openalex.org/W2734989445","https://openalex.org/W2602600938","https://openalex.org/W2403770454"],"abstract_inverted_index":{"We":[0,39],"consider":[1],"a":[2,9,15,41,74,98],"stochastic":[3,21],"variational":[4],"inequality":[5],"(SVI)":[6],"problem":[7],"with":[8,97],"continuous":[10],"and":[11,17,32,52],"monotone":[12],"mapping":[13],"over":[14],"compact":[16],"convex":[18],"set.":[19],"Traditionally,":[20],"approximation":[22],"(SA)":[23],"schemes":[24],"for":[25],"SVIs":[26],"have":[27],"relied":[28],"on":[29,61],"strong":[30],"monotonicity":[31],"Lipschitzian":[33],"properties":[34],"of":[35],"the":[36,49,62,67,93],"underlying":[37],"map.":[38],"present":[40],"regularized":[42],"smoothed":[43],"SA":[44],"(RSSA)":[45],"scheme":[46],"where":[47],"in":[48,76],"stepsize,":[50],"smoothing,":[51],"regularization":[53],"parameters":[54],"are":[55],"diminishing":[56],"sequences.":[57],"Under":[58],"suitable":[59],"assumptions":[60],"sequences,":[63],"we":[64,81],"show":[65],"that":[66,71,85],"algorithm":[68],"generates":[69],"iterates":[70,87],"converge":[72],"to":[73,88],"solution":[75],"an":[77],"almost-sure":[78],"sense.":[79],"Additionally,":[80],"provide":[82],"rate":[83],"estimates":[84],"relate":[86],"their":[89],"counterparts":[90],"derived":[91],"from":[92],"Tikhonov":[94],"trajectory":[95],"associated":[96],"deterministic":[99],"problem.":[100]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-02T15:55:50.835912","created_date":"2025-10-10T00:00:00"}